Basic Algebra/Proportions and Proportional Reasoning/Percents

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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 , 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 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 , 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.

Cross-multiplying gives us , and .

We also could have noticed that , 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]