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Subtraction Property of Equality

Last Updated : 01 Apr, 2024
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Subtraction Property of Equality is one of the many properties of equality. In this property, if two quantities a and b, are equal and we remove c from each of them, then the difference between a and c equals the difference between b and c.

Even though, we have various properties of equality such as; the additional property of Equality, subtraction Property of Equality, division Property of Equality and many more. In this article, we will focus on the subtraction property of equality and its various related terms.

What are the Properties of Equality?

The Properties of Equality in mathematics describe the relationship between two equal quantities and how equations remain balanced when operations are applied to both sides. The main properties of equality are:

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

In this article, we will discuss the subtraction property of equality in detail.

What is the Subtraction Property of Equality?

Subtraction Property of Equality is a principle in mathematics that asserts if you subtract the same amount from both sides of an equation, the equality is preserved. In simpler terms, this property tells us that if two quantities are equal, and we subtract the same value from both, they remain equal.

This property is foundational in algebra and is used frequently to solve equations, as it allows for the manipulation and simplification of equations to isolate variables.

Statement of Subtraction Property of Equality

Subtraction Property of Equality states that when both sides of an equation have the same number subtracted from them. Simply the number that is subtracted from one side has to be subtracted from the other side.

Subtraction Property of Equality Formula

In order to write down the formula for the subtraction property of equality, we first need to take an equation so that B = D. Then, we may subtract a real integer ‘C’ from the left half of the equation, which means that B – C = D – C. Hence, the formula is provided by;

B = D ⇔ B – C = D – C

Therefore, we may state that in the Subtraction property of equality, the same integer is subtracted from both sides of the equation.

Example: Simplify using subtraction property x + 5 = 10.

Solution:

So for calculating “x” we have to subtract 5 from both sides;

(x + 5) – 5 = 10 − 5

After simplifying it;

We get; x = 5

Therefore, After solving x + 5 = 10 by subtraction property of equality is x = 5.

Subtraction Property of Equality for Fractions

Subtraction Property of Equality for fractions states that if a fraction is subtracted from two equal fractions, then the differences are equal.

Suppose, we take an equation such that b/c = y/z, we can subtract the same fraction, a/d, from both sides of the equation to maintain balance in the equations. This can be represented as:

b/c = y/z ⇔ b/c – a/d = y/z – a/d

Verification of Subtraction Property of Equality

Let’s consider the following examples for verification of substraction property of equality.

Example 1: Consider an algebraic equation x + 4 = 40, and solve using subtraction property.

Solution:

Given: x + 4 = 40

In this equation, we will subtract an integer 4 from both sides.

(x + 4) – 4 = 40 – 4

⇒ x = 36

Thus, x = 36 is the solution for the given equation.

Example: Simply using subtraction property: −3y + 9 = 0.

Solution:

Given: −3y + 9 = 0

In this equation, we will subtract an integer 9 from both sides to solve for y.

−3y + 9 – 9 = 0 – 9

⇒ -3y = -9

using the division property of equality, we get

-3y/-3 = -9/-3

⇒ y = 3

Thus, y = 3 is the solution for given equation.

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Subtraction Property of Equality Examples

Example 1: Find the value of y in y + 6 = 14 using the subtraction property of equality.

Solution:

In this equation we will subtract an integer 6 from both sides.

y + 6 = 14

y + 6 – 6 = 14 – 6

y = 8

Therefore, the value of y is 8.

Example 2: Let x + 7 = 18 and y + 5 = 21. Find the value of x and y.

Solution:

Let’s see the 1st equation; x + 7 = 18

In this equation we will subtract an integer 7 from both sides.

x + 7 – 7 = 18 – 7

⇒ x = 11

Let’s see the 2nd equation; y + 5 = 21

In this equation we will subtract an integer 5 from both sides.

(y + 5) – 5 = 21 – 5

⇒ x = 16

Therefore, the value of x is 11 and y is 16.

Example 3: If y + 7 = 14, what is the value of y?

Solution:

In this equation we will subtract an integer 7 from both sides.

(y + 7) – 7 = 14 – 7

⇒ y = 7

Therefore, the value of y is 7.

Practice Questions: Subtraction Property of Equality

Q1: If x + 3 = 22, what is the value of x ?

Q2: Solve for c in the equation c + 10 = 30.

Q3: If m + 8 = 20, what is the value of m?

Q4: Solve the equation a/2 ​− 4 = 6 for a.

FAQs on Subtraction Property of Equality

Define Property of Equalities.

Properties of equalities are fundamental rules that govern equations and ensure that the relationship between the two sides of an equation remains balanced and equal.

Write an Example of a Subtraction Property?

An example of subtaction property is:

8 = x + 3

⇒ 8 – 3 = x + 3 – 3

⇒ 5 = x

What is Subtraction Property of Equality for Fractions?

Subtraction property of equality for fractions is the same as the normal subtraction property, but it is applied to fractions instead of integers.

Is there any Subtraction Property of Inequality?

Yes, there is a subtraction property of inequality, and it states “If a < b and c is any real number, then a c < b c.”



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