GCSE Maths: Percentage increase and decrease (Higher)

Method. Find 10% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 80 = 80 ÷ 10 = 8
2. Write the answer. Include the units.
   10% of 80 = 8
3. Add it to the original amount. We want the amount after the increase.
   80 + 8 = 88

Check. Multiplier check: 110% = 1.1, and 1.1 × 80 = 88. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 20% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £150 = £150 ÷ 10 = £15
2. Work out each part. Multiply to build up to the percentage you want.
   20% = 2 × 10% = 2 × £15 = £30
3. Write the answer. Include the units.
   20% of £150 = £30
4. Add it to the original amount. We want the amount after the increase.
   £150 + £30 = £180

Check. Multiplier check: 120% = 1.2, and 1.2 × £150 = £180. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 5% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 240 = 240 ÷ 10 = 24
2. Work out each part. Multiply to build up to the percentage you want.
   5% = half of 10% = 24 ÷ 2 = 12
3. Write the answer. Include the units.
   5% of 240 = 12
4. Add it to the original amount. We want the amount after the increase.
   240 + 12 = 252

Check. Multiplier check: 105% = 1.05, and 1.05 × 240 = 252. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 25% of the amount, then add it to the original.

1. Spot that 25% is a quarter. 25 out of 100 is the same as 1 out of 4.
   25% = 14
2. Find a quarter of the amount. To find a quarter, divide by 4 (or halve twice).
   £60 ÷ 4 = £15
3. Add it to the original amount. We want the amount after the increase.
   £60 + £15 = £75

Check. Multiplier check: 125% = 1.25, and 1.25 × £60 = £75. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 30% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 400 = 400 ÷ 10 = 40
2. Work out each part. Multiply to build up to the percentage you want.
   30% = 3 × 10% = 3 × 40 = 120
3. Write the answer. Include the units.
   30% of 400 = 120
4. Add it to the original amount. We want the amount after the increase.
   400 + 120 = 520

Check. Multiplier check: 130% = 1.3, and 1.3 × 400 = 520. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 40% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £35 = £35 ÷ 10 = £3.50
2. Work out each part. Multiply to build up to the percentage you want.
   40% = 4 × 10% = 4 × £3.50 = £14
3. Write the answer. Include the units.
   40% of £35 = £14
4. Add it to the original amount. We want the amount after the increase.
   £35 + £14 = £49

Check. Multiplier check: 140% = 1.4, and 1.4 × £35 = £49. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 10% of the amount, then subtract it from the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £80 = £80 ÷ 10 = £8
2. Write the answer. Include the units.
   10% of £80 = £8
3. Subtract it from the original amount. We want the amount after the decrease.
   £80 − £8 = £72

Check. Multiplier check: 90% = 0.9, and 0.9 × £80 = £72. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 25% of the amount, then subtract it from the original.

1. Spot that 25% is a quarter. 25 out of 100 is the same as 1 out of 4.
   25% = 14
2. Find a quarter of the amount. To find a quarter, divide by 4 (or halve twice).
   120 ÷ 4 = 30
3. Subtract it from the original amount. We want the amount after the decrease.
   120 − 30 = 90

Check. Multiplier check: 75% = 0.75, and 0.75 × 120 = 90. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 20% of the amount, then subtract it from the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £250 = £250 ÷ 10 = £25
2. Work out each part. Multiply to build up to the percentage you want.
   20% = 2 × 10% = 2 × £25 = £50
3. Write the answer. Include the units.
   20% of £250 = £50
4. Subtract it from the original amount. We want the amount after the decrease.
   £250 − £50 = £200

Check. Multiplier check: 80% = 0.8, and 0.8 × £250 = £200. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 50% of the amount, then subtract it from the original.

1. Spot that 50% is a half. 50 out of 100 is the same as 1 out of 2.
   50% = 12
2. Halve the amount. To find a half, divide by 2.
   64 ÷ 2 = 32
3. Subtract it from the original amount. We want the amount after the decrease.
   64 − 32 = 32

Check. Multiplier check: 50% = 0.5, and 0.5 × 64 = 32. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 30% of the amount, then subtract it from the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £90 = £90 ÷ 10 = £9
2. Work out each part. Multiply to build up to the percentage you want.
   30% = 3 × 10% = 3 × £9 = £27
3. Write the answer. Include the units.
   30% of £90 = £27
4. Subtract it from the original amount. We want the amount after the decrease.
   £90 − £27 = £63

Check. Multiplier check: 70% = 0.7, and 0.7 × £90 = £63. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 15% of the amount, then subtract it from the original.

1. Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.
   15% = 10% + 5%
2. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 300 = 300 ÷ 10 = 30
3. Work out each part. Use the 10% or 1% you found.
   10% = 30
   5% = half of 10% = 30 ÷ 2 = 15
4. Add the parts together. The parts together make up the whole percentage.
   30 + 15 = 45
5. Subtract it from the original amount. We want the amount after the decrease.
   300 − 45 = 255

Check. Multiplier check: 85% = 0.85, and 0.85 × 300 = 255. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. A increase of 10% means the new amount is 110% of the original. Write 110% as a decimal.

1. Work out the new percentage. The original is 100%. For a increase we add 10%.
   100% + 10% = 110%
2. Divide by 100. To change a percentage to a decimal.
   110% = 110 ÷ 100 = 1.1
3. Check the size of the multiplier. A increase should give a multiplier above 1.
   1.1 is above 1, so it makes the amount bigger.

Check. Multiplying 100 by 1.1 gives 110, which is a 10% increase on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A increase of 4% means the new amount is 104% of the original. Write 104% as a decimal.

1. Work out the new percentage. The original is 100%. For a increase we add 4%.
   100% + 4% = 104%
2. Divide by 100. To change a percentage to a decimal.
   104% = 104 ÷ 100 = 1.04
3. Check the size of the multiplier. A increase should give a multiplier above 1.
   1.04 is above 1, so it makes the amount bigger.

Check. Multiplying 100 by 1.04 gives 104, which is a 4% increase on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A decrease of 20% means the new amount is 80% of the original. Write 80% as a decimal.

1. Work out the new percentage. The original is 100%. For a decrease we subtract 20%.
   100% − 20% = 80%
2. Divide by 100. To change a percentage to a decimal.
   80% = 80 ÷ 100 = 0.8
3. Check the size of the multiplier. A decrease should give a multiplier below 1.
   0.8 is below 1, so it makes the amount smaller.

Check. Multiplying 100 by 0.8 gives 80, which is a 20% decrease on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A decrease of 3% means the new amount is 97% of the original. Write 97% as a decimal.

1. Work out the new percentage. The original is 100%. For a decrease we subtract 3%.
   100% − 3% = 97%
2. Divide by 100. To change a percentage to a decimal.
   97% = 97 ÷ 100 = 0.97
3. Check the size of the multiplier. A decrease should give a multiplier below 1.
   0.97 is below 1, so it makes the amount smaller.

Check. Multiplying 100 by 0.97 gives 97, which is a 3% decrease on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A increase of 35% means the new amount is 135% of the original. Write 135% as a decimal.

1. Work out the new percentage. The original is 100%. For a increase we add 35%.
   100% + 35% = 135%
2. Divide by 100. To change a percentage to a decimal.
   135% = 135 ÷ 100 = 1.35
3. Check the size of the multiplier. A increase should give a multiplier above 1.
   1.35 is above 1, so it makes the amount bigger.

Check. Multiplying 100 by 1.35 gives 135, which is a 35% increase on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A decrease of 45% means the new amount is 55% of the original. Write 55% as a decimal.

1. Work out the new percentage. The original is 100%. For a decrease we subtract 45%.
   100% − 45% = 55%
2. Divide by 100. To change a percentage to a decimal.
   55% = 55 ÷ 100 = 0.55
3. Check the size of the multiplier. A decrease should give a multiplier below 1.
   0.55 is below 1, so it makes the amount smaller.

Check. Multiplying 100 by 0.55 gives 55, which is a 45% decrease on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   1.2 × 100 = 120%
2. Compare with 100%. The original is 100%. 120% is more than 100%.
   120% − 100% = 20%
3. Say it in words.
   a 20% increase

Check. 100 × 1.2 = 120, which is 20 more than 100. ✓

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   1.07 × 100 = 107%
2. Compare with 100%. The original is 100%. 107% is more than 100%.
   107% − 100% = 7%
3. Say it in words.
   a 7% increase

Check. 100 × 1.07 = 107, which is 7 more than 100. ✓

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   0.9 × 100 = 90%
2. Compare with 100%. The original is 100%. 90% is less than 100%.
   90% − 100% = −10%
3. Say it in words.
   a 10% decrease

Check. 100 × 0.9 = 90, which is 10 less than 100. ✓

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   0.65 × 100 = 65%
2. Compare with 100%. The original is 100%. 65% is less than 100%.
   65% − 100% = −35%
3. Say it in words.
   a 35% decrease

Check. 100 × 0.65 = 65, which is 35 less than 100. ✓

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   1.5 × 100 = 150%
2. Compare with 100%. The original is 100%. 150% is more than 100%.
   150% − 100% = 50%
3. Say it in words.
   a 50% increase

Check. 100 × 1.5 = 150, which is 50 more than 100. ✓

Method. Compare the multiplier with 1 (which is 100%). More than 1 is an increase; less than 1 is a decrease.

1. Write the multiplier as a percentage. Multiply by 100.
   2 × 100 = 200%
2. Compare with 100%. The original is 100%. 200% is more than 100%.
   200% − 100% = 100%
3. Say it in words.
   a 100% increase

Check. 100 × 2 = 200, which is 100 more than 100. ✓

Method. Doubled means the new price is 2 times the old one.

1. Write the multiplier. Doubling means × 2.
   2
2. Change it to a percentage. Multiply by 100.
   2 × 100 = 200%
3. Subtract the original 100%. The increase is what is added to the original.
   200% − 100% = 100%

Check. 100% of the price added on to the price makes double. ✓

Method. Treble means the new price is 3 times the old one.

1. Write the multiplier.
   3
2. Change it to a percentage. Multiply by 100.
   3 × 100 = 300%
3. Subtract the original 100%. The increase is the part added on.
   300% − 100% = 200%

Check. Adding 200% (two more lots of the price) to the price makes three lots. ✓

Method. Halved means the new price is one half of the old one.

1. Write the multiplier. A half is 0.5.
   0.5
2. Change it to a percentage. Multiply by 100.
   0.5 × 100 = 50%
3. Subtract from 100%. The decrease is what has been taken off.
   100% − 50% = 50%

Check. Half of the price has been taken off. ✓

Method. Find 12.5% of the amount, then add it to the original.

1. Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.
   12.5% = 10% + 2.5%
2. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £800 = £800 ÷ 10 = £80
3. Work out each part. Use the 10% or 1% you found.
   10% = £80
   2.5% = a quarter of 10% = £80 ÷ 4 = £20
4. Add the parts together. The parts together make up the whole percentage.
   £80 + £20 = £100
5. Add it to the original amount. We want the amount after the increase.
   £800 + £100 = £900

Check. Multiplier check: 112.5% = 1.125, and 1.125 × £800 = £900. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 7.5% of the amount, then subtract it from the original.

1. Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.
   7.5% = 5% + 2.5%
2. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 560 = 560 ÷ 10 = 56
3. Work out each part. Use the 10% or 1% you found.
   5% = half of 10% = 56 ÷ 2 = 28
   2.5% = a quarter of 10% = 56 ÷ 4 = 14
4. Add the parts together. The parts together make up the whole percentage.
   28 + 14 = 42
5. Subtract it from the original amount. We want the amount after the decrease.
   560 − 42 = 518

Check. Multiplier check: 92.5% = 0.925, and 0.925 × 560 = 518. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 2.5% of the amount, then add it to the original.

1. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of £1,200 = £1,200 ÷ 10 = £120
2. Work out each part. Multiply to build up to the percentage you want.
   2.5% = a quarter of 10% = £120 ÷ 4 = £30
3. Write the answer. Include the units.
   2.5% of £1,200 = £30
4. Add it to the original amount. We want the amount after the increase.
   £1,200 + £30 = £1,230

Check. Multiplier check: 102.5% = 1.025, and 1.025 × £1,200 = £1,230. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. Find 17.5% of the amount, then subtract it from the original.

1. Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.
   17.5% = 10% + 5% + 2.5%
2. Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).
   10% of 240 = 240 ÷ 10 = 24
3. Work out each part. Use the 10% or 1% you found.
   10% = 24
   5% = half of 10% = 24 ÷ 2 = 12
   2.5% = a quarter of 10% = 24 ÷ 4 = 6
4. Add the parts together. The parts together make up the whole percentage.
   24 + 12 + 6 = 42
5. Subtract it from the original amount. We want the amount after the decrease.
   240 − 42 = 198

Check. Multiplier check: 82.5% = 0.825, and 0.825 × 240 = 198. ✓

Watch out. Remember the last step. Finding the percentage is not the final answer: add it on or take it off.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 8% increase is 1.08.

1. Find the percentage the new amount will be. An increase of 8% means we add 8% of the original. The original is 100%, so the new amount is 100% + 8%.
   100% + 8% = 108% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   108% = 108 ÷ 100 = 1.08
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £85 × 1.08 = £91.80

Check. Other way: 8% of £85 = 6.8; £85 + 6.8 = 91.8. ✓

Watch out. Do not multiply by 0.08 only: that finds the 8% but not the new amount. The multiplier includes the original 100%.

Method. To decrease an amount by a percentage, find the multiplier and multiply. The multiplier for a 12% decrease is 0.88.

1. Find the percentage the new amount will be. A decrease of 12% means we subtract 12% of the original. The original is 100%, so the new amount is 100% − 12%.
   100% − 12% = 88% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   88% = 88 ÷ 100 = 0.88
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £250 × 0.88 = £220

Check. Other way: 12% of £250 = 30; £250 − 30 = 220. ✓

Watch out. Do not multiply by 0.12 only: that finds the 12% but not the new amount. The multiplier is what is left after the decrease.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 3.5% increase is 1.035.

1. Find the percentage the new amount will be. An increase of 3.5% means we add 3.5% of the original. The original is 100%, so the new amount is 100% + 3.5%.
   100% + 3.5% = 103.5% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   103.5% = 103.5 ÷ 100 = 1.035
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   640 × 1.035 = 662.4

Check. Other way: 3.5% of 640 = 22.4; 640 + 22.4 = 662.4. ✓

Watch out. Do not multiply by 0.035 only: that finds the 3.5% but not the new amount. The multiplier includes the original 100%.

Method. To decrease an amount by a percentage, find the multiplier and multiply. The multiplier for a 17% decrease is 0.83.

1. Find the percentage the new amount will be. A decrease of 17% means we subtract 17% of the original. The original is 100%, so the new amount is 100% − 17%.
   100% − 17% = 83% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   83% = 83 ÷ 100 = 0.83
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   3,400 × 0.83 = 2,822

Check. Other way: 17% of 3,400 = 578; 3,400 − 578 = 2,822. ✓

Watch out. Do not multiply by 0.17 only: that finds the 17% but not the new amount. The multiplier is what is left after the decrease.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 22% increase is 1.22.

1. Find the percentage the new amount will be. An increase of 22% means we add 22% of the original. The original is 100%, so the new amount is 100% + 22%.
   100% + 22% = 122% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   122% = 122 ÷ 100 = 1.22
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   1,850 × 1.22 = 2,257

Check. Other way: 22% of 1,850 = 407; 1,850 + 407 = 2,257. ✓

Watch out. Do not multiply by 0.22 only: that finds the 22% but not the new amount. The multiplier includes the original 100%.

Method. To decrease an amount by a percentage, find the multiplier and multiply. The multiplier for a 4.5% decrease is 0.955.

1. Find the percentage the new amount will be. A decrease of 4.5% means we subtract 4.5% of the original. The original is 100%, so the new amount is 100% − 4.5%.
   100% − 4.5% = 95.5% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   95.5% = 95.5 ÷ 100 = 0.955
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   280 × 0.955 = 267.4

Check. Other way: 4.5% of 280 = 12.6; 280 − 12.6 = 267.4. ✓

Watch out. Do not multiply by 0.045 only: that finds the 4.5% but not the new amount. The multiplier is what is left after the decrease.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 15% increase is 1.15.

1. Find the percentage the new amount will be. An increase of 15% means we add 15% of the original. The original is 100%, so the new amount is 100% + 15%.
   100% + 15% = 115% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   115% = 115 ÷ 100 = 1.15
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £249.99 × 1.15 = £287.4885
4. Round the answer. Round to 2 decimal places.
   £287.4885 = £287.49

Check. Other way: 15% of £249.99 = 37.50; £249.99 + 37.50 = 287.49. ✓

Watch out. Do not multiply by 0.15 only: that finds the 15% but not the new amount. The multiplier includes the original 100%.

Method. To decrease an amount by a percentage, find the multiplier and multiply. The multiplier for a 12.5% decrease is 0.875.

1. Find the percentage the new amount will be. A decrease of 12.5% means we subtract 12.5% of the original. The original is 100%, so the new amount is 100% − 12.5%.
   100% − 12.5% = 87.5% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   87.5% = 87.5 ÷ 100 = 0.875
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £64.50 × 0.875 = £56.4375
4. Round the answer. Round to 2 decimal places.
   £56.4375 = £56.44

Check. Other way: 12.5% of £64.50 = 8.06; £64.50 − 8.06 = 56.44. ✓

Watch out. Do not multiply by 0.125 only: that finds the 12.5% but not the new amount. The multiplier is what is left after the decrease.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 2.9% increase is 1.029.

1. Find the percentage the new amount will be. An increase of 2.9% means we add 2.9% of the original. The original is 100%, so the new amount is 100% + 2.9%.
   100% + 2.9% = 102.9% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   102.9% = 102.9 ÷ 100 = 1.029
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £1,875 × 1.029 = £1,929.375
4. Round the answer. Round to 2 decimal places.
   £1,929.375 = £1,929.38

Check. Other way: 2.9% of £1,875 = 54.38; £1,875 + 54.38 = 1,929.38. ✓

Watch out. Do not multiply by 0.029 only: that finds the 2.9% but not the new amount. The multiplier includes the original 100%.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 150% increase is 2.5.

1. Find the percentage the new amount will be. An increase of 150% means we add 150% of the original. The original is 100%, so the new amount is 100% + 150%.
   100% + 150% = 250% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   250% = 250 ÷ 100 = 2.5
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   40 × 2.5 = 100

Check. Other way: 150% of 40 = 60; 40 + 60 = 100. ✓

Watch out. Do not multiply by 1.5 only: that finds the 150% but not the new amount. The multiplier includes the original 100%.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 200% increase is 3.

1. Find the percentage the new amount will be. An increase of 200% means we add 200% of the original. The original is 100%, so the new amount is 100% + 200%.
   100% + 200% = 300% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   300% = 300 ÷ 100 = 3
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   £80 × 3 = £240

Check. Other way: 200% of £80 = 160; £80 + 160 = 240. ✓

Watch out. Do not multiply by 2 only: that finds the 200% but not the new amount. The multiplier includes the original 100%.

Method. To increase an amount by a percentage, find the multiplier and multiply. The multiplier for a 120% increase is 2.2.

1. Find the percentage the new amount will be. An increase of 120% means we add 120% of the original. The original is 100%, so the new amount is 100% + 120%.
   100% + 120% = 220% of the original
2. Write that percentage as a decimal: this is the multiplier. Divide by 100.
   220% = 220 ÷ 100 = 2.2
3. Multiply the original amount by the multiplier. One multiplication gives the new amount straight away.
   25 × 2.2 = 55

Check. Other way: 120% of 25 = 30; 25 + 30 = 55. ✓

Watch out. Do not multiply by 1.2 only: that finds the 120% but not the new amount. The multiplier includes the original 100%.

Method. A increase of 0.5% means the new amount is 100.5% of the original. Write 100.5% as a decimal.

1. Work out the new percentage. The original is 100%. For a increase we add 0.5%.
   100% + 0.5% = 100.5%
2. Divide by 100. To change a percentage to a decimal.
   100.5% = 100.5 ÷ 100 = 1.005
3. Check the size of the multiplier. A increase should give a multiplier above 1.
   1.005 is above 1, so it makes the amount bigger.

Check. Multiplying 100 by 1.005 gives 100.5, which is a 0.5% increase on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A decrease of 0.5% means the new amount is 99.5% of the original. Write 99.5% as a decimal.

1. Work out the new percentage. The original is 100%. For a decrease we subtract 0.5%.
   100% − 0.5% = 99.5%
2. Divide by 100. To change a percentage to a decimal.
   99.5% = 99.5 ÷ 100 = 0.995
3. Check the size of the multiplier. A decrease should give a multiplier below 1.
   0.995 is below 1, so it makes the amount smaller.

Check. Multiplying 100 by 0.995 gives 99.5, which is a 0.5% decrease on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A increase of 12.5% means the new amount is 112.5% of the original. Write 112.5% as a decimal.

1. Work out the new percentage. The original is 100%. For a increase we add 12.5%.
   100% + 12.5% = 112.5%
2. Divide by 100. To change a percentage to a decimal.
   112.5% = 112.5 ÷ 100 = 1.125
3. Check the size of the multiplier. A increase should give a multiplier above 1.
   1.125 is above 1, so it makes the amount bigger.

Check. Multiplying 100 by 1.125 gives 112.5, which is a 12.5% increase on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.

Method. A decrease of 7.25% means the new amount is 92.75% of the original. Write 92.75% as a decimal.

1. Work out the new percentage. The original is 100%. For a decrease we subtract 7.25%.
   100% − 7.25% = 92.75%
2. Divide by 100. To change a percentage to a decimal.
   92.75% = 92.75 ÷ 100 = 0.9275
3. Check the size of the multiplier. A decrease should give a multiplier below 1.
   0.9275 is below 1, so it makes the amount smaller.

Check. Multiplying 100 by 0.9275 gives 92.75, which is a 7.25% decrease on 100. ✓

Watch out. A decrease multiplier is less than 1; an increase multiplier is more than 1.