## What is 56 divided by 4 using long division?

Confused by long division? By the end of this article you'll be able to divide 56 by 4 using long division and be able to apply the same technique to any other long division problem you have! Let's take a look.

Want to quickly learn or show students how to solve 56 divided by 4 using long division? Play this very quick and fun video now!

Okay so the first thing we need to do is clarify the terms so that you know what each part of the division is:

• The first number, 56, is called the dividend.
• The second number, 4 is called the divisor.

What we'll do here is break down each step of the long division process for 56 divided by 4 and explain each of them so you understand exactly what is going on.

## 56 divided by 4 step-by-step guide

The first step is to set up our division problem with the divisor on the left side and the dividend on the right side, like we have it below:

We can work out that the divisor (4) goes into the first digit of the dividend (5), 1 time(s). Now we know that, we can put 1 at the top:

If we multiply the divisor by the result in the previous step (4 x 1 = 4), we can now add that answer below the dividend:

Next, we will subtract the result from the previous step from the second digit of the dividend (5 - 4 = 1) and write that answer below:

Move the second digit of the dividend (6) down like so:

The divisor (4) goes into the bottom number (16), 4 time(s), so we can put 4 on top:

If we multiply the divisor by the result in the previous step (4 x 4 = 16), we can now add that answer below the dividend:

Next, we will subtract the result from the previous step from the third digit of the dividend (16 - 16 = 0) and write that answer below:

## So, what is the answer to 56 divided by 4?

If you made it this far into the tutorial, well done! There are no more digits to move down from the dividend, which means we have completed the long division problem.

Your answer is the top number, and any remainder will be the bottom number. So, for 56 divided by 4, the final solution is:

Remainder 0

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## Extra calculations for you

Now you've learned the long division approach to 56 divided by 4, here are a few other ways you might do the calculation:

• Using a calculator, if you typed in 56 divided by 4, you'd get 14.
• You could also express 56/4 as a mixed fraction: 14 0/4
• If you look at the mixed fraction 14 0/4, you'll see that the numerator is the same as the remainder (0), the denominator is our original divisor (4), and the whole number is our final answer (14).

## Long Division Calculator

Enter another long division problem to solve

## Next Long Division Problem

Eager for more long division but can't be bothered to type two numbers into the calculator above? No worries. Here's the next problem for you to solve:

What is 56 divided by 5 using long division?

## Random Long Division Problems

If you made it this far down the page then you must REALLY love long division problems, huh? Below are a bunch of randomly generated calculations for your long dividing pleasure:

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## Course: Algebra 1   >   Unit 6

• Systems of equations with elimination: King's cupcakes
• Elimination strategies
• Combining equations
• Systems of equations with elimination: x-4y=-18 & -x+3y=11
• Systems of equations with elimination
• Systems of equations with elimination: potato chips
• Systems of equations with elimination (and manipulation)
• Systems of equations with elimination challenge

## Elimination method review (systems of linear equations)

What is the elimination method.

• an integer, like 6 ‍
• a simplified proper fraction, like 3 / 5 ‍
• a simplified improper fraction, like 7 / 4 ‍
• a mixed number, like 1   3 / 4 ‍
• an exact decimal, like 0.75 ‍
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍

## Want to join the conversation?

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• 2.2 Solve Equations using the Division and Multiplication Properties of Equality
• Introduction
• 1.1 Introduction to Whole Numbers
• 1.2 Use the Language of Algebra
• 1.3 Add and Subtract Integers
• 1.4 Multiply and Divide Integers
• 1.5 Visualize Fractions
• 1.6 Add and Subtract Fractions
• 1.7 Decimals
• 1.8 The Real Numbers
• 1.9 Properties of Real Numbers
• 1.10 Systems of Measurement
• Key Concepts
• Review Exercises
• Practice Test
• 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
• 2.3 Solve Equations with Variables and Constants on Both Sides
• 2.4 Use a General Strategy to Solve Linear Equations
• 2.5 Solve Equations with Fractions or Decimals
• 2.6 Solve a Formula for a Specific Variable
• 2.7 Solve Linear Inequalities
• 3.1 Use a Problem-Solving Strategy
• 3.2 Solve Percent Applications
• 3.3 Solve Mixture Applications
• 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
• 3.5 Solve Uniform Motion Applications
• 3.6 Solve Applications with Linear Inequalities
• 4.1 Use the Rectangular Coordinate System
• 4.2 Graph Linear Equations in Two Variables
• 4.3 Graph with Intercepts
• 4.4 Understand Slope of a Line
• 4.5 Use the Slope-Intercept Form of an Equation of a Line
• 4.6 Find the Equation of a Line
• 4.7 Graphs of Linear Inequalities
• 5.1 Solve Systems of Equations by Graphing
• 5.2 Solving Systems of Equations by Substitution
• 5.3 Solve Systems of Equations by Elimination
• 5.4 Solve Applications with Systems of Equations
• 5.5 Solve Mixture Applications with Systems of Equations
• 5.6 Graphing Systems of Linear Inequalities
• 6.1 Add and Subtract Polynomials
• 6.2 Use Multiplication Properties of Exponents
• 6.3 Multiply Polynomials
• 6.4 Special Products
• 6.5 Divide Monomials
• 6.6 Divide Polynomials
• 6.7 Integer Exponents and Scientific Notation
• 7.1 Greatest Common Factor and Factor by Grouping
• 7.2 Factor Trinomials of the Form x2+bx+c
• 7.3 Factor Trinomials of the Form ax2+bx+c
• 7.4 Factor Special Products
• 7.5 General Strategy for Factoring Polynomials
• 8.1 Simplify Rational Expressions
• 8.2 Multiply and Divide Rational Expressions
• 8.3 Add and Subtract Rational Expressions with a Common Denominator
• 8.4 Add and Subtract Rational Expressions with Unlike Denominators
• 8.5 Simplify Complex Rational Expressions
• 8.6 Solve Rational Equations
• 8.7 Solve Proportion and Similar Figure Applications
• 8.8 Solve Uniform Motion and Work Applications
• 8.9 Use Direct and Inverse Variation
• 9.1 Simplify and Use Square Roots
• 9.2 Simplify Square Roots
• 9.3 Add and Subtract Square Roots
• 9.4 Multiply Square Roots
• 9.5 Divide Square Roots
• 9.6 Solve Equations with Square Roots
• 9.7 Higher Roots
• 9.8 Rational Exponents
• 10.1 Solve Quadratic Equations Using the Square Root Property
• 10.2 Solve Quadratic Equations by Completing the Square
• 10.4 Solve Applications Modeled by Quadratic Equations
• 10.5 Graphing Quadratic Equations in Two Variables

## Learning Objectives

By the end of this section, you will be able to:

• Solve equations using the Division and Multiplication Properties of Equality
• Solve equations that require simplification
• Translate to an equation and solve
• Translate and solve applications

## Be Prepared 2.5

Before you get started, take this readiness quiz.

Simplify: −7 ( 1 −7 ) . −7 ( 1 −7 ) . If you missed this problem, review Example 1.68 .

## Be Prepared 2.6

Evaluate 9 x + 2 9 x + 2 when x = −3 x = −3 . If you missed this problem, review Example 1.57 .

Solve Equations Using the Division and Multiplication Properties of Equality

You may have noticed that all of the equations we have solved so far have been of the form x + a = b x + a = b or x − a = b x − a = b . We were able to isolate the variable by adding or subtracting the constant term on the side of the equation with the variable. Now we will see how to solve equations that have a variable multiplied by a constant and so will require division to isolate the variable.

Let’s look at our puzzle again with the envelopes and counters in Figure 2.5 .

In the illustration there are two identical envelopes that contain the same number of counters. Remember, the left side of the workspace must equal the right side, but the counters on the left side are “hidden” in the envelopes. So how many counters are in each envelope?

How do we determine the number? We have to separate the counters on the right side into two groups of the same size to correspond with the two envelopes on the left side. The 6 counters divided into 2 equal groups gives 3 counters in each group (since 6 ÷ 2 = 3 6 ÷ 2 = 3 ).

What equation models the situation shown in Figure 2.6 ? There are two envelopes, and each contains x x counters. Together, the two envelopes must contain a total of 6 counters.

We found that each envelope contains 3 counters. Does this check? We know 2 · 3 = 6 2 · 3 = 6 , so it works! Three counters in each of two envelopes does equal six!

This example leads to the Division Property of Equality .

## The Division Property of Equality

For any numbers a , b , and c , and c ≠ 0 c ≠ 0 ,

When you divide both sides of an equation by any non-zero number, you still have equality.

## Manipulative Mathematics

The goal in solving an equation is to ‘undo’ the operation on the variable. In the next example, the variable is multiplied by 5, so we will divide both sides by 5 to ‘undo’ the multiplication.

## Example 2.13

Solve: 5 x = −27 . 5 x = −27 .

## Try It 2.25

Solve: 3 y = −41 . 3 y = −41 .

## Try It 2.26

Solve: 4 z = −55 . 4 z = −55 .

Consider the equation x 4 = 3 x 4 = 3 . We want to know what number divided by 4 gives 3. So to “undo” the division, we will need to multiply by 4. The Multiplication Property of Equality will allow us to do this. This property says that if we start with two equal quantities and multiply both by the same number, the results are equal.

## The Multiplication Property of Equality

For any numbers a , b , and c ,

If you multiply both sides of an equation by the same number, you still have equality.

## Example 2.14

Solve: y −7 = −14 . y −7 = −14 .

Here y y is divided by −7 −7 . We must multiply by −7 −7 to isolate y y .

## Try It 2.27

Solve: a −7 = −42 . a −7 = −42 .

## Try It 2.28

Solve: b −6 = −24 . b −6 = −24 .

## Example 2.15

Solve: − n = 9 . − n = 9 .

## Try It 2.29

Solve: − k = 8 . − k = 8 .

## Try It 2.30

Solve: − g = 3 . − g = 3 .

## Example 2.16

Solve: 3 4 x = 12 . 3 4 x = 12 .

Since the product of a number and its reciprocal is 1, our strategy will be to isolate x x by multiplying by the reciprocal of 3 4 3 4 .

## Try It 2.31

Solve: 2 5 n = 14 . 2 5 n = 14 .

## Try It 2.32

Solve: 5 6 y = 15 . 5 6 y = 15 .

In the next example, all the variable terms are on the right side of the equation. As always, our goal in solving the equation is to isolate the variable.

## Example 2.17

Solve: 8 15 = − 4 5 x . 8 15 = − 4 5 x .

## Try It 2.33

Solve: 9 25 = − 4 5 z . 9 25 = − 4 5 z .

## Try It 2.34

Solve: 5 6 = − 8 3 r . 5 6 = − 8 3 r .

Solve Equations That Require Simplification

Many equations start out more complicated than the ones we have been working with.

With these more complicated equations the first step is to simplify both sides of the equation as much as possible. This usually involves combining like terms or using the distributive property.

## Example 2.18

Solve: 14 − 23 = 12 y − 4 y − 5 y . 14 − 23 = 12 y − 4 y − 5 y .

Begin by simplifying each side of the equation.

## Try It 2.35

Solve: 18 − 27 = 15 c − 9 c − 3 c . 18 − 27 = 15 c − 9 c − 3 c .

## Try It 2.36

Solve: 18 − 22 = 12 x − x − 4 x . 18 − 22 = 12 x − x − 4 x .

## Example 2.19

Solve: −4 ( a − 3 ) − 7 = 25 . −4 ( a − 3 ) − 7 = 25 .

Here we will simplify each side of the equation by using the distributive property first.

## Try It 2.37

Solve: −4 ( q − 2 ) − 8 = 24 . −4 ( q − 2 ) − 8 = 24 .

## Try It 2.38

Solve: −6 ( r − 2 ) − 12 = 30 . −6 ( r − 2 ) − 12 = 30 .

Now we have covered all four properties of equality—subtraction, addition, division, and multiplication. We’ll list them all together here for easy reference.

## Properties of Equality

When you add, subtract, multiply, or divide the same quantity from both sides of an equation, you still have equality.

Translate to an Equation and Solve

In the next few examples, we will translate sentences into equations and then solve the equations. You might want to review the translation table in the previous chapter.

## Example 2.20

Translate and solve: The number 143 is the product of −11 −11 and y .

Begin by translating the sentence into an equation.

## Try It 2.39

Translate and solve: The number 132 is the product of −12 and y .

## Try It 2.40

Translate and solve: The number 117 is the product of −13 and z .

## Example 2.21

Translate and solve: n n divided by 8 is −32 −32 .

## Try It 2.41

Translate and solve: n n divided by 7 is equal to −21 −21 .

## Try It 2.42

Translate and solve: n n divided by 8 is equal to −56 −56 .

## Example 2.22

Translate and solve: The quotient of y y and −4 −4 is 68 68 .

## Try It 2.43

Translate and solve: The quotient of q q and −8 −8 is 72.

## Try It 2.44

Translate and solve: The quotient of p p and −9 −9 is 81.

## Example 2.23

Translate and solve: Three-fourths of p p is 18.

Begin by translating the sentence into an equation. Remember, “of” translates into multiplication.

## Try It 2.45

Translate and solve: Two-fifths of f f is 16.

## Try It 2.46

Translate and solve: Three-fourths of f f is 21.

## Example 2.24

Translate and solve: The sum of three-eighths and x x is one-half.

## Try It 2.47

Translate and solve: The sum of five-eighths and x is one-fourth.

## Try It 2.48

Translate and solve: The sum of three-fourths and x is five-sixths.

Translate and Solve Applications

To solve applications using the Division and Multiplication Properties of Equality, we will follow the same steps we used in the last section. We will restate the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve.

## Example 2.25

Denae bought 6 pounds of grapes for \$10.74. What was the cost of one pound of grapes?

## Try It 2.49

Translate and solve:

Arianna bought a 24-pack of water bottles for \$9.36. What was the cost of one water bottle?

## Try It 2.50

At JB’s Bowling Alley, 6 people can play on one lane for \$34.98. What is the cost for each person?

## Example 2.26

Andreas bought a used car for \$12,000. Because the car was 4-years old, its price was 3 4 3 4 of the original price, when the car was new. What was the original price of the car?

## Try It 2.51

The annual property tax on the Mehta’s house is \$1,800, calculated as 15 1,000 15 1,000 of the assessed value of the house. What is the assessed value of the Mehta’s house?

## Try It 2.52

Stella planted 14 flats of flowers in 2 3 2 3 of her garden. How many flats of flowers would she need to fill the whole garden?

## Section 2.2 Exercises

Practice makes perfect.

In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution.

8 x = 56 8 x = 56

7 p = 63 7 p = 63

−5 c = 55 −5 c = 55

−9 x = −27 −9 x = −27

−809 = 15 y −809 = 15 y

−731 = 19 y −731 = 19 y

−37 p = −541 −37 p = −541

−19 m = −586 −19 m = −586

0.25 z = 3.25 0.25 z = 3.25

0.75 a = 11.25 0.75 a = 11.25

−13 x = 0 −13 x = 0

24 x = 0 24 x = 0

x 4 = 35 x 4 = 35

z 2 = 54 z 2 = 54

−20 = q −5 −20 = q −5

c −3 = −12 c −3 = −12

y 9 = −16 y 9 = −16

q 6 = −38 q 6 = −38

m −12 = 45 m −12 = 45

−24 = p −20 −24 = p −20

− y = 6 − y = 6

− u = 15 − u = 15

− v = −72 − v = −72

− x = −39 − x = −39

2 3 y = 48 2 3 y = 48

3 5 r = 75 3 5 r = 75

− 5 8 w = 40 − 5 8 w = 40

24 = − 3 4 x 24 = − 3 4 x

− 2 5 = 1 10 a − 2 5 = 1 10 a

− 1 3 q = − 5 6 − 1 3 q = − 5 6

− 7 10 x = − 14 3 − 7 10 x = − 14 3

3 8 y = − 1 4 3 8 y = − 1 4

7 12 = − 3 4 p 7 12 = − 3 4 p

11 18 = − 5 6 q 11 18 = − 5 6 q

− 5 18 = − 10 9 u − 5 18 = − 10 9 u

− 7 20 = − 7 4 v − 7 20 = − 7 4 v

In the following exercises, solve each equation requiring simplification.

100 − 16 = 4 p − 10 p − p 100 − 16 = 4 p − 10 p − p

−18 − 7 = 5 t − 9 t − 6 t −18 − 7 = 5 t − 9 t − 6 t

7 8 n − 3 4 n = 9 + 2 7 8 n − 3 4 n = 9 + 2

5 12 q + 1 2 q = 25 − 3 5 12 q + 1 2 q = 25 − 3

0.25 d + 0.10 d = 6 − 0.75 0.25 d + 0.10 d = 6 − 0.75

0.05 p − 0.01 p = 2 + 0.24 0.05 p − 0.01 p = 2 + 0.24

−10 ( q − 4 ) − 57 = 93 −10 ( q − 4 ) − 57 = 93

−12 ( d − 5 ) − 29 = 43 −12 ( d − 5 ) − 29 = 43

−10 ( x + 4 ) − 19 = 85 −10 ( x + 4 ) − 19 = 85

−15 ( z + 9 ) − 11 = 75 −15 ( z + 9 ) − 11 = 75

Mixed Practice

In the following exercises, solve each equation.

9 10 x = 90 9 10 x = 90

5 12 y = 60 5 12 y = 60

y + 46 = 55 y + 46 = 55

x + 33 = 41 x + 33 = 41

w −2 = 99 w −2 = 99

s −3 = −60 s −3 = −60

27 = 6 a 27 = 6 a

− a = 7 − a = 7

− x = 2 − x = 2

z − 16 = −59 z − 16 = −59

m − 41 = −14 m − 41 = −14

0.04 r = 52.60 0.04 r = 52.60

63.90 = 0.03 p 63.90 = 0.03 p

−15 x = −120 −15 x = −120

84 = −12 z 84 = −12 z

19.36 = x − 0.2 x 19.36 = x − 0.2 x

c − 0.3 c = 35.70 c − 0.3 c = 35.70

− y = −9 − y = −9

− x = −8 − x = −8

In the following exercises, translate to an equation and then solve.

187 is the product of −17 −17 and m .

133 is the product of −19 −19 and n .

−184 −184 is the product of 23 and p .

−152 −152 is the product of 8 and q .

u divided by 7 is equal to −49 −49 .

r divided by 12 is equal to −48 −48 .

h divided by −13 −13 is equal to −65 −65 .

j divided by −20 −20 is equal to −80 −80 .

The quotient c c and −19 −19 is 38.

The quotient of b b and −6 −6 is 18.

The quotient of h h and 26 is −52 −52 .

The quotient k k and 22 is −66 −66 .

Five-sixths of y is 15.

Three-tenths of x is 15.

Four-thirds of w is 36.

Five-halves of v is 50.

The sum of nine-tenths and g is two-thirds.

The sum of two-fifths and f is one-half.

The difference of p and one-sixth is two-thirds.

The difference of q and one-eighth is three-fourths.

In the following exercises, translate into an equation and solve.

Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?

Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?

Tickets Mollie paid \$36.25 for 5 movie tickets. What was the price of each ticket?

Shopping Serena paid \$12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?

Sewing Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?

MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?

Height Aiden is 27 inches tall. He is 3 8 3 8 as tall as his father. How tall is his father?

Real estate Bea earned \$11,700 commission for selling a house, calculated as 6 100 6 100 of the selling price. What was the selling price of the house?

## Everyday Math

Commission Every week Perry gets paid \$150 plus 12% of his total sales amount over \$1,250. Solve the equation 840 = 150 + 0.12 ( a − 1250 ) 840 = 150 + 0.12 ( a − 1250 ) for a , to find the total amount Perry must sell in order to be paid \$840 one week.

Stamps Travis bought \$9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49 s + 0.21 ​ ( s − 5 ) ​ ​ = 9.45 0.49 s + 0.21 ​ ( s − 5 ) ​ ​ = 9.45 for s , to find the number of 49-cent stamps Travis bought.

## Writing Exercises

Frida started to solve the equation −3 x = 36 −3 x = 36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.

Emiliano thinks x = 40 x = 40 is the solution to the equation 1 2 x = 80 1 2 x = 80 . Explain why he is wrong.

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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• Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis
• Publisher/website: OpenStax
• Book title: Elementary Algebra 2e
• Publication date: Apr 22, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/elementary-algebra-2e/pages/1-introduction
• Section URL: https://openstax.org/books/elementary-algebra-2e/pages/2-2-solve-equations-using-the-division-and-multiplication-properties-of-equality

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