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 $\frac{17}{100}$ , 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 $17 %$ of the squares are shaded. The $%$ 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 $9 %$ , 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.

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

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

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

Practice Games

Practice Problems

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