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## Big Number Brainwork: How to Solve Word Problems with Large Whole Number Operations

Real-world scenarios often involve large numbers, especially when dealing with populations, budgets, or vast quantities. Let's explore how to tackle word problems that require adding and subtracting whole numbers, even those in the billions.

## Adding and Subtracting Whole Numbers in Word Problems

The population of Country A in 2020 was \(3,456,789,012\). By 2025, it increased by \(1,234,567,890\). What was the population in 2025?

Solution Process:

Add the population increase to the 2020 population.

3,456,789,012

+ 1,234,567,890

________________

4,691,356,902

The population in 2025 was \(4,691,356,902\).

The Absolute Best Book for 5th Grade Students

## Mastering Grade 5 Math The Ultimate Step by Step Guide to Acing 5th Grade Math

The government had a budget of \(7,890,123,456\) dollars. They spent \(5,678,912,345\) dollars on infrastructure. How much of the budget remains?

Subtract the amount spent from the total budget.

7,890,123,456

– 5,678,912,345

2,211,211,111

The remaining budget is \(2,211,211,111\) dollars.

Word problems involving large numbers can initially seem intimidating. However, by carefully extracting the relevant data and applying basic addition or subtraction, you can easily find the solution. Always remember to read the problem thoroughly, identify the operation needed, and align numbers correctly. With practice, you’ll become adept at solving these real-world challenges involving big numbers!

## Practice Questions:

1. A company made sales of \(4,567,890,123\) dollars in 2020 and \(3,456,789,012\) dollars in 2021. What was the total sales for both years?

2. The world’s largest forest had \(6,789,012,345\) trees. Due to deforestation, \(1,234,567,890\) trees were cut down. How many trees remain?

3. A charity received donations of \(1,234,567,890\) dollars in the first year and \(9,876,543,210\) dollars in the second year. How much did they receive in total?

4. A city had a water reserve of \(5,678,901,234\) liters. Due to a drought, \(2,345,678,901\) liters evaporated. How much water remains in the reserve?

5. A tech company sold \(7,890,123,456\) devices in the first quarter and \(1,111,111,111\) devices in the second quarter. What was their total sales for both quarters?

A Perfect Book for Grade 5 Math Word Problems!

## Mastering Grade 5 Math Word Problems The Ultimate Guide to Tackling 5th Grade Math Word Problems

1. \(8,024,679,135\) dollars

2. \(5,554,444,455\) trees

3. \(11,111,111,100\) dollars

4. \(3,333,222,333\) liters

5. \(9,001,234,567\) devices

The Best Math Books for Elementary Students

## Mastering Grade 4 Math Word Problems The Ultimate Guide to Tackling 4th Grade Math Word Problems

by: Effortless Math Team about 5 months ago (category: Articles )

## Effortless Math Team

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## ChatGPT for Teachers

Trauma-informed practices in schools, teacher well-being, cultivating diversity, equity, & inclusion, integrating technology in the classroom, social-emotional development, covid-19 resources, invest in resilience: summer toolkit, civics & resilience, all toolkits, degree programs, trauma-informed professional development, teacher licensure & certification, how to become - career information, classroom management, instructional design, lifestyle & self-care, online higher ed teaching, current events, 10 ways to do fast math: tricks and tips for doing math in your head.

You don’t have to be a math teacher to know that a lot of students—and likely a lot of parents (it’s been awhile!)—are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math , improve math skills and understanding, and excel in advanced courses.

If it’s your job to teach those, here’s a great refresher.

Fast math tricks infographic

## 10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

## 1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 – 8 = 882

So the answer to 644 +238 is 882.

## 2. Subtracting from 1,000

Here’s a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 – 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

## 3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

- Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
- Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

- Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
- Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

## 4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

- 10 if the number ends in 0
- 9 when the digits are added together and the total is evenly divisible by 9
- 8 if the last three digits are evenly divisible by 8 or are 000
- 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
- 5 if it ends in a 0 or 5
- 4 if it ends in 00 or a two digit number that is evenly divisible by 4
- 3 when the digits are added together and the result is evenly divisible by the number 3
- 2 if it ends in 0, 2, 4, 6, or 8

## 5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1 : Subtract 1 from the number that is being multiplied by 9.

3 – 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2 : Subtract that number from the number 9.

9 – 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

## 6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

(8 + 1)_6_8

There is the answer to 11 x 88: 968

## 7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

- Step 1: Move the decimal point over by one place, 235 becomes 23.5.
- Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

## 8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

- Step 1: Multiply the first digit by itself plus 1.
- Step 2: Put a 25 at the end.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

## 9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

## 10. Multiplying numbers that end in zero

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

Step 1: Multiply the 2 times the 4

Step 2: Put all four of the zeros after the 8

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics—and unafraid to work with numbers in the future.

## You may also like to read

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- Tips in Teaching a Hands-On Math Curriculum
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- 3 Tips for Running an Elementary School Math Workshop
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## Real-life problems, large numbers

Common Core Standards: Grade 4 Measurement & Data

CCSS.Math.Content.4.MD.A.2

This worksheet originally published in Math Made Easy for 5th Grade by © Dorling Kindersley Limited .

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## Introduction to Large Numbers

Large numbers are those numbers that have a bigger value than the numbers that we use in daily life. Such numbers tend to create a sense of fear among children and they often skip solving problems that have large numbers in them. For example, 1 million, 1 billion , etc., are large numbers that are used either to show the population of a country or express large amounts of money in a bank account.

## Meaning of Large Numbers

Everyone learns how to count numbers at a very young age starting from a single-digit up to seven digits. This is done with the help of the place value system. There are two place value systems that are followed - the Indian Place Value System and International Place Value System.

While writing large numbers, we always keep the place value system in mind to ensure that it is written correctly. According to the Indian place-value system, when a number is written in the standard form, each group of digits separated by a comma is called a period. These periods are named as ones, thousands, lakhs and so on. The ones period consists of the first three digits of the large number, starting from the right. The thousands period consists of the next two digits. The lakhs period consists of the next two digits and it continues.

According to the International place value system also, the numbers are divided into periods. These periods are named as ones, thousands, millions, billions and so on. In this system, each period has three digits.

Let us look at this example: 12,457, 891. According to the International Place Value system, this is read as twelve million, four hundred fifty-seven thousand, eight hundred ninety-one.

Some other large numbers are read and written as follows:

1,000,000,000 = one billion

1,000,000,000,000 = one thousand billion

The following table shows how to read and write numbers as per the International Place Value System.

## Addition of Large Numbers

We add large numbers in the same way as we work with other numbers. We arrange the numbers in a column according to their place values. The addition process begins from the ones column, the next tens column, the hundreds column, and so on. The numbers that need to be carried forward, are placed in the adjacent column along with the existing numbers. This entire process has to be followed until the last column where we get our final number.

Example 1: Find the sum of the following large numbers: 67,34,903, 2,61,89,403, and 12,79,40,674.

Solution:

First, we arrange the numbers in columns according to their place value and then we add them.

Therefore, the sum of the given numbers is 160,864,980.

## Subtraction of Large Numbers

For subtraction of large numbers, the same order of columns that were used for addition is followed. Once the numbers are arranged in the columns, we begin with ones and move forward to the left side. Numbers are borrowed as and when required from the left side.

Example 2: Find the difference between the following large numbers: 67,89,540 and 23,78,954.

First, we arrange the numbers in columns according to their place value and then we subtract them.

Therefore, the difference of the given numbers is 4,410,586.

## Multiplication of Large Numbers

The multiplication of large numbers is done in the same way as the other numbers. After the numbers are placed in the columns, we take the bottom number and start with the number in ones place. We multiply this number with all the numbers in the top row and write the product below the line. In the next step, before we start multiplying the next number, we need to hold the tens place by placing a zero in the ones place, so, we write zero in ones place. Then, we repeat the process and take the next number from the bottom number and multiply it with all the numbers in the top row. Place the product in the same line where we had placed the zero. Once we get the product of both the numbers, we add them column-wise to get the final answer.

Example 3: Multiply the large number 74,597 by 32.

Therefore, the product of the given numbers is 2,387,104.

## Division of Large Numbers

Division of large numbers is done by the long division method which is similar to all division problems. There is a dividend, which is divided by the divisor, to give a result called the quotient and sometimes a remainder. The process of division includes the complete cycle of division, subtraction, and multiplication.

Example 4: Divide the large number 1,260,257 by 37.

## Related Links:

- Place Value
- Indian Place Value Chart
- Number Systems
- Place Value Calculator

## Solved Examples:

Example 1 : Find the sum of these two large numbers: 234,679 and 4,659,129.

Solution: Adding the two large numbers by applying the method mentioned above.

234,679 + 4,659,129 = 4,893,808

Therefore, the sum of the numbers is 4,893,808.

Example 2: Multiply the large number 135,012 by 12.

Solution: Multiplying the large number by applying the method mentioned above.

135,012 × 12 = 1,620,144

Therefore, after multiplication, we get 1,620,144 as the product.

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## Practice Questions

Faqs on large numbers , what is the meaning of large numbers.

Large numbers are usually bigger numbers that are not used so much in our day-to-day lives. They are mostly used while calculating a country's population or while counting the money in a bank account. For example, 1 million and 1 billion are considered as large numbers.

## How do we Read Large Numbers?

While reading or writing large numbers, we always begin from the left and move on to the right. It is always better to position the numbers according to their place value system. According to the Indian place-value system while reading large numbers we divide the numbers into periods named as units, thousands, and lakhs. For example: 24,12,340 is written and read as twenty-four lakh, twelve thousand, three hundred and forty. According to the International place value system, the periods are named as ones, thousands, millions, and billions, and so on. So, the same number 2,412,340 is written and read as two million, four hundred twelve thousand, three hundred and forty.

## What is 1000000 in Large Numbers?

1,000,000 is read as one million as per the international place value system.

## Is a 10-digit Number a Billion?

Yes, a 10-digit number is read as a billion. For example, 4,000,000,000 is read as Four billion.

## How do we Write Large Numbers?

Large numbers are written in their expanded form keeping in mind their respective place values. For examp le, 456790 is written as four lakh, fifty-six thousand, seven hundred and ninety as per the Indian place value system. As per the International place value system, the same number is written as four hundred fifty-six thousand, seven hundred and ninety.

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Here are some examples solving number problems.

When 6 times a number is increased by 4, the result is 40. Find the number.

First, circle what you must find— the number. Letting x stand for the number gives the equation

6 x + 4 = 40

Subtracting 4 from each side gives

Dividing by 6 gives

So the number is 6.

One number exceeds another number by 5. If the sum of the two numbers is 39, find the smaller number.

First, circle what you are looking for— the smaller number. Now, let the smaller number equal x. Therefore, the larger number equals x + 5. Now, use the problem to set up an equation.

Therefore, the smaller number is 17.

If one number is three times as large as another number and the smaller number is increased by 19, the result is 6 less than twice the larger number. What is the larger number?

First, circle what you must find— the larger number. Let the smaller number equal x . Therefore, the larger number will be 3 x . Now, using the problem, set up an equation.

Therefore, the larger number, 3 x , is 3(5), or 15.

The sum of three consecutive integers is 306. What is the largest integer?

First, circle what you must find— the largest integer. Let the smallest integer equal x ; let x + 1 equal the next integer; let the largest integer equal x + 2. Now, use the problem to set up an equation.

Therefore, the largest integer, x + 2 = 101 + 2 = 103.

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## Step-by-Step Guide to Solving Operations on Large Numbers Worksheets for Class 5

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Learning to work with large numbers is an important skill for students in class.

Understand place value and number notation. Before tackling large numbers, it’s important for students to have a solid understanding of place value and number notation. This means understanding that each digit in a number represents a different value based on its position. For example, in the number 456, the 4 represents 400, the 5 represents 50, and the 6 represents 6. Students should also be familiar with number notation, including standard form, expanded form, and word form. Once they have a strong foundation in these concepts, they will be better equipped to tackle larger numbers.

Break down large numbers into smaller parts.

When faced with a large number, it can be overwhelming for students to try to solve it all at once. Breaking the number down into smaller parts can make it more manageable. For example, if the number is 3,456,789, students can start by focusing on the thousands place and the ones place. They can then work their way through the number, tackling each place value one at a time. This approach can help students avoid errors and build confidence as they solve larger numbers.

Use addition and subtraction to solve problems.

One of the most effective ways to solve large numbers is to use addition and subtraction. Students can break down the number into smaller parts and add or subtract them to find the answer. For example, if the problem is 5,678 + 3,456, students can start by adding the ones place (8 + 6 = 14) and carrying over the remainder (1) to the tens place. They can then add the tens place (7 + 5 + 1 = 13) and carry over the remainder (1) to the hundreds place, and so on. This method can be applied to subtraction problems as well, making it a versatile tool for solving large numbers.

Practice regrouping and borrowing.

Regrouping and borrowing are important concepts when it comes to solving large numbers. Regrouping involves moving a number from one place value to another, while borrowing involves taking a number from a higher place value and adding it to a lower place value. These concepts can be practiced through various worksheets and exercises, allowing students to become more comfortable with solving large numbers using regrouping and borrowing techniques. With practice, students can become more confident in their ability to tackle even the most challenging large number problems.

Check your work for accuracy.

Once your child has completed their large number worksheet, it’s important to check their work for accuracy. Encourage them to double-check their calculations and make sure they have regrouped and borrowed correctly. One helpful tip is to have them work backwards to ensure their answer makes sense. For example, if the problem asks for the sum of 456 and 789, they can check their answer by subtracting 456 from their answer and making sure the result is 789. By checking their work, your child can catch any mistakes and improve their problem-solving skills.

If you're a teacher or parent looking for large numbers class 5 worksheets with answers, you've come to the right place! We have a wide range of worksheets that cover various topics related to large numbers, suitable for class 5 students. Our worksheets come in different formats, including pdf and printable versions, making them convenient for both online and offline learning.

One of our popular worksheets is the worksheet on large numbers for class 5, which covers the basics of large numbers such as place value, reading and writing large numbers, and comparing large numbers. We also have a large numbers worksheet for class 5 pdf that focuses on operations on large numbers, including addition, subtraction, multiplication, and division.

In addition to large numbers worksheets, we have other related worksheets that cover different aspects of numbers, such as the big and small numbers worksheet, dodging numbers 1 to 20 worksheet, small to big numbers worksheet, bigger number worksheet, numbers between worksheet, ascending order worksheet for class 5, and number system worksheet for class 5. These worksheets provide a comprehensive approach to learning numbers and numeration, suitable for class 5 students.

Our worksheets are designed to be engaging and interactive, with clear instructions and plenty of exercises that reinforce learning. We also provide answers to all the exercises, making it easy for teachers and parents to assess their students' progress.

If you're looking for worksheets that cover specific topics within class 5 math, we have worksheets on chapter 1 of class 5 math, numbers and numeration class 5, and operations on large numbers class 5 worksheets with answers. We also have worksheets on number names, put the sign, ascending and descending order, and the international number system.

Our worksheets are aligned with the NCERT and CBSE curriculum for class 5 math, ensuring that they provide a comprehensive and relevant learning experience. We also have worksheets that are suitable for other standards, such as class 1 and class 2.

In conclusion, our large numbers class 5 worksheets with answers provide a comprehensive and engaging approach to learning numbers and numeration. With a wide range of topics and format s, our worksheets cater to different learning styles and preferences, making them suitable for both teachers and parents. So why wait? Download our worksheets today and start your child's journey to mastering large numbers!

- What are large numbers in math?

Large numbers are numbers that have more than two digits. In class 5, students learn to work with numbers that are up to 7 digits long.

- What are the operations on large numbers in math?

The operations on large numbers include addition, subtraction, multiplication, and division.

- How do you add large numbers?

To add large numbers, align the digits according to their place values and then add them up, starting from the rightmost digit.

- How do you subtract large numbers?

To subtract large numbers, align the digits according to their place values and then subtract them, starting from the rightmost digit.

- How do you multiply large numbers?

To multiply large numbers, align the digits according to their place values and then multiply them, starting from the rightmost digit. Add up the partial products to get the final answer.

- How do you divide large numbers?

To divide large numbers, use long division. Divide the divisor into the dividend, starting from the leftmost digit, and then repeat until the entire dividend is divided.

- What is the order of operations in math?

The order of operations in math is PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.

- How do you simplify large expressions in math?

To simplify large expressions, use the order of operations and simplify each part of the expression separately before combining them.

- What are some common mistakes students make when working with large numbers?

Common mistakes students make when working with large numbers include forgetting to align the digits, forgetting to carry or borrow, and making errors in addition or subtraction.

- How can I practice working with large numbers?

You can practice working with large numbers by doing exercises and worksheets, practicing mental math, and using real-life examples to apply the concepts.

In conclusion, operations on large numbers class 5 is an important topic that requires practice and attention to detail. By understanding the concepts and practicing regularly, students can master this topic and feel confident in their math abilities.

25 Marks question paper on Operation on large Numbers for class 5th

Section A: Multiple Choice Questions (10 marks)

Which of the following is a large number? a) 10 b) 100 c) 1000 d) 10000

What is the place value of 5 in the number 35,678? a) 5 b) 50 c) 500 d) 5000

Which of the following is the correct way to write the number 8,950,763 in words? a) Eight thousand nine hundred fifty seven hundred sixty three b) Eighty nine thousand five hundred seventy six three c) Eight million nine hundred fifty thousand seven hundred sixty three d) Eight million nine hundred fifty thousand seven hundred six three

What is the smallest 7-digit number? a) 1,000,000 b) 10,000,000 c) 100,000,000 d) 1,000,000,000

Which of the following is the largest number? a) 4,567,890 b) 4,678,905 c) 4,789,056 d) 4,890,567

Section B: Short Answer Questions (10 marks)

Write the expanded form of the number 3,254,178.

Find the value of the digit 6 in the number 86,752.

Subtract 5,673 from 8,956.

Multiply 467 by 23.

Divide 8,930 by 5.

Section C: Long Answer Questions (5 marks each)

Write the Roman numeral for the number 56.

Write the number that comes after 98,765.

Compare the numbers 6,789 and 6,987 and write the greater number.

Find the missing digit in the number 3_,456,789 so that it is divisible by 9.

Write the number 10,000,000 in words.

- Large numbers
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- All GRADE 5 worksheet

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## Millions and Billions

This lesson plan must be purchased as part of a lesson packet or as part of a full curriculum that is available in our store..

15 minutes (Part 1); 1 hour (Part 2); 30 minutes (Part 3)

SUBJECTS: Math

TOPICS: Math - Large Numbers

## Resource Overview

Through riddles, an art project, and small group problem solving, students gain an appreciation for large numbers and specifically, the difference between a million and a billion.

## Students will be able to:

- Recognize that one billion is a thousand millions, which is a thousand thousands.
- Evaluate the difference between millions and billions.
- Solve math problems using standard measurement conversions and base 10 operations.

## Features of This Resource

- Students practice measurement with formal units
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## Other Resources You Might Like:

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## Addition and Subtraction - Subtracting Two- and Three-Digit Numbers

Addition and subtraction -, subtracting two- and three-digit numbers, addition and subtraction subtracting two- and three-digit numbers.

## Addition and Subtraction: Subtracting Two- and Three-Digit Numbers

Lesson 5: subtracting two- and three-digit numbers.

/en/additionsubtraction/introduction-to-subtraction/content/

## Subtracting larger numbers

In Introduction to Subtraction , we learned that counting and using visuals can be useful for solving basic subtraction problems. For instance, say you have 9 apples and you use 6 to make a pie. To find out how many apples are left, you could represent the situation like this:

It's easy to count and see that 3 apples are left.

What if you need to solve a subtraction problem that starts with a large number? For instance, let's say instead of making an apple pie, you want to pick apples from an apple tree. The tree has 30 apples and you pick 21 . We could write this as 30 - 21 .

You might see why counting to solve this problem isn't a good idea. When you have a subtraction problem that starts with a large number, it could take a long time to set up the problem. Imagine the time it would take to count out 30 objects and then take away 21! Also, it would be easy to lose track as you counted. You could end up with the wrong answer.

For this reason, when people solve a subtraction problem with large numbers, they set up the problem in a way that makes it easy to solve one step at a time. Let's see how this works with another problem: 79 - 13 .

In the last lesson, we learned how to write expressions. However, subtracting with larger numbers is easier when the expressions are written in a different way.

Instead of writing the numbers side by side…

Place the numbers so they are stacked — one number on top and one number on the bottom.

With a stacked subtraction expression, the larger number is always written on top. Here, that number is 79 .

Write the amount being subtracted underneath the top number. That's 13 .

Put the minus sign to the left of the numbers.

Instead of an equals sign, put a line underneath the bottom number.

When you stack a subtraction expression, make sure the numbers are lined up correctly. They are always lined up on the right. Here, we lined up 9 and 3 .

Here's another problem, 576 - 2 . With this problem, see how we lined up the numbers to the right?

No matter how many digits are in the numbers, always line up the numbers to the right.

## Solving Stacked Subtraction Problems

If you feel comfortable with the subtraction skills from Introduction to Subtraction , you're ready to start solving stacked subtraction problems.

Let's try to solve 49 - 7 .

With all stacked subtraction problems, we start with the digits that are farthest to the right. Here, we'll begin with 9 and 7 .

9 - 7 = 2 . The difference is 2 . It's important to write 2 directly beneath the digits we just subtracted.

Now let's find the difference of the digits to the left. The top digit is 4 , but there's nothing beneath it.

4 minus nothing is 4 , so we'll write 4 beneath the line.

Our result is 42 . 49 - 7 = 42 .

Let's see how this works with another problem: 88 - 62 .

As always, start with the digits that are farthest to the right. Here, they are 8 and 2 .

8 - 2 = 6 . Make sure to write 6 below the line.

Next, find the difference of the digits to the left, 8 and 6 .

8 - 6 is 2 . Write 2 below the line.

The answer is 26 . 88 - 62 = 26 .

In the slideshow, you saw that stacked subtraction problems are always solved from right to left . The expressions below are solved the same way. First, the bottom right digit is subtracted from the top right digit. Then, the bottom left digit is subtracted from the top left digit.

Stack these subtraction problems and solve them. Then, check your answer by typing it into the box.

## Subtracting Larger Numbers

Stacked subtraction can also be used for finding the difference of larger numbers. No matter how many digits there are, you subtract the same way every time — from right to left.

These subtraction problems have larger numbers. Solve them, and then check your answer by typing it into the box.

Sometimes when you subtract, you will notice that the top digit is smaller than the bottom. For example, take a look at this problem:

Normally, we'd start on the right with 5 - 9. However, since 9 is bigger than 5, we can't subtract normally. Instead, we have to use a technique called borrowing .

Let's see how it works.

First, we'll make sure the expression is set up correctly. The larger number is stacked on top of the smaller number.

As with all stacked subtraction problems, begin with the digits farthest to the right. Here, they are 5 and 9 .

5 is smaller than 9 , so we'll need to borrow to make 5 larger.

We'll borrow from the digit to the left of 5 . Here, it's 7 . We'll take 1 from it....

7 - 1 = 6 . To help us remember that we subtracted 1, we'll cross out the 7 and write 6 above it.

Then, we'll place the 1 we took next to the 5 ...

5 becomes 15 . See how it looks like 15?

15 is larger than 9, which means we can subtract. We'll solve for 15 - 9 .

15 - 9 = 6 . We'll write 6 beneath the line.

Next, find the difference of the digits to the left: 6 - 2 .

6 - 2 = 4 . We'll write 4 beneath the line.

Our answer is 46 . 75 - 29 = 46 .

As you borrow, always cross out the digit you borrow from and write the new value above it. Remember to always place the 1 next to the smaller digit.

Try these problems to practice borrowing. Check your answer by typing it into the box.

## Borrowing More Than Once

Sometimes the top number might have two or more digits that are smaller than the digits beneath them. In that case, you'll need to borrow more than once. It will always work the same way. You'll always subtract 1 from the digit to the left and place 1 next to the smaller digit.

In some cases, you might notice that the number to the left is zero. Check out the slideshow below to see an example of what to do.

Let's look at the example 300 minus 54. We would begin on the right with 0 minus 4 . However, zero is smaller than 4, so we would need to borrow from the next digit to the left.

The next digit to the left, however, is zero ! We can't borrow if nothing is there. So what do we do?

We have to go to the next digit to the left. Think of it like asking your neighbor for a cup of sugar. If the first neighbor doesn't have any, you would move to the next neighbor over to ask for some to borrow.

Since the next number over is 3 , we'll borrow from that.

Just like when we borrow normally, we'll subtract 1 from 3 to make it 2 . We'll place the 1 next to the number on the right to make it 10 .

Remember though, we originally needed to borrow in order to do 0 minus 4 . Now that we have 10 in the middle, we can borrow from it.

Cross out the 10 and subtract 1 to make it 9 .

Then, place the 1 next to the 0 in order to make it 10 . Now you're ready to subtract.

10 minus 4 is 6.

9 minus 5 is 4.

There is nothing to subtract from the 2, so we just bring it down, and we're finished!

The answer is 246 .

Try solving these subtraction problems to practice borrowing more than one time. Check your answer by typing it in the box.

## Checking Your Work

In the last few lessons, you learned how to solve addition and subtraction problems. As you practice these math skills, it's a good idea to get into the habit of checking your work . Checking will help you know if your answers are correct. When you're ready to check the answer to subtraction problems, you'll need to use addition.

Let's look at this problem: 9 - 7 = 2 .

How do we know that 2 is the correct answer? We can check by adding.

Let's set up our addition problem. First, we'll write the subtraction problem's answer. That means we'll write 2 .

Next, we'll add the amount that was subtracted, 7 .

Time to add. 2 + 7 = 9 .

If we subtracted correctly, the answer will match the larger number in our subtraction problem.

They match — 9 and 9 . Our answer was correct.

Let's try using addition to check the answer to another subtraction problem: 54 - 21 = 33 .

Let's set up our addition problem. First write the answer to the subtraction problem, 33 .

Then add back the number that was subtracted, 21 .

Now it's time to add. 33 + 21 = 54 .

Finally, we'll check to see if 54 matches the larger number in our subtraction problem. It does!

Practice subtracting these problems. You'll have to use borrowing to solve some of the problems. There are 4 sets of problems with 3 problems each.

/en/additionsubtraction/video-subtraction/content/

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## Unit 2: Addition and subtraction

About this unit, basic addition and subtraction.

- Basic addition (Opens a modal)
- Basic subtraction (Opens a modal)
- Add and subtract: pieces of fruit (Opens a modal)
- Relating addition and subtraction (Opens a modal)
- Add within 5 7 questions Practice
- Subtract within 5 7 questions Practice
- Add within 10 7 questions Practice
- Subtract within 10 7 questions Practice
- Relate addition and subtraction 7 questions Practice
- Getting to 10 by filling boxes (Opens a modal)
- Adding to 10 (Opens a modal)
- Make 10 (grids and number bonds) 7 questions Practice
- Make 10 7 questions Practice

## Addition and subtraction word problems within 10

- Addition word problems within 10 (Opens a modal)
- Subtraction word problems within 10 (Opens a modal)
- Addition word problems within 10 7 questions Practice
- Subtraction word problems within 10 7 questions Practice

## Addition and subtraction within 20

- Adding within 20 using place value blocks (Opens a modal)
- Adding within 20 using ten frames (Opens a modal)
- Adding 7 + 6 (Opens a modal)
- Adding 8 + 7 (Opens a modal)
- Adding with arrays (Opens a modal)
- Subtracting different ways (Opens a modal)
- Subtract within 20 using a number line (Opens a modal)
- Subtract within 20 using place value blocks (Opens a modal)
- Subtract within 20 using ten frames (Opens a modal)
- Subtracting 14 - 6 (Opens a modal)
- Add within 20 visually 7 questions Practice
- Add within 20 7 questions Practice
- Adding with arrays 4 questions Practice
- Subtract within 20 visually 7 questions Practice
- Subtract within 20 7 questions Practice
- Find missing number (add and subtract within 20) 7 questions Practice
- Add & subtract within 20 7 questions Practice

## Word problems within 20

- Addition and subtraction word problems: superheroes (Opens a modal)
- Addition and subtraction word problems: gorillas (Opens a modal)
- Addition and subtraction word problems 1 7 questions Practice
- Addition and subtraction word problems 2 7 questions Practice
- Add and subtract within 20 word problems 7 questions Practice

## Word problems with "more" and "fewer"

- Comparison word problems: marbles (Opens a modal)
- Comparison word problems: roly-polies (Opens a modal)
- Word problems with "more" and "fewer" 2 7 questions Practice

## Intro to addition with 2-digit numbers

- Adding 2-digit numbers without regrouping (Opens a modal)
- Adding 2-digit numbers without regrouping 1 (Opens a modal)
- Example: Adding 2-digit numbers (no carrying) (Opens a modal)
- Breaking apart 2-digit addition problems (Opens a modal)
- Regrouping to add 1-digit number (Opens a modal)
- Adding up to four 2-digit numbers 4 questions Practice
- Break apart 2-digit addition problems 4 questions Practice
- Regroup when adding 1-digit numbers 7 questions Practice

## Intro to subtraction with 2-digit numbers

- Subtracting two-digit numbers without regrouping (Opens a modal)
- Subtracting 2-digit numbers without regrouping 1 (Opens a modal)
- Subtracting a 1-digit number with regrouping (Opens a modal)
- Subtract within 100 using place value blocks 4 questions Practice
- Subtract within 100 using a number line 4 questions Practice
- Subtract 1-digit numbers with regrouping 7 questions Practice

## Strategies for adding and subtracting within 100

- Adding 53+17 by making a group of 10 (Opens a modal)
- Adding by making a group of 10 (Opens a modal)
- Strategies for adding 2-digit numbers (Opens a modal)
- Addition and subtraction with number lines (Opens a modal)
- Add 2-digit numbers by making tens 4 questions Practice
- Add 2-digit numbers by making tens 2 4 questions Practice
- Select strategies for adding within 100 4 questions Practice
- Add within 100 using a number line 4 questions Practice

## Addition within 100

- Understanding place value when adding ones (Opens a modal)
- Understanding place value when adding tens (Opens a modal)
- Adding with regrouping (Opens a modal)
- Add within 100 using place value blocks 4 questions Practice

## Subtraction within 100

- Subtracting with regrouping (borrowing) (Opens a modal)

## Word problems within 100

- Adding and subtracting on number line word problems (Opens a modal)
- Adding two digit numbers on a number line (Opens a modal)
- Subtraction word problem: tennis balls (Opens a modal)
- Addition word problem: horses (Opens a modal)
- Subtraction word problem: snow (Opens a modal)
- Subtraction word problem: crayons (Opens a modal)
- Multi step addition word problem (Opens a modal)
- Multi-step subtraction word problem (Opens a modal)
- Add and subtract on the number line word problems 4 questions Practice
- Addition word problems within 100 4 questions Practice
- Subtraction word problems within 100 4 questions Practice
- 2-step addition word problems within 100 4 questions Practice
- 2-step subtraction word problems within 100 4 questions Practice

## Adding 1s, 10s, and 100s

- Adding 10 or 100 (Opens a modal)
- Adding 1s, 10s, and 100s (Opens a modal)
- Adding 3-digit numbers (no regrouping) (Opens a modal)
- Add 10s and 100s (no regrouping) 4 questions Practice
- Add within 1,000 using place value blocks 4 questions Practice

## Subtracting 1s, 10s, and 100s

- Subtracting 1, 10, or 100 (Opens a modal)
- Subtracting 1s, 10s, and 100s (Opens a modal)
- Subtracting 3-digit numbers (no regrouping) (Opens a modal)
- Subtract 10s and 100s (no regrouping) 7 questions Practice
- Subtract within 1,000 using place value blocks 4 questions Practice

## Strategies for adding 2- and 3-digit numbers

- Breaking apart 3-digit addition problems (Opens a modal)
- Solving 3-digit addition in your head (Opens a modal)
- Addition using groups of 10 and 100 (Opens a modal)
- Adding and subtracting on number line (Opens a modal)
- Break apart 3-digit addition problems 4 questions Practice
- Add using groups of 10 and 100 4 questions Practice
- Add on a number line 4 questions Practice
- Select strategies for adding within 1000 4 questions Practice

## Addition with regrouping within 1000

- Using place value to add 3-digit numbers: part 2 (Opens a modal)
- Adding 3-digit numbers (Opens a modal)
- Add within 1000 4 questions Practice

## Subtraction with regrouping within 1000

- Worked example: Subtracting 3-digit numbers (regrouping) (Opens a modal)
- Worked example: Subtracting 3-digit numbers (regrouping twice) (Opens a modal)
- Worked example: Subtracting 3-digit numbers (regrouping from 0) (Opens a modal)
- Subtracting in your head (no regrouping) (Opens a modal)
- Subtract on a number line 4 questions Practice
- Subtract within 1000 4 questions Practice

## Addition and subtraction missing value problems

- Missing numbers in addition and subtraction (Opens a modal)
- Missing number for 3-digit addition within 1000 (Opens a modal)
- Find the missing number (add and subtract within 100) 4 questions Practice
- Find the missing number (add and subtract within 1000) 4 questions Practice

## Addition and subtraction greater than 1000

- Relate place value to standard algorithm for multi-digit addition (Opens a modal)
- Multi-digit addition with regrouping (Opens a modal)
- Multi-digit subtraction with regrouping: 6798-3359 (Opens a modal)
- Multi-digit subtraction with regrouping: 7329-6278 (Opens a modal)
- Multi-digit subtraction with regrouping twice (Opens a modal)
- Alternate mental subtraction method (Opens a modal)
- Adding multi-digit numbers: 48,029+233,930 (Opens a modal)
- Relate place value to standard algorithm for multi-digit subtraction (Opens a modal)
- Multi-digit subtraction: 389,002-76,151 (Opens a modal)
- Multi-digit addition 4 questions Practice
- Multi-digit subtraction 4 questions Practice

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## Advanced Subtraction Worksheets: Large Numbers

These dynamically created multi-digit subtraction worksheets are recommended for students of Grades 4 and grade 5. An endless supply of large number subtraction problems that feature 4-digit, 5-digit, 6-digit and 7- digit numbers in the vertical format are displayed here. Students need to regroup (borrow) numbers wherever required.

## List of Subtracting Large Numbers Worksheets

Explore the subtracting large numbers worksheets in detail.

4-digit subtraction

Download and print this array of 4-digit subtraction worksheets. A variety of engaging topics like grid subtraction, decode the riddles, line up and subtract and many more are on offer here.

5-digit subtraction

Access our wide selection of ready-to-print worksheets on 5-digit subtraction. Find the difference between 5-digit and 3- ,4-, or 5-digit numbers. A few interesting word problems are included for variety.

6-digit subtraction

Help students master the concept of regrouping (borrowing) with this set of 6-digit column subtraction problems. Exclusive fact-based word problems are incorporated in some of the worksheets.

7-digit subtraction

Get ample practice on the concept of large number subtraction problems along with the scenario-based word problems. Minuends contain 7-digit numbers and subtrahends feature 5-, 6- or 7-digit numbers.

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## Subtracting Large Numbers | Multi-digit Subtraction Worksheets

- Number Sense >
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Excel in subtracting large numbers with our multi-digit subtraction worksheets! Chock-a-block with practice in finding the difference between two large numbers ranging between 4 digits and 7 digits, this bundle of subtracting large numbers pdfs also gives insight into subtraction with borrowing or regrouping. As you scroll through the topics, don't forget to access the few free worksheets on multi-digit subtraction.

These worksheets are recommended for 4th grade and 5th grade students.

## Exclusive Multi-digit Subtraction Worksheets

- 4-Digit Subtraction
- 5-Digit Subtraction
- 6-Digit Subtraction
- 7-Digit Subtraction

Multi-digit Subtraction | Standard

Ace every test on multi-digit subtraction with our printable worksheets. Featuring 15 problems, each pdf helps students in 4th grade and 5th grade practice multi-digit subtraction with gritted teeth.

Multi-digit Subtraction | With Word Problems

Well stocked with word problems and subtraction problems, this fabulous resource aids young learners in understanding how multi-digit subtraction plays a key role in everyday life.

Multi-digit Subtraction | Line Up - 3, 4, and 5 Digits

Get students in grade 4 and grade 5 to line up numbers with 3, 4, or 5 digits according to their place values and find the difference between 2 large numbers.

Multi-digit Subtraction | Line Up - 5, 6, and 7 Digits

Progress to the next level with this set of subtracting large numbers pdfs. Presented here are numbers with 5, 6, and 7 digits; kids are required to line up the numbers and subtract.

Multi-digit Subtraction Word Problems

Waiting to help kids here are subtraction word problems involving large numbers with and without borrowing. Students get a taste of large number subtraction in real life with these word problems.

Related Printable Worksheets

▶ Subtracting Across Zeros

▶ 3-Digit Subtraction

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## Word Problems on Addition and Subtraction of Whole Numbers

We will learn how to solve step-by-step the word problems on addition and subtraction of whole numbers. We know, we need to do addition and subtraction in our daily life. Let us solve some word problem examples.

Word problems on adding and subtracting of large numbers:

1. The population of a country in 1990 was 906450600 and next year it is increased by 9889700. What was the population of that country in the year of 1991?

The population of a country in 1990 = 906450600

Increased population by next year = + 9889700

Total population of that country in 1991 = 916340300

Therefore, the population of that country in the year of 1991 is 916340300.

2. Aaron bought two houses for $1668000 and $2454000. How much did he spend in all?

Cost of one house = $ 1668000

Cost of other house = + $ 2454000

Total cost of both houses = $ 4122000

Amount of money spent in all $4122000.

3. The sum of two numbers is 41482308. If one number is 3918695 then, find the other number.

Sum of two numbers = 41482308

One of the number = - 3918695

Second number = 37563613

Therefore, the other number is 37563613.

4. Mr. Jones deposited $278475 in a bank in his account. Later he withdrew $155755 from his account. How much money was left in the bank in his account?

Amount deposited = $ 278475

Amount withdrawn = - $ 155755

Amount left = $ 122720

Therefore, Mr. Jones has $ 122720in his bank account.

Note: We need to be careful while arranging the addends in columns.

5th Grade Math Problems From Word Problems on Addition and Subtraction of Whole Numbers to HOME PAGE

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## Can you solve it? The magical maths that keeps your data safe

How to protect machines against random failures

UPDATE: The solutions can be read here

I’ve temporarily moved to Berkeley, California, where I am the “science communicator in residence” at the Simons Institute , the world’s leading institute for collaborative research in theoretical computer science.

One nano-collaboration is today’s puzzle – told to me by a computer scientist at Microsoft I befriended over tea. It’s about data centres – those warehouses containing endless rows of computers that store all our data.

One problem faced by data centres is the unreliability of physical machines. Hard drives fail all the time, and when they do, all their data may be lost. How do companies like Microsoft make sure that they can recover the data from failed hard drives? The solution to the puzzle below is, in essence, the answer to this question.

An obvious strategy that a data centre could use to protect its machines from random failures is for every machine to have a duplicate. In this case, if a hard drive fails, you recover the data from the duplicate. This strategy, however, is not used because it is very inefficient. If you have 100 machines, you would need another 100 duplicates. There are better ways, as you will hopefully deduce!

The disappearing boxes

You have 100 boxes. Each box contains a single number in it, and no two boxes have the same number.

1. You are told that one of the boxes at random will be removed. But before it is removed you are given an extra box , and allowed to put a single number in it. What number do you put in the extra box that guarantees you will be able to recover the number of whichever box is removed?

2. You are told that two of the boxes at random will be removed. But before it is removed you are given two extra boxes, and allowed to put one number in each of them. What (different) numbers do you put in these two boxes that guarantees you will be able to recover the numbers of both removed boxes?

I’ll be back with the answers at 5pm UK. Meanwhile, NO SPOILERS, please discuss your favourite hard drives.

UPDATE: The solutions can be read here.

The analogy here is that each box is a hard drive, the number in the box is the data, and the removal of a box is the failure of the hard drive. With one extra hard drive, we are secure against the random failure of a single hard drive, and with two, we are secure against the failure of two. It seems magical that we can protect such a lot of information against random failures with minimal back-up.

The field of “error-correcting codes” is a large body of beautiful theories that provide answers to questions such as how to minimise the number of machines needed to protect against random failures of hard drives. And the theories work! Data centres never lose your data because of mechanical failure.

My tea companion was Sivakanth Gopi, a Principal Researcher at Microsoft. He said: “The magic of error correcting codes allows us to build reliable systems using noisy and faulty components. Thanks to them, we can communicate with someone as far away as the ends of our solar system and store billions of terabytes of data safely in the cloud. We can forget about the noise and complexity of this world and instead enjoy its beauty.”

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me .

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## Computer Science > Artificial Intelligence

Title: self-discover: large language models self-compose reasoning structures.

Abstract: We introduce SELF-DISCOVER, a general framework for LLMs to self-discover the task-intrinsic reasoning structures to tackle complex reasoning problems that are challenging for typical prompting methods. Core to the framework is a self-discovery process where LLMs select multiple atomic reasoning modules such as critical thinking and step-by-step thinking, and compose them into an explicit reasoning structure for LLMs to follow during decoding. SELF-DISCOVER substantially improves GPT-4 and PaLM 2's performance on challenging reasoning benchmarks such as BigBench-Hard, grounded agent reasoning, and MATH, by as much as 32% compared to Chain of Thought (CoT). Furthermore, SELF-DISCOVER outperforms inference-intensive methods such as CoT-Self-Consistency by more than 20%, while requiring 10-40x fewer inference compute. Finally, we show that the self-discovered reasoning structures are universally applicable across model families: from PaLM 2-L to GPT-4, and from GPT-4 to Llama2, and share commonalities with human reasoning patterns.

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## No Problems are Too Big for God to Solve - Love Worth Finding - February 24

February 24, 2024 – No Problems are Too Big for God to Solve Philippians 2:3-4 Sermon: 1417 Marriage: The Real Thing

Pray Over This

“Let nothing be done through selfish ambition or conceit, but in lowliness of mind let each esteem others better than himself. Let each of you look out not only for his own interests, but also for the interests of others.” Philippians 2:3-4

Ponder This

Do you know what most of our arguments are? Ego against ego! Self against self! Before long there’s going to be a war between those two kingdoms. The husband needs to step down from the throne of his life and enthrone King Jesus. The same is true for the wife!

How many kingdoms are there? There is just one kingdom—Jesus rules both thrones. And here’s a wonderful secret: The Jesus in the husband is not going to fight the Jesus in the wife. If Christ is on the throne of both lives, the husband and wife will be one spiritually. You’re going to be able to pray together and worship together. Because you’re one spiritually, is it easier to be one psychologically? Not always! Where is the problem psychologically? Why can’t we heal our arguments? Because of our egos. But when we take ourselves off the throne and enthrone Christ, we can solve those problems. There are no problems too big to solve; just people too small to solve them.

- When has your ego affected an argument in which you were involved?
- How can you get past your ego? What makes that so difficult?

Practice This

Pray and repent for the ways your ego has hurt your relationships with others.

For more from Love Worth Finding and Pastor Adrian Rogers, please visit www.lwf.org .

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Watch Adrian Rogers and Love Worth Finding Video Online.

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- February 23, 2024 • 25:48 Trump’s Cash Crunch
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- February 13, 2024 • 27:23 Why the Race to Replace George Santos Is So Close
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- February 11, 2024 • 42:04 The Sunday Read: ‘The Unthinkable Mental Health Crisis That Shook a New England College’
- February 9, 2024 • 34:05 Kick Trump Off the Ballot? Even Liberal Justices Are Skeptical.

## Trump’s Cash Crunch

The ruling in former president donald j. trump’s civil fraud case could cost him all his available cash..

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## Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Last week, when a civil court judge in New York ruled against Donald J. Trump, he imposed a set of penalties so severe that they could temporarily sever the former president from his real-estate empire and wipe out all of his cash.

Jonah Bromwich, who covers criminal justice in New York, and Maggie Haberman, a senior political correspondent for The Times, explain what that will mean for Mr. Trump as a businessman and as a candidate.

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## Reduce, reuse, redirect outrage: How plastic makers used recycling as a fig leaf

Michael Copley

A registered scavenger, who mainly collects plastic waste to sell, walking in a landfill in Indonesia. Yasuyoshi Chiba /AFP via Getty Images hide caption

A registered scavenger, who mainly collects plastic waste to sell, walking in a landfill in Indonesia.

The plastics industry has worked for decades to convince people and policymakers that recycling would keep waste out of landfills and the environment. Consumers sort their trash so plastic packaging can be repurposed, and local governments use taxpayer money to gather and process the material. Yet from the early days of recycling, plastic makers, including oil and gas companies, knew that it wasn't a viable solution to deal with increasing amounts of waste, according to documents uncovered by the Center for Climate Integrity .

Around the time the plastics industry launched its recycling campaign, the head of a trade group called the Vinyl Institute acknowledged at a 1989 conference that "recycling cannot go on indefinitely, and does not solve the solid waste problem."

One of the biggest challenges is that making new plastic is relatively cheap. But recycling generally costs as much as or more than the material is worth, a director of environmental solutions at B.F. Goodrich explained at another industry meeting in 1992 . The "basic issue," he said, "is economics."

## Investigations

How big oil misled the public into believing plastic would be recycled.

But the industry appears to have championed recycling mainly for its public relations value, rather than as a tool for avoiding environmental damage, the documents suggest. "We are committed to the activities, but not committed to the results," a vice president at Exxon Chemical said during a meeting in 1994 with staff for the American Plastics Council, a trade group.

Ross Eisenberg, president of an industry group called America's Plastic Makers, said in a statement that the report from the Center for Climate Integrity "cites outdated, decades-old technologies, and works against our goals to be more sustainable by mischaracterizing the industry and the state of today's recycling technologies. This undermines the essential benefits of plastics and the important work underway to improve the way plastics are used and reused to meet society's needs."

America's Plastic Makers has set a goal for all plastic packaging in the U.S. to be "reused, recycled, recovered by 2040," Eisenberg said.

The Center for Climate Integrity compiled the documents in a report titled " The Fraud of Plastic Recycling: How Big Oil and the plastics industry deceived the public for decades and caused the plastic waste crisis ." It builds on earlier investigations, including by NPR , that have shown the plastics industry promoted recycling even though its officials have long known that the activity would probably never be effective on a large scale.

## The world is awash in plastic. Oil producers want a say in how it's cleaned up

Former industry officials have said the goal was to avoid regulations and ensure that demand for plastics, which are made from fossil fuels, kept growing. Despite years of recycling campaigns, less than 10% of plastic waste gets recycled globally , and the amount of plastic waste that's dumped in the environment continues to soar .

The idea that recycling can solve the problem of plastic waste "has always been a fraud, and it's always been a way for the industry to sell more plastic," says Richard Wiles, president of the Center for Climate Integrity, which says it is working to hold oil and gas companies accountable for their role in fueling climate change.

A pile of plastic waste and other garbage next to children playing on a bridge in the Philippines. George Calvelo /AFP via Getty Images hide caption

A pile of plastic waste and other garbage next to children playing on a bridge in the Philippines.

## The U.N. is leading negotiations for a global plastics treaty

The Center for Climate Integrity published its report two months before the next round of United Nations talks is held in Canada for a legally binding global agreement on plastic waste. Negotiators from around 150 countries are expected to attend, as well as public health advocates, human rights activists, environmentalists and the oil and gas industry.

There's recently been growing concern among those who want deep cuts in plastic waste that plastic producers — corporations as well as countries such as China, Russia and Saudi Arabia — could weaken a global treaty by prioritizing recycling and other forms of waste management, rather than substantial cuts in new plastic production.

## Global talks to cut plastic waste stall as industry and environmental groups clash

For fossil fuel producers, the petrochemical sector, which includes plastics, is crucial to business. As technologies like electric vehicles grow more popular, demand for products such as gasoline and diesel fuel is expected to decline . But oil and gas demand for petrochemicals is projected to continue rising for years . That's why the fossil fuel industry has a big stake in the outcome of the U.N. talks. If countries agree to reduce plastic manufacturing, it could hurt the industry's future profits.

Some experts say that creates a conflict of interest. Reducing how much new plastic gets made in the first place is a "prerequisite" to getting pollution under control, Carsten Wachholz, who works at the Ellen MacArthur Foundation and co-leads the Business Coalition for a Global Plastics Treaty, said late last year. But "if your businesses depend on extracting more oil and gas, and plastics is the fastest growing market for fossil fuels, it's hard to imagine that you would be a credible voice to say we need to limit plastic production," he said.

## Global shift to clean energy means fossil fuel demand will peak soon, IEA says

After the last round of negotiations ended in Kenya in November 2023, environmental groups complained that oil and gas producers blocked a final decision on how to advance the deliberations.

An industry advocacy group called American Fuel & Petrochemical Manufacturers has said that restricting fossil fuel production and plastic manufacturing are not good solutions. Instead, it said the goals of the treaty can be achieved "if waste is recyclable, properly managed and kept out of the environment."

An ExxonMobil spokesperson said in a statement in November 2023 that the company is "launching real solutions to address plastic waste and improve recycling rates." The company has previously said the problem of plastic waste can be solved without cutting how much plastic society uses.

Exxon is among a group of companies that have been investing in what the industry calls "advanced recycling" plants. The facilities are designed to turn plastic waste, including material that can't be processed through traditional mechanical recycling, into liquids and gasses that can then be used to make new plastics and other chemical products.

"Advanced recycling is a real, proven solution that can help address plastic waste and improve recycling rates," Exxon said in a statement to NPR.

However, critics say the technology is ineffective and harmful to the environment and human health.

The economics of plastic recycling "haven't changed at all. Not at all. And if virgin [plastic] was always cheaper and of higher quality, that's still the case today," says Wiles of the Center for Climate Integrity.

He says the plastics industry continues to mislead the public and needs to be held responsible for it.

"And from there, you can begin to have a conversation about how we're going to solve the problem," Wiles says. "But without accountability, you just can't get to solutions."

- microplastics
- oil and gas
- climate change

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## COMMENTS

Answer: The remaining budget is \ (2,211,211,111\) dollars. Word problems involving large numbers can initially seem intimidating. However, by carefully extracting the relevant data and applying basic addition or subtraction, you can easily find the solution.

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example: 644 + 238 While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240. Now, add 650 and 240 together.

Real-life problems, large numbers This math worksheet gives your child practice solving word problems involving adding and subtracting mulit-digit numbers. MATH | GRADE: 4th Print full size Skills Adding multi-digit numbers, Money math, Solving word problems Common Core Standards: Grade 4 Measurement & Data CCSS.Math.Content.4.MD.A.2

Multiply 4-digit or 5-digit with 2-digit numbers to solve each problem. Real-life problems are included. Standard With Word Problems Download the set Multiplying 3-Digit by 3-Digit Long multiplication problems where 3-digit multiplies 3-digit. The numbers to be multiplied are vertically arranged. Standard With Word Problems Download the set

Solution: First, we arrange the numbers in columns according to their place value and then we add them. Therefore, the sum of the given numbers is 160,864,980. Subtraction of Large Numbers For subtraction of large numbers, the same order of columns that were used for addition is followed.

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Here are some examples solving number problems. Example 1 When 6 times a number is increased by 4, the result is 40. Find the number. First, circle what you must find— the number. Letting x stand for the number gives the equation 6 x + 4 = 40 Subtracting 4 from each side gives 6 x = 36 Dividing by 6 gives x = 6 So the number is 6. Example 2

Use addition and subtraction to solve problems. One of the most effective ways to solve large numbers is to use addition and subtraction. Students can break down the number into smaller parts and add or subtract them to find the answer. For example, if the problem is 5,678 + 3,456, students can start by adding the ones place (8 + 6 = 14) and ...

Through riddles, an art project, and small group problem solving, students gain an appreciation for large numbers and specifically, the difference between a million and a billion. Students will be able to: Recognize that one billion is a thousand millions, which is a thousand thousands. Evaluate the difference between millions and billions.

Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...

Large Numbers Addition Worksheets: Large Numbers Want to master multi-digit addition? A myriad collection of printable addition worksheets involving large numbers i.e. 4-digit, 5-digit, 6-digit and more is at your service.

For this reason, when people solve a subtraction problem with large numbers, they set up the problem in a way that makes it easy to solve one step at a time. ... These subtraction problems have larger numbers. Solve them, and then check your answer by typing it into the box. 225 - 100 = 199 - 21 = 634 - 623 =

Rounding 6-digit numbers to the nearest 1000, 10 000 and 100 000. Key Learning. Copy Lesson Link. View Lesson in classroom. Lesson overview. 2 Quizzes. 17 m Video. Presentation (PPT) Worksheet.

Multi-step word problems with whole numbers. Google Classroom. After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs.

Answers Complexity=1 Order the numbers from greatest to least. Use arrow keys and the tab key instead of your mouse. Complexity=10 Order the numbers from least to greatest. Use arrow keys and the tab key instead of your mouse. Complexity=100 Order the numbers from least to greatest. Use arrow keys and the tab key instead of your mouse.

Test your understanding of Addition and subtraction with these % (num)s questions. Start test. In this topic, we will add and subtract whole numbers. The topic starts with 1+1=2 and goes through adding and subtracting within 1000. We will cover regrouping, borrowing, and word problems.

A few interesting word problems are included for variety. 6-digit subtraction Help students master the concept of regrouping (borrowing) with this set of 6-digit column subtraction problems. Exclusive fact-based word problems are incorporated in some of the worksheets. 7-digit subtraction

Multi-digit. Excel in subtracting large numbers with our multi-digit subtraction worksheets! Chock-a-block with practice in finding the difference between two large numbers ranging between 4 digits and 7 digits, this bundle of subtracting large numbers pdfs also gives insight into subtraction with borrowing or regrouping.

Math Practice Problems - Rounding Large Numbers MathScore EduFighter is one of the best math games on the Internet today. You can start playing for free! Rounding Large Numbers - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families.

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Using these kinds of word problems in your class provides scaffolding that allows students the opportunity to develop a better understanding of the structure of word problems and how to make a plan to solve them. Each "problem set" in this addition and subtraction of large numbers resource contains 4 pages. The first page has the prob

Let us solve some word problem examples. Word problems on adding and subtracting of large numbers: 1. The population of a country in 1990 was 906450600 and next year it is increased by 9889700. What was the population of that country in the year of 1991? The population of a country in 1990 = 906450600 Increased population by next year = + 9889700

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