Basic Algebra/Proportions and Proportional Reasoning/Percents

From Wikibooks, open books for an open world
Jump to: navigation, search

Vocabulary[edit]

Percent: Parts per one hundred

Lesson[edit]

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 = 50x, 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.

Example Problems[edit]

  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?

Answer them and put the answers to them

Practice Games[edit]

Practice Problems[edit]