111 LearnersLast updated on July 15th, 2025
Addition Property of Equality
The addition property of equality is a fundamental property in mathematics. It states that adding the same number to both sides of an equation maintains the equality. In this article, we will discuss the addition property of equality, its formula, and some examples.
What is Equality?
In mathematics, equality is the fundamental concept where two mathematical expressions represent the same quantity. It is represented by the symbol =. For example, in the equation 3x + 2x = 5x; both sides represent the same quantity: 5x.
What is Addition Property of Equality?
The addition property of equality states that if the same number is added to both sides of an equation, the equality remains true. In other words, adding the same value to each side of the equation doesn’t affect the equality.
For example, x = 4
If we add 3 to both sides, the equation becomes:
x + 3 = 4 + 3
x + 3 = 7
What is the Formula for Addition Property of Equality?
For an equation x = y, the addition property of equality states that if the same number n is added to both sides, the equality remains true.
Mathematically it can be represented as: if x = y, then x + n = y + n
Here x and y can be numbers or algebraic expressions, n is a real number. The addition property of equality is applicable to both arithmetic and algebraic equations.
For example, 5 + 7 = 12, if we add 2 to both sides
Verifying x + n = y + n
Here, x = 5 + 7
y = 12
n = 2
5 + 7 + 2 = 12 + 2
Verifying LHS: 5 + 7 + 2 = 14
RHS: 12 + 2 = 14
So, LHS = RHS
For example, x + 2 = 8, adding 5 to both sides
x + 2 = 8
Adding 5 on both sides
x + 2 + 5 = 8 + 5
x + 7 = 13
What is Addition Property of Equality with Fractions?
The addition property of equality is also applicable to fractions. In other words, adding the same fraction to both sides of the equation keeps the equation balanced. It can be represented as:
a/b + x/y = c/d +x/y
For example, add 1/3 to both sides of: 3x/4 = 5/2:
That is 3x/4 = 5/2
3x/4 + 1/3 = 5/2 + 1/3
RHS: 5/2 + 1/3 = (15 + 2)/6 = 17/6
LHS: 3x/4 + 1/3
3x/4 + 1/3 = 17/6
3x/4 = 17/6 - 1/3
3x/4 = (51 - 6)/18
3x/4 = 45/18
3x = 45/18 × 4
3x = 10
x = 10/3
Real-world Applications of Addition Property of Equality
We use the addition property of equality in our everyday life for budgeting, cooking, distance calculation. In this section, we will learn a few applications of the addition property of equality.
- In cooking, to adjust the recipes, we use the addition property of equality to maintain the proportions. For example, if we add 2 cups of flour and 1 cup of sugar for a cake then for 2 cakes we add 2 + 2 = 4 cups of flour and 1 + 1 = 2 cups of sugar.
- To solve algebraic equations, we use the addition property of equality. For example when solving x -3 = 7, to solve we add 3 on both sides, that is x - 3 + 3 = 7 + 3 → x = 10. By adding the same value to both sides of the equation to balance and find the unknown value.
- In inventory management, we use the addition property of equality to track inventory. When new stocks arrive, we add the same quantity to both the manual and digital records.
Common Mistakes and How to Avoid Them in Addition Property of Equality
Students often make mistakes when using the addition property of equality. Here are some common mistakes and the ways to avoid them.
Mistake 1
Adding different values to each side
Students add different numbers to both sides of the equation, for example, x - 5 = 10 → x - 5 + 5 = 10 + 2 → x = 12, which is wrong. So, always verify whether you added the same number on both sides or not.
For example, x - 5 = 10 → x - 5 + 5 = 10 + 5 → x = 15.
Mistake 2
Forgetting to add the value to both sides
Forgetting to add the value on both sides of the equation,
For example, adding 2 to x + 4 = 10 → x + 4 + 2 = 10 → x + 6 = 10. Here, the error is that they only add it on one side. So always remember to add the same number on both sides of the equation. The correct approach is x + 4 = 10 → x + 4 + 2 = 10 + 2 → x + 6 = 12
Mistake 3
Subtracting instead of adding
Confusing the addition property with subtraction leads to incorrect operations. So, always remember that in addition property of equality, we will be adding the number on both sides of the equation.
For e.g., x−5=10→x−5−5=10, which is incorrect.
Mistake 4
Arithmetic errors
Students make arithmetic errors when adding negative numbers, which results in an error.
For example, x - 5 = -2 adding 5 on both sides x = -2 + 5 = -7 instead of 3. So be careful when adding negative numbers.
Mistake 5
Not simplifying the equation after adding
Students sometimes add the number but forget to simplify the equations.
For example, in the equation 2x - 5 = 3, when adding 5 to both sides of the equation, that is 2x - 5 + 5 = 3 + 5 it can be simplified to 2x = 8
Solved Examples of Addition Property of Equality
Problem 1
Find the value of x in x - 7 = 12 - 5
x = 14
Explanation
Given, x - 7 = 12 - 5
Simplifying the RHS: 12 - 5 = 7
So, x - 7 = 7
Adding 7 to both sides: x - 7 + 7 = 7 + 7
x = 14
Problem 2
Solve the equation using the addition property of equality: 3x + 9 = x + 15.
x = 3
Explanation
Finding the value of x in 3x + 9 = x + 15 using addition property of equality
Adding -x to both sides:
3x + 9 -x = x + 15 - x
2x +9 = 15
Adding -9 on both sides:
2x + 9 -9 = 15 -9
2x = 6
x = 6/2
x = 3
Problem 3
If a = b and b = 3c, use the addition property of equality to show that a + c = 3c + c
If a = b and b = 3c, then a + c = 3c + c
Explanation
To verify if a = b and b = 3c, then a + c = 3c + c
In the equation a = b adding c on both sides::
a + c = b + c
Adding c on both sides of b = 3c
b + c = 3c + c
As b + c = a + c
Therefore, a + c = b + c
Problem 4
A number increased by 4 gives 10, what is the number?
x = 6
Explanation
Let’s consider the number as x
So, x + 4 = 10
Adding -4 on both sides:
X + 4 - 4 = 10 - 4
x = 6
Problem 5
Find the value of x in x - 4 = 10
Here, x = 14
Explanation
Adding 4 on both sides to find the value of x in x - 4 = 10
x - 4 + 4 = 10 + 4
x = 14
FAQs on Addition Property of Equality
1.What is the addition property of equality?
2.What is the formula for the addition property of equality?
3.Is the addition property of equality applicable to fractions?
4.What is an addition property of inequality?
5.Find the value of x in x/3 + 5 = 10
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Addition Property of Equality?
8.How do technology and digital tools in Philippines support learning Algebra and Addition Property of Equality?
9.Does learning Algebra support future career opportunities for students in Philippines?
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
