Year 6 Maths reasoning (SATs) · Ratio and proportion reasoning · Test yourself

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

Part of the Year 6 Maths reasoning (SATs) ratio and proportion reasoning chapter. Chapter overview · whole chapter on one page

Exercise 3Z Check-up

Non-calculator

Write the ratio 28:35 in its simplest form.

4:5

Method. Divide both parts of the ratio by the highest common factor.

Find the highest common factor of both numbers. The biggest number that divides 28 and 35 is 7.
HCF = 7
Divide both parts by it. 28 / 7 = 4 and 35 / 7 = 5.
4:5
Write the answer.
4:5

Check. 4 and 5 have no common factor except 1. ✓

Watch out. Both parts must be divided by the same number, just as with a fraction.

Done

The ratio of stars to circles is 3:8. There are 27 stars. How many circles are there?

Method. Find the value of one part, then multiply.

Find the value of one part. 27 is 3 parts, so one part is 27 / 3.
1 part = 9
Multiply to find the other amount. There are 8 parts of circles.
8 x 9 = 72
Write the answer.
72

Check. 72 : 27 = 3:8. ✓

Watch out. Do not add the ratio numbers to the amount. Find one part first.

Done

Leo and Ann share 180 in the ratio 2:7. How much does each person get? Write the amounts in the same order as the names.

40, 140

Method. Find the total parts, then the value of one part.

Find the total number of parts. 2 + 7 = 9 parts.
9 parts
Find the value of one part. 180 / 9 = 20.
1 part = 20
Multiply each ratio number by one part. Leo: 2 x 20 and Ann: 7 x 20
40, 140
Write the answer.
40, 140

Check. 40 + 140 = 180. ✓

Watch out. Check that the amounts add up to the total.

Done

In the ratio 3:5, what fraction of the total is the part shown by 5? Write the fraction.

5/8

Method. The total is the sum of all the parts, so the fraction is that part over the total.

Find the total number of parts. 3 + 5 = 8.
8 parts
Write the part as a fraction of the total, in simplest form. The part is 5 out of 8 parts, which simplifies to 5/8.
5/8
Write the answer.
5/8

Check. 5 + 3 = 8. ✓

Watch out. The fraction uses the total of all parts, not the other part only.

Done

A recipe for 6 people uses 360 ml of milk. How much milk is needed for 10 people? Write the amount in ml.

600 ml

Method. Find the amount for one person, then multiply.

Find the amount for one. 360 ml is for 6, so one is 360 / 6.
1 = 60 ml
Multiply for the new number. Multiply by 10.
60 x 10 = 600
Write the answer.
600 ml

Check. 600 / 10 = 60, the same amount for each person. ✓

Watch out. Doubling the people does not always need double the ingredients unless you check the unit.

Done

After 10% is taken off, a hat costs 54 pounds. What was the original price, in pounds?

Method. Find 1% of the original price, then multiply by 100.

Work out 1 per cent. 54 pounds is 90% of the price, so 1% is 54 / 90.
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 10% is 54. ✓

Watch out. The discount is taken from the original price, so the price paid is what is left.

Done

Pack P: 4 items cost 320p. Pack Q: 6 items cost 420p. Which is better value for one item? Write the name.

Pack Q

Method. Work out the price of one item for each pack, then compare.

Work out the price of one item in Pack P. 320p / 4 = 80p.
80p
Work out the price of one item in Pack Q. 420p / 6 = 70p.
70p
Compare the prices of one item. The cheaper one for one item is the better value.
Pack Q is cheaper for one item
Write the answer.
Pack Q

Check. Pack Q costs less for each item. ✓

Watch out. Compare the price of ONE item. A bigger pack is not always cheaper for each item.

Done

Ali scored 7 from 10 shots, and Jo scored 9 from 15 shots. Which had the better success rate? Write the name.

Ali

Method. Write each result as a percentage, then compare.

Work out the percentage for Ali. 7 out of 10 is 7 / 10 x 100.
70%
Work out the percentage for Jo. 9 out of 15 is 9 / 15 x 100.
60%
Compare the two percentages. The higher percentage is the better result.
Ali is higher
Write the answer.
Ali

Check. 70% and 60% are compared fairly. ✓

Watch out. Comparing 30 with 24 is not fair when the numbers of shots are different.

Done

A shape of length 6 cm is enlarged to 15 cm. What is the scale factor?

2.5

Method. Divide the new length by the original length.

Write the scale factor as a division. The scale factor is the new length divided by the original.
15 / 6
Work it out. 15 / 6 = 2.5.
2.5
Write the answer.
2.5

Check. 6 x 2.5 = 15. ✓

Watch out. A scale factor bigger than 1 makes a shape bigger.

Done

A rectangle is enlarged by scale factor 3. One side of the original is 5 cm and the matching side of the enlarged rectangle is 15 cm. Another side of the original is 4 cm. How long is that side in the enlarged rectangle?

Method. Multiply each length of the original by the scale factor.

Use the scale factor. Each length is multiplied by the scale factor 3.
4 x 3
Work it out. 4 x 3 = 12.
12
Write the answer.
12

Check. 4 x 3 = 12, and 5 x 3 = 15. ✓

Watch out. Check the scale factor with the side you know first.

Done

Total 19 marks. Allow about 19 minutes.

Exercise 3X Practice test questions

Non-calculator

FWrite the ratio 18:27 in its simplest form.[1 mark]

2:3

Method. Divide both parts of the ratio by the highest common factor.

Find the highest common factor of both numbers. The biggest number that divides 18 and 27 is 9.
HCF = 9
Divide both parts by it. 18 / 9 = 2 and 27 / 9 = 3.
2:3
Write the answer.
2:3

Check. 2 and 3 have no common factor except 1. ✓

Watch out. Both parts must be divided by the same number, just as with a fraction.

Done

FThe ratio of pens to pencils is 5:3. There are 21 pencils. How many pens are there?[1 mark]

Method. Find the value of one part, then multiply.

Find the value of one part. 21 is 3 parts, so one part is 21 / 3.
1 part = 7
Multiply to find the other amount. There are 5 parts of pens.
5 x 7 = 35
Write the answer.
35

Check. 35 : 21 = 5:3. ✓

Watch out. Do not add the ratio numbers to the amount. Find one part first.

Done

PSBen and Eve share 84 in the ratio 1:3. How much does each person get? Write the amounts in the same order as the names.[2 marks]

21, 63

Method. Find the total parts, then the value of one part.

Find the total number of parts. 1 + 3 = 4 parts.
4 parts
Find the value of one part. 84 / 4 = 21.
1 part = 21
Multiply each ratio number by one part. Ben: 1 x 21 and Eve: 3 x 21
21, 63
Write the answer.
21, 63

Check. 21 + 63 = 84. ✓

Watch out. Check that the amounts add up to the total.

Done

PSA recipe for 3 people uses 150 g of sugar. How much sugar is needed for 9 people? Write the amount in g.[2 marks]

450 g

Method. Find the amount for one person, then multiply.

Find the amount for one. 150 g is for 3, so one is 150 / 3.
1 = 50 g
Multiply for the new number. Multiply by 9.
50 x 9 = 450
Write the answer.
450 g

Check. 450 / 9 = 50, the same amount for each person. ✓

Watch out. Doubling the people does not always need double the ingredients unless you check the unit.

Done

PSTub A: 5 items cost 400p. Tub B: 3 items cost 228p. Which is better value for one item? Write the name.[2 marks]

Tub B

Method. Work out the price of one item for each pack, then compare.

Work out the price of one item in Tub A. 400p / 5 = 80p.
80p
Work out the price of one item in Tub B. 228p / 3 = 76p.
76p
Compare the prices of one item. The cheaper one for one item is the better value.
Tub B is cheaper for one item
Write the answer.
Tub B

Check. Tub B costs less for each item. ✓

Watch out. Compare the price of ONE item. A bigger pack is not always cheaper for each item.

Done

PSAda scored 20 from 25 shots, and Ben scored 24 from 40 shots. Which had the better success rate? Write the name.[2 marks]

Ada

Method. Write each result as a percentage, then compare.

Work out the percentage for Ada. 20 out of 25 is 20 / 25 x 100.
80%
Work out the percentage for Ben. 24 out of 40 is 24 / 40 x 100.
60%
Compare the two percentages. The higher percentage is the better result.
Ada is higher
Write the answer.
Ada

Check. 80% and 60% are compared fairly. ✓

Watch out. Comparing 30 with 24 is not fair when the numbers of shots are different.

Done

PSA rectangle is enlarged by scale factor 2.5. One side of the original is 4 cm and the matching side of the enlarged rectangle is 10 cm. Another side of the original is 6 cm. How long is that side in the enlarged rectangle?[2 marks]

Method. Multiply each length of the original by the scale factor.

Use the scale factor. Each length is multiplied by the scale factor 2.5.
6 x 2.5
Work it out. 6 x 2.5 = 15.
15
Write the answer.
15

Check. 6 x 2.5 = 15, and 4 x 2.5 = 10. ✓

Watch out. Check the scale factor with the side you know first.

Done

RExplain why the ratio 4:8 is the same as the ratio 1:2.[2 marks]

Accept any answer that says both parts of 4:8 are divided by 4 to give 1:2. For example: Because 4 and 8 can both be divided by 4, giving 1 and 2.

Method. Divide both parts by the same number.

Divide both parts by 4. 4 / 4 = 1 and 8 / 4 = 2.
1:2
Compare. So 4:8 = 1:2.
4:8 = 1:2
Write the answer.
Because 4 and 8 can both be divided by 4, giving 1 and 2.

Check. 1:2 x 4 = 4:8. ✓

Done

PSA bag contains red and yellow sweets in the ratio 5:4. There are 45 sweets altogether. How many yellow sweets are there?[2 marks]

Method. Find the value of one part.

Total parts. 5 + 4 = 9 parts.
9 parts
One part. 45 / 9 = 5.
5
Yellow. 4 parts: 4 x 5 = 20.
20
Write the answer.
20

Check. 25 red and 20 yellow make 45. ✓

Done

FTwo similar rectangles have a scale factor of 3. The original is 4 cm wide. What is the width of the enlarged rectangle? Choose one: 12 cm, 7 cm or 1.33 cm.[1 mark]

12 cm

Method. Test each choice against the question.

Read what the question asks. Decide what the answer must do or show.
Test the choice. 4 x 3 = 12, so the enlarged width is 12 cm.
12 cm fits
Reject the other choices. 7 would be 4 + 3, and 1.33 would be 4 divided by 3, which makes the shape smaller.
7 cm and 1.33 cm do not fit
Write the answer.
12 cm

Check. 12 cm is the one that fits. ✓

Done

RTick the statements that are true about ratios. Options: 3:6 is the same as 1:2 | 2:5 is the same as 5:2 | A ratio of 1:4 means the second part is 4 times the first | A ratio of 1:4 means one part in 4 is the first. Write the options you would tick, in the order given.[2 marks]

3:6 is the same as 1:2, A ratio of 1:4 means the second part is 4 times the first

Method. Test each option.

Check each option. Test each one against the rule or the calculation.
Tick the true ones. Each ticked statement is correct: 3:6 divided by 3 gives 1:2, and 4 parts is 4 times 1 part.
3:6 is the same as 1:2, A ratio of 1:4 means the second part is 4 times the first
Leave the others unticked. These do not match.
2:5 is the same as 5:2, A ratio of 1:4 means one part in 4 is the first are not ticked
Write the answer.
3:6 is the same as 1:2, A ratio of 1:4 means the second part is 4 times the first

Check. Each ticked option is true. ✓

Watch out. 2:5 and 5:2 are different ratios, so the order matters.

Done

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