Percentage Change

Compare 18 with the whole amount, 60.

Use all 28 matches as the whole.

The result can be greater than 100%.

Find the number that are not broken first.

Use the same length unit for both quantities.

Compare the increase with the original price.

1. Increase: 46-40=6 pounds.
2. 6\div40\times100=15\%.

Use the original mass as the base.

1. Decrease: 80-68=12 kg.
2. 12\div80\times100=15\%.

Distinguish the new price from the amount of increase.

1. The increase is £10.
2. 10\div50\times100=20\%. The new price is 120% of the old price; that is not the percentage increase.

Profit is compared with the buying cost.

1. Profit: 40-32=8 pounds.
2. 8\div32\times100=25\%.

Compare the loss with the original cost.

1. Loss: 240-198=42 pounds.
2. 42\div240\times100=17.5\%.

Calculate the increase before dividing by the old price.

1. Increase: 2.70-2.40=0.30 pounds.
2. 0.30\div2.40\times100=12.5\%.

Keep the full division result until the final rounding.

1. Decrease: 175-149=26.
2. 26\div175\times100=14.857142\ldots\%.
3. To 1 decimal place, the decrease is 14.9\%.

The whole is all available seats, not just those indoors.

1. Total seats: 24+16=40. Occupied seats: 24+6=30.
2. 30\div40\times100=75\%.

Compare each increase with its own original price.

Part (a)

1. 4\div20\times100=20\%.

Part (b)

1. 7\div50\times100=14\%.
2. B has the greater money increase, but A has the greater percentage increase.

Compare the two totals.

1. Old total: 180+220=400. New total: 192+228=420.
2. 20\div400\times100=5\%.

All the badges were paid for, including the unsold ones.

1. Income: 130\times0.50=65 pounds.
2. Profit: 65-48=17 pounds.
3. 17\div48\times100=35.4166\ldots\%, so the profit is 35.4\%.

Find total cost and total income before comparing them.

1. Cost: 60\times0.80+40\times1.20=96 pounds.
2. Income: 60\times1.20+40\times1.50=132 pounds.
3. Profit: 132-96=36 pounds.
4. 36\div96\times100=37.5\%.

Calculate both percentage increases before dividing.

1. Small box: 5\div25\times100=20\%.
2. Large box: 12\div40\times100=30\%.
3. 30\div20=1.5 times.

Calculate July’s membership, then compare it with January.

1. July membership: 300\times0.90=270.
2. Overall increase: 270-250=20 members.
3. 20\div250\times100=8\%.
4. Adding the separate percentage changes would use different bases.

Include delivery in the original cost.

1. Total cost: 80\times1.50+18=138 pounds.
2. Income: 60\times2.50+20\times1=170 pounds.
3. Profit: 170-138=32 pounds.
4. 32\div138\times100=23.1884\ldots\%, which rounds to 23.2\%.