Percent: Practice

Convert the percent to a decimal, then multiply because "of" means multiply.

$30\% = 0.30 \;\Rightarrow\; 0.30 \times 90 = 27$

So $30\%$ of $90$ is $27$.

The part is $20$ and the whole is $50$. Write the ratio over $100$: $\frac{20}{50} = \frac{p}{100}$, then cross-multiply and divide by $50$.

$p = \frac{20 \times 100}{50} = \frac{2000}{50} = 40$

So $20$ is $40\%$ of $50$.

The part is $12$ and the percent is $25$, with the whole unknown. Set up $\frac{12}{w} = \frac{25}{100}$, multiply the known diagonal $12 \times 100$, and divide by $25$.

$w = \frac{12 \times 100}{25} = \frac{1200}{25} = 48$

Check: $25\%$ of $48$ is $0.25 \times 48 = 12$.

Rewrite the fraction with a denominator of $100$. Since $100 \div 25 = 4$, scale top and bottom by $4$.

$\frac{7}{25} = \frac{7 \times 4}{25 \times 4} = \frac{28}{100} = 28\%$

Convert to a decimal and multiply.

$40\% = 0.40 \;\Rightarrow\; 0.40 \times 35 = 14$

So $40\%$ of $35$ is $14$.

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

$0.125 \times 100 = 12.5 \;\Rightarrow\; 0.125 = 12.5\%$

The part is $60$ and the whole is $80$. Set up $\frac{60}{80} = \frac{p}{100}$, cross-multiply, and divide by $80$.

$p = \frac{60 \times 100}{80} = \frac{6000}{80} = 75$

So $60$ is $75\%$ of $80$.

Scale to a denominator of $100$. Since $100 \div 20 = 5$, multiply top and bottom by $5$.

$\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} = 45\%$

The part is $15$ and the whole is $25$. Set up $\frac{15}{25} = \frac{p}{100}$, cross-multiply, and divide by $25$.

$p = \frac{15 \times 100}{25} = \frac{1500}{25} = 60$

So $15$ is $60\%$ of $25$.

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

$0.6 \times 100 = 60 \;\Rightarrow\; 0.6 = 60\%$

The part is $7$ and the percent is $20$. Set up $\frac{7}{w} = \frac{20}{100}$, multiply the known diagonal $7 \times 100$, and divide by $20$.

$w = \frac{7 \times 100}{20} = \frac{700}{20} = 35$

Check: $20\%$ of $35$ is $0.2 \times 35 = 7$.

Scale to a denominator of $100$. Since $100 \div 50 = 2$, multiply top and bottom by $2$.

$\frac{13}{50} = \frac{13 \times 2}{50 \times 2} = \frac{26}{100} = 26\%$