Percent: Practice

Convert the percent to a decimal and multiply.

$8\% = 0.08 \;\Rightarrow\; 0.08 \times 450 = 36$

So $8\%$ of $450$ is $36$.

The part is $36$ and the whole is $160$. Set up $\frac{36}{160} = \frac{p}{100}$, cross-multiply, and divide by $160$.

$p = \frac{36 \times 100}{160} = \frac{3600}{160} = 22.5$

So $36$ is $22.5\%$ of $160$.

A percent above $100$ is more than the whole. Here $150\% = 1.5$.

$1.5 \times 40 = 60$

So $150\%$ of $40$ is $60$, which is more than $40$ itself.

The part is $13$ and the whole is $52$. Set up $\frac{13}{52} = \frac{p}{100}$, cross-multiply, and divide by $52$.

$p = \frac{13 \times 100}{52} = \frac{1300}{52} = 25$

So $25\%$ of the people bike to work.

The denominator $8$ does not divide $100$ evenly, so treat it as a proportion: $\frac{5}{8} = \frac{p}{100}$. Cross-multiply and divide by $8$.

$p = \frac{5 \times 100}{8} = \frac{500}{8} = 62.5$

So $\frac{5}{8} = 62.5\%$. Dividing also works: $5 \div 8 = 0.625 = 62.5\%$.

Convert to a decimal and multiply.

$12\% = 0.12 \;\Rightarrow\; 0.12 \times 250 = 30$

So $12\%$ of $250$ is $30$.

Multiply by $100$, moving the decimal point two places to the right.

$0.004 \times 100 = 0.4 \;\Rightarrow\; 0.004 = 0.4\%$

So $0.004$ is $0.4\%$, less than one percent.

The part is $30$ and the whole is $24$. Since the part is bigger than the whole, expect a percent above $100$. Set up $\frac{30}{24} = \frac{p}{100}$, cross-multiply, and divide by $24$.

$p = \frac{30 \times 100}{24} = \frac{3000}{24} = 125$

So $30$ is $125\%$ of $24$.

The part is $63$ and the whole is $90$. Set up $\frac{63}{90} = \frac{p}{100}$, cross-multiply, and divide by $90$.

$p = \frac{63 \times 100}{90} = \frac{6300}{90} = 70$

So $70\%$ of the shirts were sold.

The denominator $8$ does not divide $100$ evenly, so set up $\frac{7}{8} = \frac{p}{100}$, cross-multiply, and divide by $8$.

$p = \frac{7 \times 100}{8} = \frac{700}{8} = 87.5$

So $\frac{7}{8} = 87.5\%$.

Find $70\%$ of $40$ questions. Convert and multiply.

$70\% = 0.70 \;\Rightarrow\; 0.70 \times 40 = 28$

So you must answer $28$ questions correctly.

The part is $15$ and the percent is $2.5$. Set up $\frac{15}{w} = \frac{2.5}{100}$, multiply the known diagonal $15 \times 100$, and divide by $2.5$.

$w = \frac{15 \times 100}{2.5} = \frac{1500}{2.5} = 600$

Check: $2.5\%$ of $600$ is $0.025 \times 600 = 15$.