problem solving worksheet grade 7

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GRADE 7 MATH WORKSHEET

Question 1 :

In a class test containing 15 questions, 4 marks are given for each correct answer and -2 marks are given for every incorrect answer. James attempts all the questions but only 9 of his answers are correct. what is his total score?

Question 2 :

A batsman scored the following number of runs in six innings :

36, 35, 50, 46, 60, 55

Calculate the runs scored by him in an inning.

Question 4 :

Solve for x :

-2(x + 3) = 8

Question 5 :

Kevin's father's age is 5 years more than three times Kevin's age.Find Kevin's age, if his father is 44 years old.

Question 6 :

If two lines intersect at a point, and if a pair of vertically opposite angles are acute angles, what will the other pair of vertically opposite angles be?

Question 7 :

In the figure shown below, if the lines L and M are parallel, find the value of x.

Question 8 :

In the figure shown below, find the value of x.

Question 9 :

I have 2 vats each containing 2 mats 2 cats sat on each of the mats each cat wore 2 hats on each hat lay to rats on each rat perched 2 thin bats how many things are there in my vats?

Question 10 :

Express the number 5985.3 in standard form.

1. Answer :

Total number of questions = 15.

Number of questions answered correctly by James = 9.

Number of questions answered incorrectly by him.

For each correct answer he will get +4 marks and for each questions he will get -2 marks.

James' total score :

=  9  ⋅ 4 + 6 ⋅ (-2)

 = 36 - 12

2. Answer :

To find the runs scored in one innings, we have to find the average.

= ⁽³⁶ ⁺ ³⁵ ⁺ ⁵⁰ ⁺ ⁴⁶ ⁺ ⁶⁰ ⁺ ⁵⁵⁾⁄₆

Therefore, the batsman scored 47 runs in one innings.

3. Answer :

Number of mangoes in small boxes = m.

Number of magoes in big box = 8m + 4.

Total number of mangoes in big box = 100.

The required equation :

8m + 4  =  100

4. Answer :

Use the distributive property.

-2(x) - 2(3) = 8

-2x - 6 = 8

Add 6 to both sides.

Divide both sides by -2.

5. Answer :

Let x be the age Kevin.

Kevin's father's age = 3x + 5.

Given : Father's age = 44.

3x + 5 = 44

Subtract 5 from both sides.

Divide both sides by 3.

Therefore, Kevin's age is 13 years.

6. Answer :

If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertical opposite angles must be obtuse angles.

7. Answer :

In the figure shown above, the lines L and M are parallel and the line t is transversal. 110° and y are linear pair.

110° + y = 180°

Subtract 110° from both sides.

Since x and y are alternate interior angles, they must be equal.

8. Answer :

Exterior Angle Theorem :

In a triangle, the measure of an exterior angle is equal to sum of the measures of two remote interior angles.

In the triangle shown above, 110 ° is an exterior angle and x and 50° are the two remote interior angles.

By Exterior Angle Theorem,

x + 50 ° = 110°

Subtract 50° from both sides.

9. Answer :

There are two vats

Number of mats in 1 vat = 2

Number of mats in 2 vats = 2 × 2 = 4

Number of cats on 1 mat = 2

Number of cats on 4 mats = 4 × 2 = 8

Number of funny old hat with 1 cat = 2

Number of funny old hat with 8 cats = 8 × 2 = 16

Number of thin rat on 1 old hat = 2

Number of thin rat on 16 old hats = 16 × 2 = 32

Number of black bats on 1 rat = 2

Number of black bats on 32 rats = 32 × 2 = 64

Number of things in in my vats :

= 64 + 32 + 16 + 8 + 4 + 2

10. Answer :

Here, non zero digit comes first and decimal point comes next. 

We have to move the decimal point to the left. 

There are three digits between the 1 st  non zero digit and the decimal point.

So, the decimal point has to be moved three digits to the left and exponent of 10 should be 3 (positive integer).

Therefore, the scientific notation of 5985.3  is

5.9853 x 10 3

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Seventh Grade (Grade 7) Problem Solving Strategies Questions

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At this level students start getting much more familiar with equations and the use of expressions. The heat is turned up on geometry as they start to introduce just a little bit of trigonometry too. Statistics and probability is the most noticeable advance at this level. We venture into the use of compound events. Many students find it to be challenging. Grade 7 Math Posters can be a super help too.

Ratios & Proportional Relationships Worksheets

• Unit Rates and Ratios of Fractions (7.RP.A.1)- Unit rates are just a very specific ration that compares two values each with their own units of measure.
• Recognizing Proportional Relationships (7.RP.A.2a)- You can spot relationships that are proportional by proving that they have the same rate. It is helpful if you write them as fractions first.
• The Constant of Proportionality (7.RP.A.2b)- We use this section to help us identify and make decisions based on mathematically relationships.
• Proportional Relationships Word Problems (7.RP.A.2c)- We identify and use proportional relationships to answer story based problems.
• Equivalent Ratios (7.RP.A.2c)- Students learn how to identify and create ratios that are equal.
• Graphs of Proportional Relationships (7.RP.A.2d)- We visualize the relationships that exist between proportional values or systems.
• Multistep Ratio and Percent Word Problems (7.RP.A.3)- These are your more difficult problems. You will need to pay specific attention to detail.
• Percent Error and Percent Increase (7.RP.A.3)- While this seems like meaningless math, there are literally tens-of thousands of people that make their living calculating this value for businesses.
• Markups and Markdowns Word Problems (7.RP.A.3)- You can test your ability with this at department stores. Why do some stores have nothing, but sales.
• Gratuities and Commissions, Fees, and Tax (7.RP.A.3)- This comes in very handy when you are having dinner at a restaurant. At least when the check comes to the table.
• Calculating Interest (7.RP.A.3)- When we are in school, this just some simple math. When we become grown-ups, this is a vital math formula we all need to understand, so that we are financially sound.
• Consumer Math (7.RP.A.3)- The forms of math we use when buying and selling anything in a real world situation. If there is one form of math you should master, this is it.
• Adding and Subtracting Percents and Decimals (7.RP.A.3)- While this seems like an easy task, many students often to pay attention to place values enough.
• Compare Percentages and Decimals (7.RP.A.3)- These two are interchangeable, with the movement of two decimal places.
• Finding Percent of Fractions Word Problem (7.RP.A.3)- I would recommend spending a little extra time on this skill.
• Percentages and Numbers Lines (7.RP.A.3)- We relate various fractions and percentages to their position on a numbers line.
• Percentage Decrease of Integers (7.RP.A.3)- Spending time with markups and a markdowns is a nice complement to this topic.
• Percentage Word Problems (7.RP.A.3)- Word problems that move and shake in financial markets.

The Number System Worksheets

• Addition and Subtraction of Integers (7.NS.A.1)- We do this across all types of different problems (number line displays, word problems, and straight operational math).
• Absolute Value and Basic Operations (7.NS.A.1c)- Within these problems students learn how to handle absolute values found within operations.
• Products of Mixed Numbers (7.NS.A.2a)- Basically a three-step process: a) convert all mixed number to improper fractions B) multiply numerators together and the same for the denominators C) write the value in the simplest form.
• Creating Reciprocals (7.NS.A.2a)- Learn how to make reciprocals of whole numbers and fractions.
• Understanding Division of Integers (7.NS.A.2b)- We look at all the different uses of division.
• Multiplication and Division of Rational Numbers (7.NS.A.2c)- We look at all the various of rational numbers and put them through this operation.
• Convert Rational Numbers to Decimals (7.NS.A.2d)- We use visual grids at time to bring this to life more for students.
• Advanced Real World Math Operations (7.NS.A.3)- These are problems that you will encounter daily when you graduate.

Expressions and Equations Worksheets

• Simplifying Linear Expressions (7.EE.A.1)- Combining like terms are the key here.
• Rewriting Expressions (7.EE.A.2)- In most cases you will be creating expressions based on math sentences.
• Real Life Middle School Math Word Problems (7.EE.B.3)- These problem types are right up your alley in this grade level.
• Business Math (7.EE.B.3)- These skills are necessary to be part of most of the workforce.
• Double Step Algebra (7.EE.B.3)- Find the variables, combine like terms, and then get the variables to one side.
• Integer Word Problems (7.EE.B.3)- This is where we need to learn to understand negative values, such as representing a loss of some kind.
• Word Problems Leading to Equations (7.EE.B.4a)- Start by identifying the variables you are working with.
• Word Problems Leading to Inequalities (7.EE.B.4b)- Before write symbols, I recommend reading the problem thoroughly.
• Consecutive Integer Problems (7.EE.B.4a)- These really helps in many different forms of computer programming.
• Scale Drawings of Geometric Figures (7.G.A.1)- This way you draw things on a small piece of paper that can be represented in a real life scale.
• Drawing Geometric Shapes with Given Conditions (7.G.A.2)- This is what architects do all day long.
• Decomposing Three-dimensional Figures (7.G.A.3)- This is a complex skill and require that have a sound understanding of basic geometric shapes.
• Area and Circumference of a Circle (7.G.B.4)- Think about all the math that goes into creating all the balls for different sports across the world.
• Angles in a Multi-Step Problems (7.G.B.5)- You will need to be able to identify complement and supplementary angles.
• Complementary and Supplementary Angles (7.G.B.5)- It is a good idea to follow this topic up with the worksheet topic just above this.
• 2D and 3D Area, Volume and Surface Area - 7.G.B.6)- These are three measures that greatly differ based on the shape you are working with.

Statistics & Probability

• Understanding Random Sampling (7.SP.A.1)- Making sure you are working in a random environment helps to validate all your math and the hypothesis you develop off of it.
• Making Inferences From Random Data (7.SP.A.2)- You will first have to organize the data and then make your conclusions based on it.
• Working With Assessing Overlapping Data Sets (7.SP.B.3)- This can save you from a great deal of confusion.
• Measures of Center and Variability (7.SP.B.4)- This will help you understand how to spot outliers.
• Likelihood of a Single Event (7.SP.C.5)- I think about this every time I buy a lottery ticket.
• Probability of a Chance Event (7.SP.C.6)- Like being struck by lightening or having an asteroid fall on your home.
• Creating Probability Models (7.SP.C.7)- This will help you make predictions to very important events.
• Probabilities of Compound Events (7.SP.C.8)- When you have a few things to take into account before calculating probability.
• Finding the Probability of Compound Events By Using Diagrams, Lists, and Tables - 7.SP.C.8c)- Guess which career path these gets you ready for?

What do students learn in Grade 7 math class?

Children that are studying in 7th grade are sharp and have the ability to grasp many math operations. Students in 7th grade are taught to solve math problems that touch every sub topic tactfully. The math curriculum covers all math strands and is not limited to just arithmetic. The most important math standards for this curriculum include number sense and operations, algebra, geometry, and spatial sense, measurements, data analysis, and probability. For students to clearly understand these concepts, interactive activities should be introduced. Worksheets, learning games, and assessments all contribute to critical thinking and efficient problem solving. With the help of various learning tools, students take more interest and readily solve math questions.

Traits of Highly Effective Grade 7 Math Students

This is a very intimidating grade level for students, especially those students who have not had much success with the subject of math in the past. There are number of habits that we see common amongst students that thrive at this level. The first trait we see commonly among successful students is patience. When you reach this level, the problems will require more reading and more thought. Make sure that you organize yourself and slowly progress through these problems and exercises. When you first begin working at this level, take your time and organize your thought process. It is even good to get in the habit of outlining how you solve problems. You will make many mistakes along the way and that is perfectly naturally and learning from them will help you get it right. Which leads us to the second common trait shared by successful students and that is persistence. You will get problems wrong, you may even botch entire concepts, but if you stick at it, you will eventually begin to fully understand what is expected of you. The only thing you can count on in math is that there is rarely only one way to come to the correct conclusion. Stick it out through those tougher exercises and make that a personal habit. The last trait we see common among highly effective students is self-recognition. Understanding which study technique works best for you to be successful is key. If something did not work for you, try a different method. Rinse and repeat that until you find a winning formula. Even after you find out what works, keep fine tuning it.

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Grade 7 Math Worksheets

Related Pages Common Core Math Lessons & Worksheets Grade 7 Common Core Math Lessons & Worksheets Grade 8 Free Math Worksheets According To Grades Math Worksheets according to Topics Interactive Zone Grade 7 Math Lessons

These free interactive math worksheets are suitable for Grade 7. Use them to practice and improve your mathematical skills.

Decimal Worksheets

Multiply Decimals by Tens Multiply Decimals by 1 -digit Whole Number Multiply Decimals by 2-digit Whole Number Multiply two Decimals (Tenths) Multiply Two Decimals (Hundredths) Multiply two Decimals (Thousandths)

Divide Decimals by Tens Divide with Decimal Quotients (Tenths) Divide with Decimal Quotients (Hundredths) Divide Two Decimals (Tenths) Divide two Decimals(Hundredths) Divide Two Decimals (Thousandths)

1-Step Addition & Subtraction 2-Step Addition & Subtraction Decimal Word Problems, Mixed Operations Decimal Word Problems, Mixed Operations 2

Integer Worksheets

Add Integers, 2 operands Add Integers, 3 or more operands Subtract Integers, 2 operands Subtract Integers, 3 or more operands Multiply Integers Divide Integers

Add Integers, 1 Digit Add Integers, 2 Digits Subtract Integers, 1 Digit Subtract Integers, 2 Digits Multiply Integers, 1 Digit Multiply Integers, 2 Digits Divide Integers, 1 Digit in Divisor Divide Integers, 2 Digits in Divisor Integers, Mixed Operations Specify your own conditions for Integer Operations

Fraction Worksheets

Add & Subtract Fractions (with common denominator & simplifying answers) Least Common Multiple or Least Common Denominator Add & Subtract Fractions (with unlike denominators & step-by-step guide) Add & Subtract Fractions (with unlike denominators) Add Fractions (dynamic) Subtract Fractions (dynamic)

Add Mixed Numbers Add Mixed Numbers (dynamic) Subtract Mixed Numbers Subtract Mixed Numbers(dynamic)

Multiply Fractions by Whole Numbers Multiply Two Fractions Divide Whole Numbers by Fractions Divide Fractions by Whole Numbers Divide Fractions by Fractions Divide Two Fractions

Multiply Mixed Numbers Multiply Mixed Numbers (dynamic) Divide Mixed Numbers Divide Mixed Numbers (dynamic)

Add & Subtract Fractions Add & Subtract Mixed Numbers (1-Step) Add & Subtract Mixed Numbers (2-Step) Add & Subtract Mixed Numbers (2-Step)

Algebra Worksheets

Evaluate Expressions by Substitution Simplify Expressions by Combining Like Terms Simplify Expressions using Distributive Property Simplify Expressions using Distributive Property & Combine Like Terms

Solving One-Step Equations Solving Two-Step Equations Solving Equations by Combining Like Terms Solving Equations with the Variable on Both Sides Solving Equations by Distributive Property Solving Multi-Step Equations Solving Multi-Step Equations Solving Word Problems using Algebra

Percent Worksheets

Change Percents to Decimals & Fractions Change Percents to Fractions in Lowest Terms Change Percents to Fractions Change Fractions to Percents Change Fractions to Percents Change Decimals to Percents

Percentages (What is X% of Y) Percentages (X is what % of Y) Percentages (X is Y% of what) Percent of a Number Finding Percent Finding the Base

Percent Word Problems Percentage Word Problems Percent Word Problems (Profit, Loss) Percent Word Problems (Increase, Decrease)

Number Patterns & Sequences (Find the n th term)

Find the sequence & n th term Find the sequence & n th term Find the n th term of a sequence with fractions

Geometry Worksheets

Give the number of sides Give the names of the polygons

Types of Angles Angles in a Straight Line Angles at a Point Complementary Angles Supplementary Angles

Area & Perimeter of Rectangles 1 Area & Perimeter of Rectangles 2 Area & Perimeter of Rectangles 3 Area & Perimeter of Parallelogram Area of Triangle Area of Parallelograms Area of Triangle & Parallelogram Area of Trapezoid (Trapezium) Area of Shapes Area of shaded Region

Surface Area and Volume of Cube Surface Area & Volume of Rectangular Prisms (Cuboids) Volume of Cylinders Volume of Sphere Volume of Prisms & Pyramids Volume of Square Pyramids Volume of Cones Surface Area of Cylinder Surface Area of Sphere Surface Area of Solids I Surface Area of Solids II Surface Area of Solids III Surface Area of Solids IV Surface Area of Solids V Surface Area of Cylinders & Pipes Surface Area of Cylinders & Spheres Volume and Surface Area of Cylinder Volume and Surface Area of Sphere

Circumference of Circle Area of Circle Area & Circumference of Circle Circle Problems: Circumference, Area Circle Word Problems 1 Circle Word Problems 2 Area of shaded regions that include circles Area of figures that include circles Area of figures that include circles

Coordinate Plane Worksheets

Slope of a Line Slope and Intercept of a Line Midpoint Formula 1 Midpoint Formula 2 Distance Formula 1 Distance Formula 2

Slope and Intercept of a Line

Pythagorean Theorem Worksheets

Pythagorean Theorem (dynamic) Find the missing side Test for right triangle Pythagorean Theorem Word Problems Converse Pythagorean Theorem, Types of Triangles

Statistics Worksheets

Mode Median Mean Range Mean, Median and Mode Mean, Median and Mode Find the possible values for the Median Given the Mean, find the missing number(s) in a set Word problems that involve the Mean Word problems that involve the Mean

Probability Worksheets

Probability Problems Complementary Probability Probability Word Problems Probability & Geometry Mutually Exclusive Probability Independent Events Probability Dependent Events Probability

Division with Decimal Quotients, Multiply Two Decimals, Divide Two Decimals, Decimals and Fractions, Decimal Word Problems

Add Integers, Subtract Integers, Multiply Integers, Divide Integers

Add Fractions, Subtract Fractions, Multiply Fractions, Divide Fractions, Add Mixed Numbers, Subtract Mixed Numbers, Multiply Mixed Numbers, Divide Mixed Numbers, Fraction Word Problems

Evaluating Expressions, Simplifying Expressions, Solving Equations, Solving Word Problems

Percent, Percent Word Problems

Finding the sequence and nth term

Names of Polygons, Types of Angles, Angles in a Triangle, Angles in a Quadrilateral, Angles in a Polygon, Area and Perimeter of Polygons, Area & Circumference of Circles, Arc Length & Area of Sector, Circle Word Problems, Area of Shaded Regions, Geometry Word Problems, Volume of Solids, Surface Area of Solids

Slope of a Line, Intercept of a Line, Explore Slope & Intercept, Midpoint Formula, Distance Formula, Pythagorean Theorem

Mode, Median, Mean, Range, Statistics Word Problems

Probability Word Problems, Complementary Probability, Mutually Exclusive Probability, Independent Events Probability, Dependent Events Probability

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7th Grade Math Problems

In 7th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 7, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam.

●  Set Theory

Sets : An introduction to sets, methods for defining sets, element of set and use of set notations.

Objects Form a Set : State, whether the following objects form a set or not by giving reasons.

Elements of a Set : Learn how to find the elements of a set with the help of various types of problems on the basic concepts of sets.

Properties of Sets : Using the basic properties to represent a set learn to solve various basic types of problems on sets.

Representation of a Set : Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Different Notations in Sets : Some of the familiar notations used in sets which are generally required to solve various types of problems on sets.

Standard Sets of Numbers : Learn to represent the standard sets of numbers using the three methods i.e. statement form, roster form and set builder form.

Types of Sets : Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Pairs of Sets : Definition with examples of equal set, equivalent set, disjoint sets and overlapping set.

Subset : Definition with examples of subset and its types, super set, proper subset, power set and universal set.

Subsets of a Given Set : How to find the number of subsets of a given set and number of proper subsets of a given set.

Operations on Sets : Learn the meaning. What are the four basic operations on sets? How the operations are carried out in union of sets and intersection of sets?

Union of Sets : Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples.

Intersection of Sets : Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Difference of two Sets : Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set : Definition of complement of a set and their properties with some worked-out examples.

Cardinal number of a set : Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples.

Cardinal Properties of Sets : Learn how to solve the real-life word problems on set using the cardinal properties.

Venn Diagrams : Learn to represent the basic concepts of sets using Venn-diagram in different situations.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals : Concept for decimals in derails.

Decimal Numbers : Learn reading decimal numbers, writing decimal numbers etc,.

Decimal Fractions : Learn reading decimal fractions, writing decimal fractions.

Decimal Places : Learn reading and writing the place values of a decimal number in words.

Decimal and Fractional Expansion : Learn how to expand the decimal numbers and the decimal numbers in fractions

Like and Unlike Decimals : Learn to identify like decimals and unlike decimals.

Conversion of Unlike Decimals to Like Decimals : Learn to convert unlike decimals in like decimals

Comparing Decimals : Learn to order and compare decimal numbers, arranging decimals in ascending order and arranging decimals in descending order

Adding Decimals : Learn to add decimals in the correct order, word problems.

Subtracting Decimals : Learn to subtract decimals in the correct order, word problems

Simplify Decimals Involving Addition and Subtraction Decimals : Examples for simplifying decimals for adding and subtracting.

Multiplying Decimal by a Whole Number : Learn to multiply decimals by a whole number in the correct order, word problems

Multiplying Decimal by a Decimal Number : Learn to multiply decimals by a decimal number in the correct order, word problems

Dividing Decimal by a Whole Number : Learn to divide decimals by a whole number in the correct order, word problems

Dividing Decimal by a Decimal Number : Learn to divide decimals by a decimal number in the correct order, word problems

Simplification of Decimal : Examples for simplifying decimals, operation on decimals.

Converting Decimals to Fractions : Learn to express decimal number into fraction

Converting Fractions to Decimals : Learn to express fraction into decimal number

Rounding Decimals : Learn to round off decimals

Rounding Decimals to the Nearest Whole Number : Learn to round off decimals to the nearest whole number

Rounding Decimals to the Nearest Tenths : Learn to round off decimals to the nearest tenths

Rounding Decimals to the Nearest Hundredths : Learn to round off decimals to the nearest hundredths

Round a Decimal : Problems for rounding off decimals

H.C.F. and L.C.M. of Decimals : Learn to find the highest common factor, lowest common multiple of more than two decimal numbers

Terminating Decimal : Definition of terminating decimals, examples to identify terminating decimals

Non-Terminating Decimal : Definition of non-terminating decimal, examples to identify non-terminating decimals

Repeating or Recurring Decimal : Definition of recurring decimals, examples to identify recurring decimals

Pure Recurring Decimal : Definition of pure recurring decimal, examples to pure recurring decimal

Mixed Recurring Decimal : Definition of mixed recurring decimal, examples to identify mixed recurring decimal

Conversion of Pure Recurring Decimal into Vulgar Fraction : Learn to express pure recurring decimals to vulgar fractions with examples.

Conversion of Mixed Recurring Decimals into Vulgar Fractions : Learn to express mixed recurring decimals to vulgar fractions with examples.

BODMAS/PEMDAS rule:

BODMAS Rule : Learn how to follow the BODMAS rules to simply the order of operations.

BODMAS Rules - Involving Integers : Learn how to follow the BODMAS rules to simply the order of operations involving integers.

BODMAS/PEMDAS Rules - Involving Decimals : Learn how to follow the BODMAS rules to simply the order of operations involving decimals

PEMDAS Rule : Learn how to follow the PEMDAS rules to simply the order of operations.

PEMDAS Rules - Involving Integers : Learn how to follow the PEMDAS rules to simply the order of operations involving integers.

PEMDAS Rules - Involving Decimals : Learn how to follow the PEMDAS rules to simply the order of operations involving decimals.

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

Square of The Sum of Two Binomials : Using the formula of (a + b) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + 2ab, learn to evaluate the square of the sum of two terms.

Square of The Difference of Two Binomials : Using the formula of (a - b)\(^{2}\)  = a \(^{2}\) + b \(^{2}\) - 2ab, learn to evaluate the square of the difference of two terms.

Product of Sum and Difference of Two Binomials : Using the formula of a \(^{2}\) - b \(^{2}\) = (a + b) (a - b), learn to evaluate the product of sum and difference of two terms.

Product of Two Binomials whose First Terms are Same and Second Terms are Different : Learn to use the given formulas to evaluate the product of the two terms whose 1 \(^{st}\) terms are same and 2 \(^{nd}\) terms are different.

• (x + a) (x + b) = x \(^{2}\) + x(a + b) + ab

• (x + a) (x - b) = x \(^{2}\) + x (a – b) – ab

• (x - a) (x - b) = x \(^{2}\) – x (a + b) + ab

• (x - a) (x + b) = x \(^{2}\) + x (b – a) – ab

Square of a Trinomial : Learn to use the formula for the expansion of the square of a trinomial.

• (a + b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab + 2bc + 2ca

• (a + b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab – 2bc - 2ca

• (a - b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab – 2bc + 2ca

• (a - b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab + 2bc – 2ca

Cube of The Sum of Two Binomials : Learn the formula to determine the cube of the sum of two terms.

(a + b) \(^{3}\) = a \(^{3}\)   + 3a \(^{2}\) b + 3ab \(^{2}\)   + b \(^{3}\)

             = a \(^{3}\) + b \(^{3}\) + 3ab (a + b)

Cube of The Difference of Two Binomials : Learn the formula to determine the cube of the difference of two terms.

(a - b) \(^{3}\) = a \(^{3}\)   – 3a \(^{2}\) b + 3ab \(^{2}\)   – b \(^{3}\)

           = a \(^{3}\) – b \(^{3}\) – 3ab (a - b)

Cube of a Binomial :

Square of a Binomial :

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

● Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes :

Congruent Line-segments :

Congruent Angles :

Congruent Triangles :

Conditions for the Congruence of Triangles :

Side Side Side Congruence :

Side Angle Side Congruence : 

Angle Side Angle Congruence :

Angle Angle Side Congruence :

Right Angle Hypotenuse Side congruence :

Pythagorean Theorem :

Proof of Pythagorean Theorem :

Converse of Pythagorean Theorem :

Word problems on Pythagorean Theorem :

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

Quadrilateral : Perimeter of Quadrilateral : Angle Sum Property of a Quadrilateral : Missing angle of a Quadrilateral :

Angles of a Quadrilateral are in Ratio :

●   Symmetrical Figure

Linear Symmetry :  Identify symmetric and non-symmetric figures and also identify shapes having horizontal line of symmetry, vertical line of symmetry, both horizontal and vertical lines of symmetry, infinite lines of symmetry and no line of symmetry.

Lines of Symmetry :  Identify the geometrical shapes having 1, 2, 3, 4, 0 and so on or infinite lines of symmetry.

Point Symmetry :  How to find the point symmetry of letters of the English alphabet and the different geometrical figures. Learn the important points to find the conditions that satisfy centre of symmetry.

Reflection Symmetry :

Nets of a Solids :

Rotational Symmetry :  Learn what is rotational symmetry and types of rotation i.e. clockwise rotation and anticlockwise rotation. 

Order of Rotational Symmetry :  Learn the different orders of rotation of the shapes through 360° in clockwise direction and anticlockwise direction.

Types of Symmetry :  Learn the various symmetries i.e. linear symmetry, point symmetry and rotational symmetry of the geometrical shapes. 

Reflection :  Learn how reflection is related to math, define reflection using an image and worked-out examples on math reflection. 

Reflection of a Point in x-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in x-axis.

Reflection of a Point in y-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in y-axis.

Reflection of a point in origin :  Learn how to draw the image on the graph paper to find the reflection of a point in origin. 

Rotation :  Explanation of rotation using an image.

90 Degree Clockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees clockwise direction around the origin on a graph paper.

90 Degree Anticlockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees anticlockwise direction around the origin on a graph paper.

180 Degree Rotation :  Learn with the help of solved examples to rotate a figure 180 degrees clockwise direction and anticlockwise direction around the origin on a graph paper.

●  Coordinate System

• Coordinate Graph
• Ordered pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time

●  Mensuration

• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square

●  Mensuration - Worksheets

• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle

●   Volume and Surface Area of Solids

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

●  Statistics

• Real Life Statistics
• Terms Related to Statistics
• Frequency Distribution of Ungrouped and Grouped Data
• Use of Tally Marks
• Class Limits in Exclusive and Inclusive Form
• Construction of Bar Graphs
• Mean of the Tabulated Data
• Construction of Pie Chart
• How to Construct a Line Graph?

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Grade 7 Maths Problems With Answers

Grade 7 math word problems with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included.

• In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
• In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
• If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
• The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
• A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
• Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
• 15 cm is the height of water in a cylindrical container of radius r. What is the height of this quantity of water if it is poured into a cylindrical container of radius 2r?
• John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
• How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
• The rectangular playground in Tim's school is three times as long as it is wide. The area of the playground is 75 square meters. What is the primeter of the playground?
• John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
• N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? A) 1 1/2 B) 1 1/3 C) 5/3 D) 3/2
• In 2008, the world population is about 6,760,000,000. Write the 2008 world population in scientific notation.
• Calculate the circumference of a circular field whose radius is 5 centimeters.

Answers to the Above Questions

• 6 balls are blue
• 10 students are 10 years old
• x = 5/6 meter
• 20,000 square meters
• 368 square units
• 1250 meters per minute
• 78.74 inches
• 40 square meters
• 10? centimeters

Free Math 7 Worksheets

• Operations on Real Numbers
• Order of Operations
• Percents, Fractions, & Decimals
• Area and Perimeter
• Volume and Surface Area
• Rates, Ratios, & Proportions
• Solving Equations

Review multiplication one-step equtions. Then, cross multiply to solve for the variable.

Solve for the variable in one-step problems, worksheet #1.

Solve for the variable in one-step problems, worksheet #2.

Solve for the variable in one-step problems, worksheet #3.

Solve for the variable in one-step problems, worksheet #4.

Solve for the variable in two-step problems, worksheet #1.

Solve for the variable in two-step problems, worksheet #2.

Solve for the variable in two-step problems, worksheet #3.

Solve for the variable in two-step problems, worksheet #4.