Subtraction Property of Equality: Definition, Formula & Examples
Nivedita Dar27 Feb, 2026
Think of a seesaw that is perfectly balanced with 10 kg on each side. The seesaw will tip if you take 2 kg from the left side. To get it back to ideal equilibrium, you also need to take away exactly 2 kg from the right side. This "balancing act" is what gives the property of equality its "subtraction" aspect. This is one of the best tools for students in algebra since it helps you "isolate" a variable and find a value you don't know.
What is Subtraction Property Equality?
The subtraction property of equality definition is a fundamental algebraic rule: when an equal amount is removed from two equal quantities, the resulting differences are still equal.
In other words, the "equals" symbol (=) stays valid as long as you do the identical subtraction on both sides of an equation. It is the opposite of the addition attribute.
Subtraction Property Equality Formula
The subtraction property of equality formula employs letters to indicate that the rule works for all real numbers a, b, and c: If \ a = b, \ then \ a - c = b - c
Where:
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a and b are the original equal sides of the equation.
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c is the value being subtracted from both sides.
Subtraction Property Equality Definition Examples
Let's see how we employ this characteristic in numerous situations, from basic maths to algebra.
Example 1: Basic Arithmetic
Suppose we have the true statement: 10 = 10.
If we subtract 3 from both sides:
10 - 3 = 10 - 3
7 = 7
The equation is still true!
Example 2: Solving for x (Algebra)
This property is most commonly used to "undo" addition.
Problem: Solve for x in x + 8 = 20.
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Step 1: To get x alone, we need to remove the +8.
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Step 2: Apply the subtraction property by subtracting 8 from both sides.
x + 8 - 8 = 20 - 8 -
Step 3: Simplify.
x = 12
Example 3: Real-World Balance
Sam and Ali are pals, and they each have 50 marbles. If they each give their little brother 10 marbles, do they still have the same amount?
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Sam = Ali
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Sam - 10 = Ali - 10
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Result: Yes, they both now have 40. This is the subtraction property of equality for students in action!
Read More - Adding Exponent: Definition, Rules, Steps, and Examples
Verification of Subtraction Property Equality
The subtraction property of equality becomes easier to trust when you verify it with simple statements and algebra equations. The rule says that if two quantities are equal, subtracting the same value from both sides keeps them equal.
Arithmetic Verification
Start with a true statement:
(14 = 14)
Subtract 5 from both sides:
(14 - 5 = 14 - 5)
(9 = 9)
The statement remains true. This verifies that the subtraction property of equality works in basic arithmetic.
Algebra Verification
Take an equation:
(x + 4 = 40)
Subtract 4 from both sides:
(x + 4 - 4 = 40 - 4)
(x = 36)
Check the answer:
(36 + 4 = 40)
(40 = 40)
This confirms that subtracting the same number from both sides helps solve equations correctly while keeping the equation balanced.
Read More -Counting Numbers: Definition, Counting Chart, Examples
Subtraction Property Equality Including Fractions
The subtraction property of equality also works with fractions. The rule does not change. You still subtract the same quantity from both sides of the equation.
Fraction Example 1: Simple Verification
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Start with: 7/8 = 7/8
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Subtract 1/8 from both sides: 7/8 - 1/8 = 7/8 - 1/8
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Result: 6/8 = 6/8
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After simplification: 3/4 = 3/4
Fraction Example 2: Solving an Equation
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Solve: x + 3/5 = 11/5
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Subtract 3/5 from both sides: x + 3/5 - 3/5 = 11/5 - 3/5
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Simplify: x = 8/5
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Check: 8/5 + 3/5 = 11/5
This shows that the subtraction property of equality is just as useful in fraction equations as it is in whole-number equations.
Quick Tip
If you are adding a number to the variable the you need to use subtraction, but if you are subtracting a number or taking away a number from the variable, then you need to add it back.
This comparison helps students rapidly pick the right property when they are working on math issues.
Difference Between Addition and Subtraction Property of Equality
Students often mix up these two properties because both keep equations balanced. The difference is in the operation used to isolate the variable.
|
Property |
What You Do |
When It Is Used |
Example |
|
Addition Property of Equality |
Add the same value to both sides |
To remove subtraction from a variable |
x - 6 = 10 ⇒ x - 6 + 6 = 10 + 6 |
|
Subtraction Property of Equality |
Subtract the same value from both sides |
To remove addition from a variable |
x + 6 = 10 ⇒ x + 6 - 6 = 10 - 6 |
|
Multiplication Property of Equality |
Multiply both sides by the same value |
To remove division from a variable |
x/5 = 4 → x = 20 |
|
Division Property of Equality |
Divide both sides by the same non-zero value |
To remove multiplication from a variable |
3x = 12 → x = 4 |
Summary Table Of Subtraction Property of Equality
Let's quickly review the main points of the equality part of subtraction.
|
Feature |
Description |
|
Main Goal |
To keep an equation balanced while removing values. |
|
Inverse Relationship |
It is used to "cancel out" addition. |
|
Core Rule |
What you do to one side, you must do to the other. |
|
Application |
Solving linear equations and geometric proofs. |
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