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

Practice Problems

Use / as the fraction line and put spaces between the wholes and fractions! <quiz display=simple points="1/1"> {What percent of 91 is 137? |type="{}"} { 13700/91%|13,700/91%|150 50/91%|13700/91|13,700/91|150 50/91_11 }

{What is 260% of 70.5? |type="{}"} { 1833/10|1,833/10|183.3_11 }

{What percent of 109.5 is 49? |type="{}"} { 9800/219%|9,800/219%|44 164/219%|9800/219|9,800/219|44 164/219_11 }

{What percent of 135 is 81.7? |type="{}"} { 1634/27%|1,634/27%|60 14/27%|1634/27|1,634/27|60 14/27_11 } </quiz>