Find Percent of a Number
Finding a percent of a number means finding a part or portion of a number. A percent is another way to write a decimal or a fraction, so finding a percent of a number is the same as finding a fraction or decimal of a number. One great math rule to remember: the word "of" means multiply in math.
There are several ways to find the percent of a number. EdBoost's preferred way to to use a proportion (not necessarily because it's the easiest way to do this operation, but because there are several related operations, and using a proportion makes it clear how to solve all kinds of percent problems).
Example: Find 15% of 60
We like to use proportions that follow this format: $\dfrac{part}{whole}=\dfrac{\text{%}}{100}$
The "part" is the percentage portion of a number you are trying to find. "Whole" is the whole number you are finding a percentage portion of. "%" is the percent you are working with. "100" always represents "whole" in percents.
$$\eqalign{\text{part}&=x\\\text{whole}&=60\\\text{%}&=15\\\text{100}&=100}$$
Some people remember this proportion set us as: $\dfrac{is}{of}=\dfrac{\text{%}}{100}$
If you rephrase our question to: 15% of 60 is _____?, then 60 is your "of" number (the denominator or bottom number), and your "is" number is unknown, so $x$ goes in the numerator (top) spot.
$$\eqalign{\text{is}&=x\\\text{of}&=60\\\text{%}&=15\\\text{100}&=100}$$
With either set up, our proportion for this problem would be: $\dfrac{x}{60}=\dfrac{15}{100}$
We put an $x$ in for the "part" because that's what we're trying to solve for. Now, just cross multiply to solve the proportion for $x$.
$$\eqalign{\dfrac{x}{60}&=\dfrac{15}{100} && \text{Set up proportion}\\ x\times100&=15\times60 &&\text{Cross multiply}\\100x&=900 &&\text{Solve for variable}\\x&=9}$$
To see this done live: Using Proportions to Solve Percent Problems
Many people prefer a simpler method of finding a percent of a number. They follow these steps:
- Turn the percent into a decimal.
- Multiply the decimal times the number (remember, "of" means multiplication).
This method is simple!
$$\eqalign{60\text{%}&=.6 && \text{Turn percent into decimal}\\ .6\times 15&=9 &&\text{Multiply to find the answer}}$$
However, as you'll see in practice problems 7-12 below, sometimes turning a decimal into a percent confuses students (you always divide the percent by 100, which means moving the decimal two places to the left). We prefer the EdBoost method because it eliminates decimal point confusion, and it's great when we get to problems like "51 is what percent of 60?" and "13 is 15% of what number?"
Practice Problems:
Find Percent of a Number
- Find 10% of 52.
- What is 90% of 103?
- What is 62% of 50?
- Find 7% of 21.
- Find 41% of 16.
- What is 6% of 20?
- What is 103% of 50?
- Find 250% of 40.
- What is 18% of 6?
- Find 180% of 6.
- What is 1.8% of 6?
- Find .18% of 6.
Answer Key: