+−How do I find a percentage of an amount or number?
Multiply the number by the percentage and divide by 100. For example, 15% of 200 is 200 × 15 ÷ 100 = 30. Or move the decimal: 10% of 200 is 20, 5% is 10, so 15% is 30.
+−How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. If you got 30 marks out of 200, that’s 30 ÷ 200 × 100 = 15%.
+−How do I calculate percentage increase or decrease?
Take the difference between the new and old value, divide it by the old value, then multiply by 100. Going from €80 to €100 is (100 − 80) ÷ 80 × 100 = +25%. Going from €100 to €80 is −20%. The change is measured from where you started, which is why the two answers differ.
+−How do I take a percentage off a price?
Multiply the price by (100 − discount) ÷ 100. A €59.99 jacket at 25% off is 59.99 × 0.75 = €44.99. Use the "decrease by %" card above and it’s done for you.
+−What is a reverse percentage?
It’s working backwards: you know the final amount and the percentage, and you want the original. If a price of €138 already includes a 15% increase, the original was 138 ÷ 1.15 = €120. Dividing, not subtracting 15%, is the key step people get wrong.
+−Why is a 50% increase not cancelled by a 50% decrease?
Because the base changes. €100 increased by 50% is €150, but €150 decreased by 50% is €75, not €100. Percentage changes always apply to the current value, not the original one.
+−What is the difference between percentage change and percentage difference?
Percentage change compares a new value against an old one, so it has a direction: from €80 to €100 is +25%. Percentage difference compares two values without an order. You divide the gap by the average of the two: |100 − 80| ÷ 90 × 100 ≈ 22.2%. Use change for before/after, difference for comparing two equal alternatives.
+−How do I work out a percentage of a percentage?
Turn both into decimals and multiply. 20% of 50% is 0.20 × 0.50 = 0.10, which is 10%. The same trick handles "a further 10% off an item already 30% off": you pay 0.70 × 0.90 = 0.63 of the price, so the total discount is 37%, not 40%.
+−How do I add or remove 23% VAT?
To add VAT multiply the net price by 1.23: €200 becomes €246. To remove VAT divide the gross price by 1.23: €246 ÷ 1.23 = €200. Subtracting 23% from €246 gives €189.42, which is wrong. The same works for the 13.5% rate (multiply or divide by 1.135) and the 9% rate (1.09).
+−How do I convert Leaving Cert marks to a percentage and grade?
Divide your marks by the paper total and multiply by 100. 312 out of 400 is 312 ÷ 400 × 100 = 78%. Grades are 10% bands: 90 to 100 is H1 or O1, 80 to under 90 is H2 or O2, 70 to under 80 is H3 or O3, and so on down to below 30 for H8 or O8. So 78% is an H3 at Higher level.
+−How do I calculate a percentage on a phone calculator?
Calculator apps treat the % key differently, so the safest method is to skip it. For 20% of 204.01 type 204.01 × 0.2 and you get 40.802, so €40.80. For 30% off 44.99 type 44.99 × 0.7, which gives 31.493, so €31.49. Or type the numbers into the boards above and read the answer.