Year 6 Arithmetic (SATs) Ratio and proportion: check-up and practice test questions

Method. Divide both parts by the highest common factor.

1. Find the highest common factor of the two numbers. The biggest number that divides into 18 and 30 is 6.
   HCF = 6
2. Divide both parts of the ratio by it. Dividing both parts by the same number keeps the ratio the same.
   18 ÷ 6 = 3 and 30 ÷ 6 = 5
3. Write the answer.
   3:5

Check. 3 × 6 = 18 and 5 × 6 = 30. ✓

Method. Add the parts, then write the red part over the total.

1. Add the parts. 2 + 5 = 7.
   7
2. Red fraction. Red is 2 of the 7 parts.
   2/7
3. Write the answer.
   2/7

Check. Blue is 5/7, and 2/7 + 5/7 = 1. ✓

Method. Find one part from the boys, then multiply by 9.

1. Find the value of one unit. The boys is 4 units, so one unit is 20 ÷ 4.
   20 ÷ 4 = 5
2. Multiply by the number of units you need. The other amount has 9 units.
   5 × 9 = 45
3. Write the answer.
   45

Check. 20 boys and 45 girls is 4 : 9. ✓

Method. Share 72 in the ratio 1 : 5.

1. Add the parts of the ratio. 1 + 5 = 6, so the total is shared into 6 equal parts.
   1 + 5 = 6 parts
2. Find the value of one part. Share the total into 6 equal parts.
   72 ÷ 6 = 12
3. Find each share. Multiply the value of one part by each number in the ratio.
   1 × 12 = 12 and 5 × 12 = 60
4. Write the answer.
   60

Check. 12 + 60 = 72. ✓

Method. Share £400 into 8 parts.

1. Add the parts of the ratio. 3 + 5 = 8, so the total is shared into 8 equal parts.
   3 + 5 = 8 parts
2. Find the value of one part. Share the total into 8 equal parts.
   400 ÷ 8 = 50
3. Find each share. Multiply the value of one part by each number in the ratio.
   3 × 50 = 150 and 5 × 50 = 250
4. Write the answer.
   £150

Check. £150 + £250 = £400. ✓

Method. Find the scale factor, then the other side.

1. Find the scale factor. The scale factor is the new side divided by the old side.
   10 ÷ 4 = 5/2
2. Multiply the other side by the scale factor. Every length in the enlarged shape is multiplied by the same scale factor.
   6 × 5/2 = 15
3. Write the answer.
   15 cm

Check. 10 ÷ 4 = 2.5, and 6 × 2.5 = 15. ✓

Method. Find the weight of one bag, then multiply by 3.

1. Find the amount for one unit. 600 is shared by 4 units.
   600 ÷ 4 = 150
2. Multiply by the number of units you want. There are 3 units to find.
   150 × 3 = 450
3. Write the answer.
   450 g

Check. 150 g each, and 3 × 150 = 450 g. ✓

Method. Divide 42 by 60, then multiply by 100.

1. Write the part as a fraction of the whole. 42 out of 60.
   42/60
2. Multiply by 100 to get a percentage. Percent means out of 100.
   42/60 × 100 = 70%
3. Write the answer.
   70%

Check. 42 ÷ 60 = 0.7, which is 70%. ✓

Method. Divide 9 by 36, then multiply by 100.

1. Write the part as a fraction of the whole. 9 out of 36.
   9/36
2. Multiply by 100 to get a percentage. Percent means out of 100.
   9/36 × 100 = 25%
3. Write the answer.
   25%

Check. 9 ÷ 36 = 0.25, which is 25%. ✓

Method. Check the multiplier for each part.

1. Multiply. 2 × 2 = 4 and 5 × 2 = 10.
   4 : 10
2. Write the answer.
   Because 4 : 10 is 2 : 5 with both parts multiplied by 2.

Check. 4 ÷ 2 = 2 and 10 ÷ 2 = 5. ✓

Method. Divide both parts by 5.

1. Divide. 15 ÷ 5 = 3 and 25 ÷ 5 = 5.
   3 : 5
2. Write the answer.
   3:5

Check. 3 : 5 has no common factor. ✓

Method. Find one part from the red counters, then multiply by 5.

1. Find the value of one unit. The red is 3 units, so one unit is 24 ÷ 3.
   24 ÷ 3 = 8
2. Multiply by the number of units you need. The other amount has 5 units.
   8 × 5 = 40
3. Write the answer.
   40

Check. 24 red and 40 blue is 3 : 5. ✓

Method. Share 90 into nine parts.

1. Add the parts of the ratio. 2 + 7 = 9, so the total is shared into 9 equal parts.
   2 + 7 = 9 parts
2. Find the value of one part. Share the total into 9 equal parts.
   90 ÷ 9 = 10
3. Find each share. Multiply the value of one part by each number in the ratio.
   2 × 10 = 20 and 7 × 10 = 70
4. Write the answer.
   20

Check. 20 + 70 = 90. ✓

Method. Find the scale factor, then the other side.

1. Find the scale factor. The scale factor is the new side divided by the old side.
   12 ÷ 3 = 4
2. Multiply the other side by the scale factor. Every length in the enlarged shape is multiplied by the same scale factor.
   8 × 4 = 32
3. Write the answer.
   32 cm

Check. 12 ÷ 3 = 4, and 8 × 4 = 32. ✓

Method. Find the cost of one notebook, then multiply by 4.

1. Find the amount for one unit. 525 is shared by 7 units.
   525 ÷ 7 = 75
2. Multiply by the number of units you want. There are 4 units to find.
   75 × 4 = 300
3. Write the answer.
   300p

Check. 75p each, and 4 × 75p = 300p. ✓

Method. Divide 63 by 90, then multiply by 100.

1. Write the part as a fraction of the whole. 63 out of 90.
   63/90
2. Multiply by 100 to get a percentage. Percent means out of 100.
   63/90 × 100 = 70%
3. Write the answer.
   70%

Check. 63 ÷ 90 = 0.7, which is 70%. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what you need to find or check.
2. Test the choice. 4 : 6 divides by 2 to give 2 : 3.
   2 : 3 is right
3. Reject the other choices. 2 : 4 has a different ratio, 6 : 4 is in the wrong order, and 8 : 10 is 4 : 5.
   2 : 4 and 6 : 4 and 8 : 10 are not right
4. Write the answer.
   2 : 3

Check. 2 : 3 is right. ✓

Method. Find the value of one part.

1. Add the parts. 1 + 4 = 5.
   5
2. Find one part. 100 ÷ 5 = 20.
   20
3. Find the bigger share. 4 × 20 = 80.
   80
4. Write the answer.
   Yes, 100 ÷ 5 = 20, so the bigger share is 4 × 20 = 80.

Check. 20 + 80 = 100. ✓

Method. If 80% is 40 litres, find 10%, then 100%.

1. Find 10%. 40 ÷ 8 = 5 litres for 10%.
   5
2. Find 100%. 5 × 10 = 50 litres.
   50 litres
3. Write the answer.
   50 litres

Check. 80% of 50 is 40. ✓

Method. Share 45 into nine parts.

1. Add the parts. 4 + 5 = 9.
   9
2. Find one part. 45 ÷ 9 = 5.
   5
3. Find the bigger share. 5 × 5 = 25.
   25
4. Write the answer.
   25

Check. 20 + 25 = 45. ✓

Method. Find 25% of 80.

1. Find 25%. A quarter of 80 is 80 ÷ 4 = 20.
   20
2. Write the answer.
   20

Check. 20 is 25% of 80. ✓