Subtraction Property of Equality
The subtraction property of equality is the property in algebra that states that if a value is subtracted from two equal quantities, then the differences are also equal. In other words, we can say that if two quantities a and b are equal, and if we subtract c from both a and b, then the difference of a and c is equal to the difference of b and c. Mathematically, we can write the subtraction property of equality as, if a = b, then a  c = b  c. We have various properties of equality such as:
 Addition Property of Equality
 Subtraction Property of Equality
 Division Property of Equality
 Multiplication Property of Equality
 Reflexive Property of Equality
 Transitive Property of Equality
 Substitution Property of Equality
 Symmetric Property of Equality
In this article, we will mainly focus on the subtraction property of equality and its formula. We will verify the definition of the subtraction property of equality and its application including fractions. We will solve various examples based on the property for a better understanding of the concept.
What is Subtraction Property of Equality?
According to the subtraction property of equality, if we subtract a number from one side of the equality, then we must subtract the same number from the other side of the equality to maintain equality. This property is similar to the addition property of equality. Equality has various properties including the addition property, division property, reflexive property, multiplication property, etc. The subtraction property of equality is to balance an equation by using the same mathematical operation of subtraction on both sides of the equality.
To understand this, let us consider an example. We have two bags with 10 balls in each bag. Now, if we take out 3 balls from bag 1, then to keep the number of balls the same in bag 1 and bag 2, we must take out three balls from bag 2. So, we have seven balls left in each bag after taking three balls out.
Subtraction Property of Equality Definition
The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. In simple words, we can say that when a number is subtracted from one side of an equation, the same number must be subtracted from the other side of the equality.
Subtraction Property of Equality Formula
To write the formula of the subtraction property of equality, consider an equation X = Y, then if a real number 'b' is subtracted from LHS of X = Y, then we must subtract b from Y, that X  b = Y  b. So, the formula is given by,
X = Y
⇔ X  b = Y  b
So, we can say that according to the subtraction property of equality, equality holds if the same number is subtracted from both sides of the equation.
Verification of Subtraction Property of Equality
Now that we know the subtraction property of equality, let us know verify it by taking a few examples. Arithmetically, we know that 12 + 8 = 20. Now, if we subtract 5 from both sides of the equation, we have
12 + 8  5 = 20  5
⇒ 12 + 3 = 15
This implies when the same number is subtracted from both sides of an equation, the equality still holds.
Let us take another example to understand the application of the property. Consider an algebraic equation x + 4 = 40. Now, to find the value of x, we need to subtract 4 from both sides of the equation. So, we have
x + 4 = 40
⇒ x + 4  4 = 40  4
⇒ x = 36
So, solving the algebraic equations is one of the important applications of the subtraction property of equality.
Subtraction Property of Equality Including Fractions
Since we know the concept of subtraction property of equality, now we will apply this property in the equations including fractions. Consider an equation a/b = x/y, then subtracting the same fraction c/d from both sides of the equation keeps the equation balanced, that is, we have
a/b = x/y
⇒ a/b  c/d = x/y  c/d
The subtraction property of equality works the same way for fractions and in geometry as well.
Important Notes on Subtraction Property of Equality
 The subtraction property of equality states that if the same number is subtracted from both sides of an equation, then the equality still holds.
 Subtraction property of equality formula is given by, a = b ⇔ a  c = b  c
 This property is also applicable to equations including fractions.
 An important application of the subtraction property is solving algebraic equations.
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Subtraction Property of Equality Examples

Example 1: Find the value of x for the algebraic equation x + 5 = 7 using the subtraction property of equality.
Solution: To find the value of x, subtract 5 from both sides of the equation.
x + 5 = 7
⇒ x + 5  5 = 7  5
⇒ x = 2
Answer: x = 2

Example 2: If x  10 = y  10, then choose the correct option:
i) x = y
ii) x = y  10
iii) y = x  10
Solution: Using the subtraction property of equality, we know that a = b if and only if a  c = b  c. So, in equation x  10 = y  10, 10 is being subtracted from both sides of the equation. So, we have
x  10 = y  10
⇒ x = y
Answer: Option (i) x = y is correct.

Example 3: Find the value of x, 2/3  x = 3/4
Solution: We will solve the equation using the addition and subtraction property of equality.
We have 2/3  x = 3/4. Adding x on both sides of the equation, we have
2/3  x + x = 3/4 + x
⇒ 2/3 = x + 3/4
Now, subtracting 3/4 from both sides of the equation, we have
2/3  3/4 = x + 3/4  3/4
⇒ x = 1/12
Answer: x = 1/12
FAQs on Subtraction Property of Equality
What is the Subtraction Property of Equality?
According to the subtraction property of equality, we can say that if two quantities a and b are equal, and if we subtract c from both a and b, then the difference of a and c is equal to the difference of b and c.
What is the Formula of Subtraction Property of Equality?
The formula of subtraction property of equality is given by,
X = Y
⇔ X  b = Y  b
What is the Definition of Subtraction Property of Equality?
The subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal.
What Does Subtraction Property of Inequality Mean?
According to the Subtraction Property of Inequality, if the same number is subtracted from both sides of the inequality, then the sense of the inequality remains the same.
How to Solve an Equation Using the Subtraction Property of Equality?
We can solve an algebraic equation using the subtraction property of equality by subtracting the same number from both sides of the equation and get the required result.
What is the Difference Between Addition and Subtraction Property of Equality?
The addition property of equality is defined as "When the same amount is added to both sides of an equation, the equation still holds true". On the other hand, the subtraction property of equality states that when the same number is subtracted from both sides of an equality, then the two sides of the equation still remain equal. The working of the two properties is the same.
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