Percent

Percentage #

Percent simply means out of a hundred.

Percent means out of a hundred

Read the full lesson →

Cut the whole into 100 pieces and color 40 in: $\frac{40}{100}$40/100, written 40%.

Finding a Percent #

Find ten percent first, the rest follows.

Find ten percent first and the rest follows

Read the full lesson →

Split 120 into ten equal parts: 120 ÷ 10 = 12. The lower scale reads 10%.

Three of those parts are 3 × 12 = 36, and the lower scale reads 30%.

Taking a Percent Off #

The part you take away from the whole.

A discount is the part you take away from the whole

Read the full lesson →

Take 2 of the 10 parts off the whole 100%. That is the 20% knocked off.

8 parts are left: 100% − 20% = 80%. That is what you pay.

Try it on $50: 20% of 50 is 10, so you pay 50 − 10 = $40.

Sales Tax #

A percent the till adds on top.

Sales tax is a percent the till adds on top of the price

Read the full lesson →

The shop asks $40, then the till adds tax: 5% of $40 is $2, so you pay $42.

The rate depends on where — and when — you buy: at 8%, the same ball costs $43.20.

Comparing with Percent #

Percents make two scores fair to compare.

Turning both scores into percents makes them fair to compare

Read the full lesson →

Two scores out of different totals. You cannot compare them yet.

Cut each of the 20 into 5: 20 × 5 = 100 pieces, and 15 × 5 = 75 colored.

Do the same to $\frac{16}{25}$16/25: cut each of the 25 into 4, and 16 × 4 = 64 out of 100.

Both are out of 100 now: 75% against 64%, so $\frac{15}{20}$15/20 is the better score.

Percentage Increase #

The whole plus the extra, in one multiply.

Adding a percent on is one multiplication by the whole-plus-extra

Read the full lesson →

A 20% rise keeps all 100% and adds 20% on top.

Try it on 40: 20% of 40 is 8, and 40 + 8 = 48.

48 is 120% of 40. As a multiplier, 120% is $\frac{120}{100}=1.2$120/100 = 1.2, so 40 × 1.2 = 48.

Falls work the same way: down 20% keeps 80%, and one step does it: ×0.8.

Percentage Change #

The difference, out of where you started.

Percentage change compares the difference with where you started

Read the full lesson →

From 40 up to 50: the change is 50 − 40 = 10. But 10 out of what?

Out of where you started: 40 splits into four 10s, so 10 out of 40 is $\frac{1}{4}$1/4.

A quarter of 100 is 25, so $\frac{10}{40}=\frac{25}{100}$10/40 = 25/100 — a 25% change.

From 20% to 25%: up 5 percentage points — and since 5 is a quarter of 20, up 25%.

Reverse Percentages #

Divide by the multiplier to get back.

To undo a percent change, divide by the multiplier that made it

Read the full lesson →

After a 20% rise the price is $60, so $60 is 120% of the old price.

120% of the old price means old × 1.2, and that landed on 60.

Undo the ×1.2 by dividing: 60 ÷ 1.2 = 50, so the old price was $50.

The wrong route: 20% off 60 gives 48. The rise was 20% of 50, not of 60.

Depreciation #

Falling by the same percent every year.

Losing the same percent each year is multiplying by the same number each year

Read the full lesson →

A value that falls 20% keeps 80% — percent off in one step: ×0.8.

A $500 phone loses 20% in its first year: $500 × 0.8 = $400.

Two years means ×0.8 twice, giving $320 — not $500 with $100 taken off twice.

Fractions, Decimals and Percents #

One amount, three ways of writing it.

One amount, three ways of writing it

Read the full lesson →

3 of the 4 pieces are colored in.

Cut into 100 pieces instead and the very same amount reads 0.75.

Or 75 out of 100, which is 75%. The coloring never changed!

Comparing Percents, Fractions and Decimals #

Convert to one language before comparing.

Convert everything to one notation before comparing

Read the full lesson →

Three discounts on one jacket: $\frac{1}{4}$1/4 off, 0.3 off, 27% off. Turn all three into percents.

Lined up as 25, 27 and 30, the sizes are plain: 0.3 is the biggest discount.