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 $$9 \times 100 = 50x$$, 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!  {What percent of 91 is 137? { 13700/91%|13,700/91%|150 50/91%|13700/91|13,700/91|150 50/91_11 }
 * type="{}"}

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

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

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