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Division Property of Equality – Definition With Examples

Jessica Kaminski

reviewed by Jo-ann Caballes

Updated on February 26, 2026

In math, there are 8 properties of equality that state how an equation’s equality can be maintained through arithmetic operations (addition, multiplication, subtraction, and division) or logic. 

Here, we discuss the division property of equality, solve examples of division property of equality, share practice problems, and recommend worksheets.

What Is Division Property of Equality?

The division property of equality is the rule that states that when we divide two sides of an equation by a number greater or less than 0, the result of both sides will be the same.

Division property of equality definition

The division property definition is the mathematical principle that states that when we divide two sides of an equation by a number that is unequal to 0, both sides will be equal to each other 

Examples of division property of equality

Let’s look at a division property of equality example:  Imagine two freshly baked pies. When we cut both of them in halves (½), we are left with the same amount of pies: 

Therefore, because we divided both sides by the same number (2), the result is the same.

The Inverse of Division Property: Multiplication Property of Equality

The inverse of division is multiplication, therefore, the inverse of the division property is the multiplication property.

The multiplication property states that when we multiply both sides of an equation with a number not equal to zero, the resulting equation will be equal on both sides.

This means if a is equal to b, then by multiplying both sides by c (a number not equal to 0), the equation remains the same.

Formula of Division Property of Equality

The division property of equality formula is:

If a = b and c ≠ 0, then a/c = b/c.

Division Property of Equality Calculator

Solving division property is a straightforward process. However, it can be calculated faster with the division property of equality calculator. There are online hubs that provide this resource to make calculations faster.

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Division Property of Equality in Geometry

The division property of equality also applies to geometry in the same way it applies to natural numbers. Whether we are calculating angles, segments, areas, or volumes of shapes, and we are faced with an equation of two sides, we can maintain equality by dividing both sides by a number unequal to 0.

Division Property of Equality with Fractions

For fractions too, the division property of equality also applies. However, we divide both sides of the equation by a fraction. The numbers may be different but the ratio is  the same.

What Are the 8 Properties of Equality?

The 8 properties of equality are mathematical rules that help us maintain equality in calculations. They are:

1. Reflexive property
2. Symmetric property
3. Transitive property
4. Addition property
5. Subtraction property
6. Substitution property 
7. Division property
8. Multiplication property.

Here are the corresponding formulas that explain what each of these properties of equality states:

How Is the Division Property of Equality Used?

The division property of equality may be used to isolate a variable m attached to a coefficient 

For example, if we want to find the value of X when 5X = 10, we can use this property by dividing both sides by 5, meaning X = 2.

When both sides of the equation are divided by a common non-zero number (5), the sides become equal.

Here’s a step-by-step process: 

Solved Examples on Division Property of Equality

Solved math problem 1

In the equation, 24x = 96, how can we solve it using the division property of equality? 

Solution

24x/ 24 = 96/ 24

Solved math problem 2

Find z in the equation 27 = 3z

Solution

27/3 = 3z/3

Solved math problem 3

Which equation requires the division property of equality to be solved?

• y/4 = 10
• x + 5 = 40
• 5z = 25

Solution

The third equation is the most appropriate to solve with the division property:

5z/5 = 25/5

Practice Problems on Division Property of Equality

Division property of equality: worksheets

Learn more about the division property of equality with our free worksheets:

• Solving Equations With Variables On Both Sides Worksheets
• Algebra Equations Worksheets
• Multiplication and Division Worksheets Grade 3

Frequently Asked Questions on Division Property of Equality

What is the Division Property of Equality?

The division property of equality is a principle that states that if an equation is divided by a number, not equal to zero, the equation is equal

How does the Division Property of Equality work?

The division property states that if a = b and c is not equal to 0, then if we divide a and b by c, a and b are equal.

Can the Division Property of Equality be used with fractions?

Yes. The division property of equality can be used with fractions, decimals, and we can use the division property of equality in geometry . However, for fractions, both sides are instead divided by a fraction.

How is the Division Property of Equality used in real-life situations?

We may use the division property of equality for financial planning, allocating items, calculating ratios, and more.

Jessica Kaminski

91 articles

Jessica is a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.