Finding a Number from its Percent
What Does This Mean?
When we know a part of something and what percent that part represents, we can find the whole number. This is the reverse of finding a percent of a number!
Forward Problem
"What is 25% of 80?"
80 × 0.25 = 20
We know the whole, find the part
Reverse Problem (Today's Topic!)
"25% of what number is 20?"
20 ÷ 0.25 = 80
We know the part, find the whole
The Main Formula
Whole = Part ÷ (Percent ÷ 100)
or simply:
Whole = Part ÷ Decimal Form of Percent
Visual Representation of the Formula
WHOLE (100%)
= ?
PART (25%)
25%
If 25% = 20, then 100% = 20 ÷ 0.25 = 80
The PART divided by the PERCENT gives the WHOLE
Method 1: Using Decimals
- Convert the percent to a decimal (divide by 100)
- Divide the part by this decimal
Example: 15 is 30% of what number?
Step 1: 30% = 30 ÷ 100 = 0.30
Step 2: 15 ÷ 0.30 = 50
✓ Answer: 50
Method 2: Using Fractions
- Convert the percent to a fraction
- Divide by multiplying by the reciprocal
Example: 20 is 25% of what number?
Step 1: 25% = 25/100 = 1/4
Step 2: 20 ÷ 1/4 = 20 × 4/1 = 80
✓ Answer: 80