Addition Property of Equality

The addition property of equality states that when the same quantity is added to both sides of an equation, the equation does not change. If a number x is added to both sides of an equation A = B, then the equation still holds true. It can be expressed mathematically as, A + x = B + x. Let us learn more about the addition property of equality in this article along with its formula. We shall also discuss the addition property of equality for fractions.

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". It is a very important and one of the common properties of equality in mathematics. The other properties are the subtraction property, multiplication property, and division property of equality.

The addition property of equality is used while solving equations. For example, to solve x - 3 = 5, we have to add 3 to both sides so that only the variable (x) will be left on the left side. This implies, x - 3 + 3 = 5 + 3, which can be simplified as x = 8. Let us learn the addition property of equality formula in the next section.

The formula for the addition property of equality is given below:

If the given equation is A = B, and the same quantity n is added to both sides of this equation, we get A + n = B + n, which is true and satisfies the equation. We can use this property of equality in arithmetic equations as well as in algebraic equations. In the case of an arithmetic equation, for example, 2 + 3 = 5, if we add a number to both sides, say 7, the equation will still be true. Let's verify it.

2 + 3 + 7 = 5 + 7

L.H.S = 2 + 3 + 7 = 12

R.H.S = 5 + 7 = 12

Therefore, L.H.S = R.H.S.

Let us take one more example of an algebraic equation, x - 4 = 12. It can be solved using the addition property of equality, as shown below.

x - 4 = 12

By adding 4 to both sides of the equation, we get, x - 4 + 4 = 12 + 4.

⇒ x = 16

Therefore, the value of x is 16. It is the application of the addition property of equality in math.

The addition property of equality works with fractions as well. The same integer or fraction can be added to an equation containing fractions. For example, if 2x/3 + 5/6 = y + 5/6, this implies that 2x/3 = y. The general form of addition property of equality with fractions is written below:

A/B + x/y = C/D + x/y

Here, A/B = C/D is the given equation and x/y is the fraction added to both sides without changing the equality.

Important Notes on Addition Property of Equality

• The addition property of equality states that when the same number is added on both sides of an equation, the equality still holds.
• The formula for the addition property of equality is given by, A = B ⇒ A + n = B + n.
• The property holds for numbers with fractions.

► Related Articles

• Associative Property of Addition
• Transitive Property
• Solving Linear Equations

What does Addition Property of Equality Mean?

The addition property of equality is defined as a condition where the same number added to both sides of an equation does not change the equality. If a is any real number and P = Q is the equation, we can have P + a = Q + a.

What is an Example of Addition Property of Equality?

The example of addition property of equality is given as 2x + 7 = y + 7. Here, 7 is added to both sides, so if we remove it from both sides, the equation will still be true. This implies, 2x = y.

What does the Addition Property of Equality State?

The addition property of equality states that if the same amount is added to both sides of an equation, the equation still holds true. It is mathematically expressed as, X + n = Y + n, where n is any real number and X = Y is the given equation.

What is the Addition Property of Equality and Inequality?

The addition property holds true in the case of equations as well as with inequalities. With equations, the same quantity added to both sides does not change the equality between both sides. While, in the case of inequalities as well, the same quantity can be added to both sides without changing the relationship. If x > y, this implies x + a > y + a, ∀ a ∈ R.

How to Solve an Equation Using the Addition Property of Equality?

If an equation is given, say, m - 3 = 14, then we can apply the addition property of equality to solve for the variable 'm'. Add 3 to both sides so that only the variable will remain on the left side. By this, we get,

m - 3 + 3 = 14 + 3

m = 17

Therefore, the value of m is 17. This is how we solve an equation using the addition property of equality.

How to Use Addition Property of Equality?

The addition property of equality in math is used to solve equations in math. The same number can be added to both sides of a given equation without changing the result.

What is the Addition Property of Equality Formula?

If the given equation is A = B, and the same quantity n is added to both sides of this equation, we get A + n = B + n. Hence, the formula for the addition property of equality is A = B ⇒ A + n = B + n.