Percent: Additional Practice (Set 1)

Convert the percent to a decimal and multiply.

$35\% = 0.35 \;\Rightarrow\; 0.35 \times 80 = 28$

So $35\%$ of $80$ is $28$.

The part is $48$ and the percent is $80$. Set up $\frac{48}{w} = \frac{80}{100}$, multiply the known diagonal $48 \times 100$, and divide by $80$.

$w = \frac{48 \times 100}{80} = \frac{4800}{80} = 60$

Check: $80\%$ of $60$ is $0.8 \times 60 = 48$.

The denominator $8$ does not divide $100$ evenly, so set up $\frac{3}{8} = \frac{p}{100}$, cross-multiply, and divide by $8$.

$p = \frac{3 \times 100}{8} = \frac{300}{8} = 37.5$

So $\frac{3}{8} = 37.5\%$.

Find $64\%$ of $25$ liters. Convert and multiply.

$64\% = 0.64 \;\Rightarrow\; 0.64 \times 25 = 16$

So the backpack holds $16$ liters.

The part is $54$ and the whole is $40$. Since the part is larger, expect a percent above $100$. Set up $\frac{54}{40} = \frac{p}{100}$, cross-multiply, and divide by $40$.

$p = \frac{54 \times 100}{40} = \frac{5400}{40} = 135$

So $54$ is $135\%$ of $40$.

The part is $57$ and the percent is $76$. Set up $\frac{57}{w} = \frac{76}{100}$, multiply the known diagonal $57 \times 100$, and divide by $76$.

$w = \frac{57 \times 100}{76} = \frac{5700}{76} = 75$

Check: $76\%$ of $75$ is $0.76 \times 75 = 57$.

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

$1.35 \times 100 = 135 \;\Rightarrow\; 1.35 = 135\%$

A decimal above $1$ becomes a percent above $100$.

Convert to a decimal and multiply. Note that $7.5\% = 0.075$.

$0.075 \times 240 = 18$

So $7.5\%$ of $240$ is $18$.

The part is $2$ and the whole is $80$. Set up $\frac{2}{80} = \frac{p}{100}$, cross-multiply, and divide by $80$.

$p = \frac{2 \times 100}{80} = \frac{200}{80} = 2.5$

So $2$ is $2.5\%$ of $80$.

The denominator $40$ does not divide $100$ evenly, so set up $\frac{11}{40} = \frac{p}{100}$, cross-multiply, and divide by $40$.

$p = \frac{11 \times 100}{40} = \frac{1100}{40} = 27.5$

So $\frac{11}{40} = 27.5\%$.

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

$0.875 \times 100 = 87.5 \;\Rightarrow\; 0.875 = 87.5\%$

The part is $39$ and the whole is $60$. Set up $\frac{39}{60} = \frac{p}{100}$, cross-multiply, and divide by $60$.

$p = \frac{39 \times 100}{60} = \frac{3900}{60} = 65$

So $65\%$ of the class is girls.