Lesson 48: Percent of a Whole

New Concept

A percent is a ratio that compares a part to a whole, where the whole is always considered to be $100\%$.

What’s next

Next, you'll tackle worked examples using our three-row ratio table to solve for missing totals and percentages.

Property

A percent is a ratio used to describe part of a whole. Use a three-row ratio table to find the total by setting up a proportion with the part you know: $\frac{\text{Part Percent}}{100} = \frac{\text{Part Count}}{\text{Total}}$.

Examples

20% of a town voted. If 1600 people did not vote, find the total voters (t): $\frac{80}{100} = \frac{1600}{t}$, so $t=2000$.
A recipe uses 30% of a flour bag. If 700 grams remain, find the original amount (w): $\frac{70}{100} = \frac{700}{w}$, so $w=1000$ grams.

Explanation

Think of the ratio table as a detective tool! If you know that 60% of your game is complete, you can use that clue to figure out the total time needed to reach 100%. This method connects the part you know to the whole you want to find.

Property

To find an unknown percent, use a proportion. If you know the part count and the total count, you can set up a ratio table to solve for the missing percent (p): $\frac{p}{100} = \frac{\text{Part Count}}{\text{Total Count}}$.

Examples

James made 12 out of 15 free throws. Find the percent (c) he made: $\frac{c}{100} = \frac{12}{15}$, so $c=80\%$.
Of 50 pets in a shelter, 35 are dogs. Find the percent of dogs (d): $\frac{d}{100} = \frac{35}{50}$, so $d=70\%$.

Explanation

Ever wonder what your quiz score is as a percentage? If you got 9 questions right out of 10, this method easily converts that into a shiny percent. The ratio table helps you organize the numbers perfectly to solve for that missing percentage value every single time!

Property

The whole is always 100%. Therefore, the different parts must add up to the total. For example, the percent of questions answered correctly and the percent answered incorrectly must add up to 100%.

Examples

If a player makes 80% of her free throws, she misses $100\% - 80\% = 20\%$ of them.
If 56% of voters chose Candidate A, then $100\% - 56\% = 44\%$ of voters chose someone else.

Explanation

Think of 100% as a full pizza. If you know you ate 75% of it, you automatically know 25% is left. It works the same with any percentage problem! Knowing the 'yes' part instantly tells you the 'no' part because they both must add up to the whole 100%.