What Percent Is One Number of Another?

$30\%$

$\tfrac{15}{50} = 0.3$, so $30\%$.

$45\%$

$\tfrac{9}{20} = 0.45$, so $45\%$.

Simplify the fraction first if it helps.

$75\%$

$\tfrac{21}{28} = \tfrac{3}{4} = 0.75$, so $75\%$.

$37.5\%$

$\tfrac{3}{8} = 0.375$, so $37.5\%$.

$23.3\%$

$\tfrac{14}{60} = 0.2\overline{3}$, so $23.\overline{3}\%$, which is $23.3\%$ to one decimal place.

The part and the percent are known, so divide.

$45$

$\tfrac{27}{0.6} = 45$.

Checking: $0.6 \times 45 = 27$ ✓

$70$

$\tfrac{84}{1.2} = 70$.

The answer is smaller than $84$, which is right — $84$ is more than the whole, since the percent is above $100$.

Which number is the original price?

$15\%$

The reduction is measured against the original $60: $\tfrac{9}{60} = 0.15$, so $15\%$.

Two ways to get there. Do both and check they agree.

$35\%$

It lost $20 - 13 = 7$ games, so $\tfrac{7}{20} = 0.35$, giving $35\%$.

Or: it won $\tfrac{13}{20} = 65\%$, and the rest is $100 - 65 = 35\%$. The two routes agreeing is a check on both.

Can a part of a whole be four times the whole?

He divided $32$ by $8$ instead of $8$ by $32$. The answer is $25\%$.

$8$ is a part of $32$, so the answer has to be below $100\%$. Any result above that fails before the arithmetic is checked.

Correctly: $\tfrac{8}{32} = 0.25$, so $25\%$ — which fits, since $8$ is a quarter of $32$.