Division Property of Equality
2026-02-28 17:16 Diff
https://brightchamps.com/en-us/math/algebra/division-property-of-equality

168 Learners

Last updated on October 29, 2025

The division property of equality states that if two numbers or expressions are equal, dividing both sides of the equation by the same non-zero number maintains their equality. This article discusses the division property of equality in detail.

What is Equality?

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

When two things have the same value, we call them equal. In math, we use the ‘=’ sign to show that both sides are equal.

For example, 2 + 3 = 5. Here, the left-hand side (LHS) is equal to the right-hand side (RHS). 

How to Divide an Equation Equally?

According to the division property of equality, when both sides of an equation are divided by the same non-zero number, the equality stays true. In other words, if a = b, and \(\quad c \neq 0\), then \(\frac{a}{c} = \frac{b}{c}\).

Example:

Start with the equation 10 = 10

Now divide both sides by 5

\(\frac{10}{5} = \frac{10}{5}\)

2 = 2

LHS = RHS. So both sides are equal.

Properties of Equality

The properties of equality are basic rules in math that explain how we can work with equations while keeping both sides equal. They help us perform basic operations like addition, subtraction, multiplication, and division without altering the meaning of the equation. Some of the properties of equality are given below:

  • Reflexive Property of Equality
  • Symmetric Property of Equality
  • Transitive Property of Equality
  • Substitution Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality
  • Multiplication Property of Equality
  • Division of Property of Equality
     

Explore Our Programs

The Inverse of Division Property: Multiplication Property of Equality

The multiplication property of equality states that if two values are equal, we can multiply both sides of the equation by the same number, and they’ll still be equal. In other words, if a = b, and c is any real number, then: a × c = b × c.  

Example:

Consider an equation 2 = 2

Now multiply both sides by 4:

2 × 4 = 2 × 4

8 = 8.

How is the Division Property of Equality Used?

We use the division property of equality in various mathematical fields. It is often used in algebra when solving for the unknowns. This property also plays a crucial role while learning how logical steps keep equations balanced.

For example, let’s say the given equation is 4x = 20. To isolate and solve for x, we have to divide both sides by 4:

\(\frac{4x}{4} = \frac{20}{4} \)

x = 5.

Tips and Tricks of Division Property of Equality

The Division Property of Equality means that if we divide both sides of an equation by the same number, it stays equal. This rule helps children learn how to solve equations step by step. With your help, they can understand it better through daily examples, like sharing things equally. The tips below will guide you in making this concept clear and fun for your child.

  • If you divide one side of an equation, make sure to divide the other side by the same number to keep it balanced.
  • Dividing by zero is not allowed, it makes the equation meaningless.
  • If a variable is being multiplied, use division to find its value.
  • Once you find the value of x, plug it back into the original equation to see if both sides match.
  • Draw two sides of a balance with weights or stickers to show that equality means both sides are the same even after dividing.

Common Mistakes and How to Avoid Them in Division Property of Equality

Students make mistakes while learning and working with the division of property of equality. Below are some common mistakes and their solutions.

Real Life Applications of Division Property of Equality

Whenever we want to split or share something equally, or when we need to find the value of one part of a whole, we use the division property of equality. We often use this in our daily lives without even realizing it, especially when dealing with sharing, measuring, or calculating costs. Given below are some real-life applications of the division property of equality

Architecture: Architects use the Division Property of Equality to scale drawings, divide spaces equally, and maintain balance and symmetry in designs.

Robotics: In robotics, programmers and engineers divide values equally to balance motion and power. In an example, If a motor’s total torque must be shared equally among 4 robot arms, they divide the torque by 4 to maintain balance and equal performance.

Animation and Graphics: Animators and graphic designers often divide frames, movements, or pixels equally to keep scenes smooth and proportionate.

Physics: In physics, almost every formula involves balancing both sides of an equation.
Example: From \(v = \frac{d}{t}\), if d = vt, dividing both sides by t helps find v.

Engineering: Engineers often use the Division Property of Equality to solve equations when calculating force, pressure, speed, or resistance.

Download Worksheets

Problem 1

Solve 5x = 25 using the division property of equality

Okay, lets begin

 x = 5
 

Explanation

 We can divide both sides of the equation by 5.

\(\frac{5x}{5} = \frac{25}{5}\)

Therefore, x = 5

Well explained 👍

Problem 2

If 6 pencils cost $42, how much does one pencil cost?

Okay, lets begin

$7 per pencil
 

Explanation

 To find the price of one pencil, we have to divide the total cost by the number of pencils.

\(\frac{42}{6} = 7\)

So, each pencil costs $7.

Well explained 👍

Problem 3

Solve the equation 12y = 60 using the division property of equality.

Okay, lets begin

 y = 5
 

Explanation

To isolate y, we should divide both sides of the equation by 12:

\(\frac{12y}{12} = \frac{60}{12}\)

y = 5.

So the value of y is 5.

Well explained 👍

Problem 4

A car travels 240 km in 4 hours. What is the speed per hour?

Okay, lets begin

 60 km/h
 

Explanation

To find the speed, divide the total distance by time.

\(\frac{240}{4} = 60\)

So, the speed of the car is 60 km/h

Well explained 👍

Problem 5

Solve -9x = 27

Okay, lets begin

 x = -3
 

Explanation

Divide both sides by -9

\(\frac{-9x}{-9} = \frac{27}{-9}\)

x = -3

Well explained 👍

FAQs on Division Property of Equality

1.What does the division property of equality mean?

It means that if two values are equal, then we can divide both sides by the same non-zero number, and the equality will still hold true.
 

2.Why isn’t division by zero allowed?

Dividing by 0 is not allowed because we cannot multiply any number by 0 to get a result other than 0. Therefore, division is not possible and the result will be undefined. 
 

3.Can I divide both sides by a negative number?

Yes, you can divide as long as the number is not 0. 

4.Does dividing both sides of an equation change the answer?

No, dividing both sides of an equation by the same non-zero number does not change the answer.
 

5.Why is division the opposite of multiplication?

Division is the opposite of multiplication because it undoes what multiplication does.
 

6.How can parents explain the Division Property of Equality to their child in simple terms?

You can say, “If you and your friend both have 10 chocolates and each of you shares them equally between two people, you’ll still have the same number of chocolates. That’s just like dividing both sides of an equation.”

7.How can parents connect this property to solving bigger algebra problems later on?

Explain that this property is a stepping stone for solving complex equations in higher grades. Mastering it now makes future topics like ratios, proportions, and algebraic equations much easier.

8.What can parents say if their child asks, “Why do we have to divide both sides?”

Tell them, “In math, both sides of the equation are like two sides of a scale. If you divide one side, you must divide the other to keep the scale even.”

9.How can parents help if their child gets confused between multiplying and dividing while solving equations?

Parents can remind their child that division is the opposite of multiplication. If an equation involves multiplication (like 5x = 20), dividing both sides by 5 helps find the value of x.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.