Percentages

A phone battery at 80%, a second bubble tea at half price — really paying 75% for the pair — a striker scoring on 45% of shots. Why do all these situations prefer percentages? Because the denominator is always 100, so "more or less" is visible at a glance.

Percent: how many out of one hundred

The percent sign % simply means "divided by 100". Every percentage owns three interchangeable outfits:

$37\% = \frac{37}{100} = 0.37$

• Read aloud as "thirty-seven percent";
• As a fraction, 37 parts out of 100;
• As a decimal, drop the sign and move the point two steps left.

All three outfits hold the same amount. Half a glass of water can be written $\frac{1}{2}$, 0.5, or 50%. Fractions and decimals are its closest relatives.

How to use

Discount %37

37% = 37/100 = 0.37 = 37/100

Three friendly benchmarks

For mental math, memorize three friends:

• 50% is one half — just divide by 2;
• 25% is one quarter — just divide by 4;
• 10% is the flexible one: move the decimal point one step left.

With 10% in hand you can build many others: 20% is two tens, and 5% is half of a ten.

Finding a percent of a number

Question: what is 30% of 240?

1. First find 10%: shift the point one step left, $240 \times 10\% = 24$;
2. Then 30% is three tens: $24 \times 3 = 72$.

No long columns, no calculator. For 5%, cut a ten in half: 5% of 240 is 12. This trick shines during sales season — see discounts and percentages for the full workout.

Up and down

A membership fee of 80 rises by 25%. What is the new price?

$80 \times (1 + 25\%) = 80 + 20 = 100$

First find the increase (25% of 80 is 20), then add it on. Decreases work the same way: find the drop, then subtract it.

Check yourself

Quick quiz

Try again

0 / 3 correct0 / 3 correct

1. 1. 37% equals which pair?

   37/100 and 0.373.7 and 37/100.037 and 37/1000

2. 2. What is 30% of 240?

   247280

3. 3. A fee of 80 rises by 25%. What is the new price?

   95100105