Basic Algebra/Proportions and Proportional Reasoning/Percents

Vocabulary

Percent: Parts per one hundred

Lesson

Suppose we had a grid of 100 squares, of which 17 are shaded in. There are several ways to express this as a ratio, as you learned in the previous lesson, such as ${\displaystyle {\frac {17}{100}}}$, the number of shaded squares compared to the number of squares in total. However, we can also write this as a percent. Since there are 17 shaded squares and 100 total, we say that ${\displaystyle 17\%}$ of the squares are shaded. The ${\displaystyle \%}$ symbol stands for "percent".

Now suppose that instead of 100 squares, we have 50 squares, with 9 of them shaded. The percent shaded would not be ${\displaystyle 9\%}$, because percent means "per 100", and we have 9 shaded squares out of 50 total squares. To find the percent, we need some number over 100, so we can set up a proportion.

${\displaystyle {\frac {9}{50}}={\frac {x}{100}}}$

Cross-multiplying gives us ${\displaystyle 9\times 100=50x}$, and ${\displaystyle x=18}$.

We also could have noticed that ${\displaystyle 50\times 2=100}$, so we just need to multiply the numerator, 9, by 2 to get our answer, 18.

Practice Problems

Use / as the fraction line and put spaces between the wholes and fractions!

1

What percent of 91 is 137?

2

What is 260% of 70.5?

3

What percent of 109.5 is 49?

4

What percent of 135 is 81.7?