Basic Algebra/Proportions and Proportional Reasoning/Percents

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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 popcicels 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

What percent of 91 is 137%?
What is 260% of 70.5?
What percent of 109.5 is 49?
What percent of 135 is 81.7?

Answer them and put the answers to them

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