Subtraction of Equality
2026-02-28 10:07 Diff
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Last updated on September 8, 2025

The mathematical operation of finding the difference between two equal quantities is known as the subtraction of equality. It helps simplify equations and solve problems that involve constants, variables, and arithmetic operations.

What is Subtraction of Equality?

Subtracting equality involves finding the difference between equal quantities by introducing the concept of maintaining balance. It requires ensuring that both sides of an equation remain equal after the subtraction.

There are three components of an expression in subtraction of equality:

Coefficients: These are constant values like -1, 4, etc.

Variables: These are unknown quantities like x, y, z, etc.

Operators: For subtraction, the operator is the minus (-) symbol.

How to do Subtraction of Equality?

When subtracting to maintain equality, students should follow these rules:

Maintain balance: Subtract the same value from both sides of the equation to keep it balanced.

Combine like terms: Only like terms can be subtracted from one another, so group all like terms together on each side of the equation.

Simplifying result: After all like terms are combined, simplify the equation to see if further operations are necessary to solve for variables.

Methods to do Subtraction of Equality

The following methods are used for subtraction while maintaining equality:

Method 1: Horizontal Method

To apply the horizontal method for subtraction while maintaining equality, use these steps.

Step 1: Write the equation with the expressions on both sides.

Step 2: Subtract the same value from both sides.

Step 3: Combine like terms on each side. Let's apply these steps to an example:

Question: Subtract 3 from both sides of the equation x + 5 = 10.

Step 1: Write the equation x + 5 = 10.

Step 2: Subtract 3 from both sides: x + 5 - 3 = 10 - 3.

Step 3: Simplify: x + 2 = 7.

Method 2: Column Method

When subtracting while maintaining equality using the column method, align the expressions vertically. Make sure to subtract the same value from both sides and combine like terms.

For example, Subtract 4 from both sides of the equation 2x + 3 = 11.

Solution: Arrange the equation vertically: 2x + 3 ← Left side - 4 ← Subtracted value ---------- 2x - 1 = 7

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Properties of Subtraction of Equality

In algebra, subtraction while maintaining equality has several properties:

  1. Subtraction must maintain balance To keep an equation balanced, any operation performed on one side must be performed on the other.
  2. Subtraction is not commutative In maintaining equality, the order of operations matters.
  3. Subtraction is not associative Operations performed in different groupings can lead to different results.
  4. Subtraction of zero Subtracting zero from an equation does not change its balance: A - 0 = A

Tips and Tricks for Subtraction of Equality

These tips can help students efficiently subtract while maintaining equality:

Tip 1: Always perform the same operation on both sides to maintain balance.

Tip 2: Double-check the signs when subtracting to prevent errors.

Tip 3: Use the column method for visual clarity, especially with complex equations.

Ignoring balance

Students may forget to perform the same operation on both sides. Always ensure balance by checking both sides of the equation.

Problem 1

Subtract 2 from both sides: x + 7 - 2 = 12 - 2 x + 5 = 10

Okay, lets begin

Subtract 5 from both sides of the equation 3a + 4 = 15.

Well explained 👍

Problem 2

Subtract 5 from both sides: 3a + 4 - 5 = 15 - 5 3a - 1 = 10

Okay, lets begin

Subtract 7 from both sides of the equation 4x + 9 = 23.

Well explained 👍

Problem 3

Subtract 7 from both sides: 4x + 9 - 7 = 23 - 7 4x + 2 = 16

Okay, lets begin

Subtract 6 from both sides of the equation 5p + 8 = 20.

Well explained 👍

Problem 4

Subtract 6 from both sides: 5p + 8 - 6 = 20 - 6 5p + 2 = 14

Okay, lets begin

Subtract 9 from both sides of the equation 2x + 10 = 19.

Well explained 👍

No, subtracting different values from each side will disrupt the balance of the equation.

1.Is subtraction commutative when maintaining equality?

No, in equality maintenance, the order of operations is crucial, and subtraction is not commutative.

2.What is the purpose of maintaining balance in equations?

Maintaining balance ensures that both sides of an equation remain equal, which is essential for solving equations accurately.

3.What is the first step in subtracting while maintaining equality?

The first step is to decide the value to be subtracted and ensure it is subtracted from both sides of the equation.

4.What methods are used for subtraction while maintaining equality?

The horizontal method and the column method are used to subtract while maintaining equality.

Common Mistakes and How to Avoid Them in Subtraction of Equality

Subtracting while maintaining equality can be challenging, often leading to common mistakes. Awareness of these errors can help students avoid them.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.