How to Find a Percent of a Number

Find $10\%$ first, then double it.

$30$

$10\%$ of $150$ is $15$, so $20\%$ is $30$.

The long way agrees: $0.2 \times 150 = 30$.

$36$

$0.45 \times 80 = 36$. Under half of $80$, as it should be.

$75\%$ is three quarters.

$36$

A quarter of $48$ is $12$, so three quarters is $36$.

$14$

$1\%$ of $200$ is $2$, so $7\%$ is $14$.

$10\%$ plus two lots of $1\%$.

$30$

$10\%$ of $250$ is $25$, and $1\%$ is $2.5$, so $2\%$ is $5$.

$25 + 5 = 30$.

$66$

$1.1 \times 60 = 66$.

Or split it: $60$ plus $10\%$ of $60$, which is $60 + 6$.

$50\%$ of $6$, and the answer is $3$.

Both give $3$, because the order of multiplication does not matter. Half of $6$ is a one-step calculation; $0.06 \times 50$ is not.

$10\% + 5\% + 2\% + 1\%$, or take $20\%$ and subtract $2\%$.

$8.28

$0.18 \times 46 = 8.28$.

Mentally: $10\%$ is $4.60$ and $20\%$ is $9.20$. Since $2\%$ is $0.92$, take it off: $9.20 - 0.92 = 8.28$.

$224$ students

$0.35 \times 640 = 224$.

Checking the size: $35\%$ is about a third, and a third of $640$ is roughly $213$. The answer is close to that, so it is the right order of magnitude.

Should the answer be bigger or smaller than $80$?

She multiplied by $1.5$ instead of $0.15$. The answer is $12$.

$15\%$ is less than $100\%$, so the answer has to be smaller than $80$. An answer of $120$ fails that check before any arithmetic is rechecked.

Correctly: $0.15 \times 80 = 12$. Her $120$ is $150\%$ of $80$, which is what $1.5$ would give — the decimal point moved one place too few.