What is a mark-up in math?

A mark-up is an amount added on top of a starting price, given as a percent of that price. A shop that buys a lamp for 80 and marks it up by 25% adds 20, because 25% of 80 is 20. It then sells the lamp for 100. A mark-up raises a price, while a discount lowers it.

How do you calculate percent change between two numbers?

To calculate percent change, find the difference between the new and the old number, then work out what percent of the old number that difference is. From 40 to 46, the difference is 6, and 6 is 15% of 40, because 10% of 40 is 4 and 5% is 2. So the rise is 15%. From 40 to 30, the drop is 10, which is 25% of 40.

Is there a trick for working out percentages in your head?

Yes: you can swap the two numbers, because 45% of 20 equals 20% of 45. Both mean the two numbers multiplied together, then divided by 100, so the order does not matter. And 20% is one fifth, so 20% of 45 is 9. A round of 45% off 20 therefore needs 20 − 9 = 11.

Why doesn’t 20% off and then 20% on get back to the start?

The two 20% steps are taken from different amounts, so they are not the same size. Take 20% off 100 and you remove 20, leaving 80. Then 20% of 80 is only 16, so adding it on gives 96, not 100. To climb from 80 back to 100, you would need to add 25%.

Is this percentage game free for teachers to use in class?

Yes: pupils play both levels free, straight from a browser, without an account or any install. In class, write 120 on the board and call out 25% off, 10% on and 50% off, each applied to 120 itself. Pupils first say whether each result lands above or below 120, then work it out: 90, 132 and 60. The schools plan is charged per student and gives the teacher a dashboard of who is getting better at percentages.

Math practice · reimagined

Percentages Game

This percentage game sets discounts like 30% off 140 and mark-ups like 60 plus 30%, with percents from 5% to 50% and answers that always come out whole. Take the percent off or add it on before your rival, and your fighter punches first.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is percent change?

Percent change is a rise or fall in an amount, measured as a percentage of the amount you started with. Percent, written %, means “out of every 100”. So 10% off 200 removes 10 for each 100, which is 20, and leaves 180. Add 10% to 200 instead, and you reach 220.

Every level of Percent change

Example: 25% off 160, using a quarter

The problem reads 25% off 160: start at 160 and take away 25% of it.
25% means 25 out of every 100, which is one quarter, and a quarter of 160 is 40.
Take that part away from the start: 160 − 40 = 120.
A discount must leave less than 160, and 120 does, so you type 120.

Learn it step by step

A discount is a percent taken OFF — it's the maths behind every sale sign in a shop.

First work out the percent of the price, then subtract it. For 20% off 80: a tenth of 80 is 8, so 20% is 16 — take that off and you pay 64. A handy shortcut: 20% off means you still pay 80% of the price, and 80% of 80 is also 64. Either road gets you there.

Find the part, take it away, and type what's left to pay.

Tips and common mistakes

Look at the sign %: a small 0, a slash and another 0, like the 100 in “out of 100”. So 35% means 35 out of 100, or 35/100.
Watch out for taking off the percent as a plain number. 20% off 60 is not 60 − 20 = 40: 20% of 60 is 12, so the answer is 48.
Turn shopping into percentage practice. Pick a price tag, invent a sale such as 20% off 50, and ask for the new price: 50 − 10 = 40.

How to play

The first level shows discounts such as 35% off 120, and the second shows mark-ups such as 140 plus 25%. Either way you type the new amount on the keypad, not the part that changed, and it always comes out whole. Answer before your rival and Garlic strikes; the quicker your answer, the heavier the blow.

— Quick answers —

Percent change: the short FAQ

What is a mark-up in math?: A mark-up is an amount added on top of a starting price, given as a percent of that price. A shop that buys a lamp for 80 and marks it up by 25% adds 20, because 25% of 80 is 20. It then sells the lamp for 100. A mark-up raises a price, while a discount lowers it.
How do you calculate percent change between two numbers?: To calculate percent change, find the difference between the new and the old number, then work out what percent of the old number that difference is. From 40 to 46, the difference is 6, and 6 is 15% of 40, because 10% of 40 is 4 and 5% is 2. So the rise is 15%. From 40 to 30, the drop is 10, which is 25% of 40.
Is there a trick for working out percentages in your head?: Yes: you can swap the two numbers, because 45% of 20 equals 20% of 45. Both mean the two numbers multiplied together, then divided by 100, so the order does not matter. And 20% is one fifth, so 20% of 45 is 9. A round of 45% off 20 therefore needs 20 − 9 = 11.
Why doesn’t 20% off and then 20% on get back to the start?: The two 20% steps are taken from different amounts, so they are not the same size. Take 20% off 100 and you remove 20, leaving 80. Then 20% of 80 is only 16, so adding it on gives 96, not 100. To climb from 80 back to 100, you would need to add 25%.
Is this percentage game free for teachers to use in class?: Yes: pupils play both levels free, straight from a browser, without an account or any install. In class, write 120 on the board and call out 25% off, 10% on and 50% off, each applied to 120 itself. Pupils first say whether each result lands above or below 120, then work it out: 90, 132 and 60. The schools plan is charged per student and gives the teacher a dashboard of who is getting better at percentages.

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