Percentage of an Amount

Fifty per cent is one half.

Ten per cent is one tenth.

One per cent is one hundredth.

Twenty-five per cent is one quarter.

Find 10% first and then halve it.

Twenty per cent is twice ten per cent, or one fifth.

1. 20\%=\frac15.
2. 75\div5=15, so the amount is £15.

Combine 10% and 5%.

1. 10\% is 180\div10=18.
2. 5\% is 18\div2=9.
3. 15\% is 18+9=27.

Seventy-five per cent is three quarters.

1. One quarter is 64\div4=16.
2. Three quarters are 16\times3=48.

Find 1% first, then multiply by seven.

1. 1\% is 450\div100=4.5.
2. 7\% is 4.5\times7=31.5.

Write 12% as a decimal multiplier and multiply by the total mass.

1. 12\%=\frac{12}{100}=0.12.
2. Dried fruit mass: 250\times0.12=30 g.

125% is the whole amount plus one quarter of it.

1. 100\% is £56. 25\% is 56\div4=14 pounds.
2. 125\% is 56+14=70 pounds, or £70.

You can build 35% from 30% and 5%, or use a decimal multiplier.

1. 10\% is 240\div10=24, so 30\% is 24\times3=72.
2. 5\% is 24\div2=12.
3. 35\% is 72+12=84 students.

The question asks for the reduction, so find 18% of the original price.

1. 18\%=0.18.
2. The reduction is 75\times0.18=13.50, or £13.50.
3. This is the money taken off, not the sale price.

Find the percentage that has not been covered.

1. The remaining percentage is 100-65=35\%.
2. 35\%=0.35, so the amount still needed is 480\times0.35=168 pounds.
3. The club must still raise £168.

Both percentages refer to the same 90-minute total. Find the percentage left for algebra.

1. Fractions and ratio use 40+20=60\% of the time.
2. Algebra gets 100-60=40\%.
3. 10\% of 90 is 9, so 40\% is 9\times4=36 minutes.

The £42 represents 30%, not 100%. Find 10% or 1% first.

1. 30\% is £42, so 10\% is 42\div3=14 pounds.
2. The whole target is 100\%, which is ten lots of 10\%.
3. 14\times10=140, so the target is £140.

Calculate the money saved by each offer; the percentages apply to different original prices.

1. Offer A saves 64\div4=16 pounds because 25\%=\frac14.
2. Offer B saves 85\div5=17 pounds because 20\%=\frac15.
3. 17-16=1, so Offer B saves £1 more.
4. A larger percentage does not always give a larger saving when the original amounts are different.

Find the percentage left, work out that amount of money, then divide by the amount each person contributes.

1. The sponsor and donations cover 35+40=75\% of the target.
2. The remaining 25\% is one quarter: 2600\div4=650 pounds.
3. Number of people: 650\div25=26.
4. Check: 26\times25=650, so 26 people cover exactly the remaining amount.

After finding the art group, subtract it. The 25% applies to the new remaining number, not to all 80 students.

Part (a)

1. Art students: 80\div10\times3=24.
2. Students remaining: 80-24=56.
3. Drama students: 56\div4=14, because 25\%=\frac14.

Part (b)

1. After art, 56 students remained. Of these, 14 chose drama.
2. Sport students: 56-14=42. Check: 24+14+42=80.

Find the full target from the known 35%, then subtract all the money raised so far.

1. 35\% is £84, so 1\% is 84\div35=2.40 pounds.
2. The target is 100\%: 2.40\times100=240 pounds.
3. Money raised after the new donation: 84+30=114 pounds.
4. Money still needed: 240-114=126 pounds, or £126.