Subtraction Property of Equality

The Subtraction Property of Equality states that subtracting the same quantity from both sides of an equation preserves equality. Like other properties of equality such as addition, multiplication, and division, the subtraction property is used to maintain balance while solving equations.
Example: If x + 6 = 14, subtract 6 from both sides to get x = 8.
 

The subtraction property of equality shows that when you subtract the same number from both sides of an equation, it stays equal.
Formula:
If x = y, then subtracting a real number c gives:
x - c = y - c.
Let’s say x = y, and both are equal to 10. Let c = 4.
x − c = 10 − 4 = 6
y − c = 10 − 4 = 6
Since x = y, subtracting the same number yields the same result:
x − c = y − c = 6 
 

Let us check the subtraction property of equality using a few examples now that we are aware of it. We know that arithmetically, 12 + 8 = 20. Subtracting 5 from each side of the equation. Now, we have
12 + 8 – 5 = 20 – 5
⇒ 15 = 15
This shows when the same number is subtracted from both the sides of an equation, but the equality still holds.
Now, let’s take another example to understand the application of the property. Let’s consider an algebraic equation x + 4 = 40. Now, to find the value of x, we need to subtract 4 from both the 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.
 

We will now apply the subtraction property of equality to equations involving fractions, since we are familiar with the idea. Now, find the following equation, a / b = x / y. The equation remains balanced when the same fraction c/d is subtracted from both sides.
A / b = x / y
⇒ a / b - c / d = x / y - c / d
Thus, the subtraction property of equality works the same way for fractions and in geometry as well.
 

The subtraction property of equality shows an equation stays balanced. Let us see some real-life examples of the subtraction property of equality. 

• Nature: If there are 50 birds in a tree and 20 fly away, we subtract to find how many are left: 50 – 20 = 30 birds remaining.

• Architecture: To determine the usable floor space, subtract the thickness of the walls from the total building area.

• Biology: To calculate a temperature difference, subtract the normal body temperature from the current reading. For example, 101°F - 98.6°F = 2.4°F above normal.

• Art and Design: When adjusting proportions in a design, subtract unwanted elements. For example, excess measurements or dimensions to refine the final layout.

• Cooking: If a recipe calls for 5 grams of salt and 2 grams are already added, subtract 2 from 5 to know how much more to add: 5 – 2 = 3 grams.