Year 6 Maths reasoning (SATs): The unit method and percentages
Part of the Year 6 Maths reasoning (SATs) ratio and proportion reasoning chapter. Chapter overview · whole chapter on one page
The unit method and percentages
Rule
The unit method means finding the amount for ONE, then multiplying by the number you need.
For a percentage, find 1% of the whole first, then multiply by the percentage you want. If 75% costs 60 pounds, then 1% is 60 / 75 pounds, and 100% is 80 pounds.
Key ideas
- Find one first, then multiply.
- A percentage of a whole: find 1% first.
- When a percentage is taken off, the price paid is the percentage that is left.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 300 g is for 4, so one is 300 / 4.1 = 75 g
- Multiply for the new number. Multiply by 7.75 x 7 = 525
- Write the answer. 525 g
Check. 525 / 7 = 75, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find 1% of the original price, then multiply by 100.
- Work out 1 per cent. 60 pounds is 75% of the price, so 1% is 60 / 75.1% = 4/5
- Work out 100 per cent. The original price is 100%, so multiply 1% by 100.4/5 x 100 = 80
- Write the answer. 80
Check. 80 less 25% is 60. ✓
Watch out. The discount is taken from the original price, so the price paid is what is left.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 250 g is for 5, so one is 250 / 5.1 = 50 g
- Multiply for the new number. Multiply by 8.50 x 8 = 400
- Write the answer. 400 g
Check. 400 / 8 = 50, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Watch out
Watch out. When a shop takes 20% off, the price paid is 80% of the original, not 20%.
Exam tip
Practice guide. Write the amount for one at the top of a small table, then multiply down.
Exercise 3C Practice: the unit method and percentages
Non-calculatorMethod. Find the amount for one person, then multiply.
- Find the amount for one. 240 g is for 6, so one is 240 / 6.1 = 40 g
- Multiply for the new number. Multiply by 9.40 x 9 = 360
- Write the answer. 360 g
Check. 360 / 9 = 40, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 45 ml is for 3, so one is 45 / 3.1 = 15 ml
- Multiply for the new number. Multiply by 8.15 x 8 = 120
- Write the answer. 120 ml
Check. 120 / 8 = 15, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 1200 ml is for 4, so one is 1200 / 4.1 = 300 ml
- Multiply for the new number. Multiply by 6.300 x 6 = 1800
- Write the answer. 1800 ml
Check. 1800 / 6 = 300, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 350 g is for 5, so one is 350 / 5.1 = 70 g
- Multiply for the new number. Multiply by 12.70 x 12 = 840
- Write the answer. 840 g
Check. 840 / 12 = 70, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find 1% of the original price, then multiply by 100.
- Work out 1 per cent. 72 pounds is 80% of the price, so 1% is 72 / 80.1% = 9/10
- Work out 100 per cent. The original price is 100%, so multiply 1% by 100.9/10 x 100 = 90
- Write the answer. 90
Check. 90 less 20% is 72. ✓
Watch out. The discount is taken from the original price, so the price paid is what is left.
Method. Find 1% of the original price, then multiply by 100.
- Work out 1 per cent. 45 pounds is 60% of the price, so 1% is 45 / 60.1% = 3/4
- Work out 100 per cent. The original price is 100%, so multiply 1% by 100.3/4 x 100 = 75
- Write the answer. 75
Check. 75 less 40% is 45. ✓
Watch out. The discount is taken from the original price, so the price paid is what is left.
Method. Find the amount for one person, then multiply.
- Find the amount for one. 200 g is for 8, so one is 200 / 8.1 = 25 g
- Multiply for the new number. Multiply by 12.25 x 12 = 300
- Write the answer. 300 g
Check. 300 / 12 = 25, the same amount for each person. ✓
Watch out. Doubling the people does not always need double the ingredients unless you check the unit.
Method. Find the cost of one mile, then multiply by 7.
- One mile. 6 / 2 = 3 pounds.3 pounds
- Seven miles. 3 x 7 = 21 pounds.21 pounds
- Write the answer. 21
Check. 21 / 7 = 3. ✓
Method. Find the distance in one minute, then multiply by 40. Or work out how many 15-minute sets there are.
- Find the number of 15-minute sets. 40 is not a whole number of 15s, so find 5 minutes first.15 minutes = 3 km, so 5 minutes = 1 km
- Multiply for 40 minutes. 40 minutes = 8 lots of 5 minutes, so 8 km.8 x 1 km = 8 km
- Write the answer. 8
Check. 8 km in 40 minutes, because 15 minutes is 3 km and 5 minutes is 1 km. ✓
Method. Compare the number of people with the number of pizzas.
- Find the pizzas for one person. 2 pizzas for 4 people is 2/4 = 1/2 pizza each.1/2 pizza each
- Check for 8 people. 8 x 1/2 = 4 pizzas.4 pizzas
- Write the answer. Yes, because 8 people is double 4 people, so they need double the pizzas: 2 x 2 = 4.
Check. 8 x 1/2 = 4. ✓
Method. Find 1% of the original price, then multiply by 100.
- Work out 1 per cent. 48 pounds is 80% of the price, so 1% is 48 / 80.1% = 3/5
- Work out 100 per cent. The original price is 100%, so multiply 1% by 100.3/5 x 100 = 60
- Write the answer. 60
Check. 60 less 20% is 48. ✓
Watch out. The discount is taken from the original price, so the price paid is what is left.
Method. Find 1% of the original price, then multiply by 100.
- Work out 1 per cent. 36 pounds is 80% of the price, so 1% is 36 / 80.1% = 9/20
- Work out 100 per cent. The original price is 100%, so multiply 1% by 100.9/20 x 100 = 45
- Write the answer. 45
Check. 45 less 20% is 36. ✓
Watch out. The discount is taken from the original price, so the price paid is what is left.
Method. Find the cost for one, then use it.
- Cost for one litre. 2 pounds.2 pounds
- Cost for half a litre. 2 / 2 = 1 pound.1 pound
- Write the answer. Yes, because it finds the cost for one litre (2 pounds), then uses it to find the cost for half a litre (1 pound).
Check. 2 / 2 = 1. ✓
Method. Find the flour for one cake, then multiply by 4.
- One cake. 450 / 6 = 75 g.75 g
- Four cakes. 75 x 4 = 300 g.300 g
- Write the answer. 300
Check. 300 / 4 = 75. ✓