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SATs practice · Year 6Chapter 3 · Ratio and proportion reasoning
Year 6 · Chapter 3

Ratio and proportion reasoning

By the end of this chapter you will be able to

  • Simplify a ratio and find a missing amount from a ratio
  • Share an amount in a given ratio and write each share
  • Use the unit method to scale a recipe or a rate
  • Compare the price of one item to decide which is better value
  • Find a scale factor and use it to find a missing length

You should already know

  • Multiplication and division facts, and equivalent fractions (Year 4 and Year 5)
  • Fractions of amounts and percentages (Chapter 2 of this book)

Where this leads

  • Measures in context (Chapter 4 of this book)

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: Solve problems involving the relative sizes of two quantities where missing values can be found by integer multiplication or division (Year 5-6), Use the ratio language a:b and the link between ratio and fractions (Year 6), Solve problems of unequal sharing and grouping using fractions and multiples (Year 6), Use the unit method for proportion, including percentages of a whole (Year 5-6), Solve problems involving similar shapes where the scale factor is known or can be found (Year 6), Use proportional reasoning to compare prices and quantities, and explain why a comparison is or is not fair (Year 5-6).

Exercise P  Do you remember?

Non-calculator
1
FWrite the ratio 4:6 in its simplest form.
2
FWork out 1/4 of 28.
3
FWhat is 10% of 250?
4
FWork out 6 x 15.
5
FWrite the scale factor that takes 3 cm to 12 cm.
3.1

Ratio language and simplifying ratios

Year 6
Solve problems involving the relative sizes of two quantities where missing values can be found by integer multiplication or division (Year 5-6), Use the ratio language a:b and the link between ratio and fractions (Year 6)
Video lesson: Ratio language and simplifying ratiosComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. Lena is painting a wall. She mixes 3 tins of blue paint for every 5 tins of white paint, so that the shade is always the same.

Rule

A ratio compares two amounts. 3:5 means for every 3 of one thing there are 5 of the other.

Write a ratio in its simplest form by dividing both parts by the same number. 12:18 = 2:3.

To find a missing amount, find the value of one part first, then multiply.

Key ideas

  • Divide both parts of a ratio by the same number to simplify it.
  • In a ratio of 2:3 there are 5 parts altogether, so the first part is 2/5 of the total.
  • Find the value of one part, then multiply, to find a missing amount.
Worked example 3.1.1
Write the ratio 15:25 in its simplest form.

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

  1. Find the highest common factor of both numbers. The biggest number that divides 15 and 25 is 5.
    HCF = 5
  2. Divide both parts by it. 15 / 5 = 3 and 25 / 5 = 5.
    3:5
  3. Write the answer.
    3:5

Check. 3 and 5 have no common factor except 1. ✓

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

Worked example 3.1.2
The ratio of red to blue is 3:5. There are 18 red. How many blue are there?

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

  1. Find the value of one part. 18 is 3 parts, so one part is 18 / 3.
    1 part = 6
  2. Multiply to find the other amount. There are 5 parts of blue.
    5 x 6 = 30
  3. Write the answer.
    30

Check. 30 : 18 = 3:5. ✓

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

Worked example 3.1.3
The ratio of cats to dogs is 2:7. There are 21 dogs. How many cats are there?

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

  1. Find the value of one part. 21 is 7 parts, so one part is 21 / 7.
    1 part = 3
  2. Multiply to find the other amount. There are 2 parts of cats.
    2 x 3 = 6
  3. Write the answer.
    6

Check. 6 : 21 = 2:7. ✓

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

Watch out

Watch out. A ratio is not a fraction of the whole. In 2:3 there are 5 parts altogether, so the first part is 2/5 of the total.

Exam tip

Practice guide. Write the ratio above the amounts in a table, then fill in the missing value.

Exercise 3A  Practice: ratio language and simplifying

Non-calculator
1
FWrite the ratio 12:20 in its simplest form.
2
FWrite the ratio 45:30 in its simplest form.
3
FThe ratio of boys to girls is 2:3. There are 12 boys. How many girls are there?
4
FThe ratio of apples to pears is 4:5. There are 35 pears. How many apples are there?
5
FThe ratio of blue to green is 3:7. There are 49 green. How many blue are there?
6
FThe ratio of miles to laps is 5:2. There are 25 miles. How many laps are there?
7
FThe ratio of cats to dogs at a shelter is 2:5. Choose one: For every 2 cats there are 5 dogs, For every 5 cats there are 2 dogs or For every 7 cats there are 2 dogs.
8
FTick the ratios that are equivalent to 2:3. Options: 4:6 | 3:2 | 6:9 | 5:6 | 8:10. Write the options you would tick, in the order given.
9
PSThe ratio of sugar to flour is 1:4. There are 240 flour. How many sugar are there?
10
PSThe ratio of girls to boys in a class is 3:4. There are 28 pupils altogether. How many girls are there?
11
RAli says the ratio 3:6 is the same as 1:2. Is he right? Explain.
12
PSA pack of crisps has salt and vinegar flavours in the ratio 5:3. There are 40 bags altogether. How many bags are salt and vinegar? Write the number of salt and vinegar bags, in that order, separated by a comma.
13
RMaya says that in the ratio 2:5, the first part is 2/5 of the total, and the second part is 3/5 of the total. Is she right?
14
PSThe ratio of red to blue beads is 4:9. There are 36 blue beads. How many red beads are there?
15
RBen says: "A ratio of 6:9 means the same as 2:3, so I can use 2:3 for any problem about 6:9." Is he right? Write yes or no.
16
PSA bag has 20 counters in the ratio 3:2 for red and blue. What is the number of blue counters? Write one number.
3.2

Sharing in a ratio and fractions of a total

Year 6
Solve problems of unequal sharing and grouping using fractions and multiples (Year 6), Use the ratio language a:b and the link between ratio and fractions (Year 6)
Video lesson: Sharing in a ratio and fractions of a totalComing soon
Story. Ali and Bea are sharing the prize money from a sponsored walk. They agree to share the money in the ratio 1:3, because Bea walked three times as far as Ali.

Rule

To share in a ratio, add the parts to find the total number of parts. Then find the value of one part.

A part of a ratio is a fraction of the total. In 2:3, the first part is 2/5 of the total, because 2 + 3 = 5.

Key ideas

  • Total parts first: 1 + 3 = 4 parts.
  • The value of one part = total amount / total parts.
  • Each person gets their ratio number of parts.
Worked example 3.2.1
Ali and Bea share 120 in the ratio 1:3. How much does each person get? Write the amounts in the same order as the names.

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

  1. Find the total number of parts. 1 + 3 = 4 parts.
    4 parts
  2. Find the value of one part. 120 / 4 = 30.
    1 part = 30
  3. Multiply each ratio number by one part. Ali: 1 x 30 and Bea: 3 x 30
    30, 90
  4. Write the answer.
    30, 90

Check. 30 + 90 = 120. ✓

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

Worked example 3.2.2
In the ratio 2:3, what fraction of the total is the part shown by 2? Write the fraction.

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

  1. Find the total number of parts. 2 + 3 = 5.
    5 parts
  2. Write the part as a fraction of the total, in simplest form. The part is 2 out of 5 parts, which simplifies to 2/5.
    2/5
  3. Write the answer.
    2/5

Check. 2 + 3 = 5. ✓

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

Worked example 3.2.3
Ann and Ben and Cal share 300 in the ratio 2:3:5. How much does each person get? Write the amounts in the same order as the names.

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

  1. Find the total number of parts. 2 + 3 + 5 = 10 parts.
    10 parts
  2. Find the value of one part. 300 / 10 = 30.
    1 part = 30
  3. Multiply each ratio number by one part. Ann: 2 x 30 and Ben: 3 x 30 and Cal: 5 x 30
    60, 90, 150
  4. Write the answer.
    60, 90, 150

Check. 60 + 90 + 150 = 300. ✓

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

Watch out

Watch out. Share the money into the number of parts, not into the number of people.

Exam tip

Practice guide. Check that your shares add up to the total before you write the answer.

Exercise 3B  Practice: sharing in a ratio

Non-calculator
1
FTom and Sam share 90 in the ratio 1:2. How much does each person get? Write the amounts in the same order as the names.
2
FMia and Leo share 144 in the ratio 3:5. How much does each person get? Write the amounts in the same order as the names.
3
FAva and Ben and Cy share 500 in the ratio 2:3:5. How much does each person get? Write the amounts in the same order as the names.
4
FIn the ratio 3:4, what fraction of the total is the part shown by 4? Write the fraction.
5
FIn the ratio 1:3, what fraction of the total is the part shown by 1? Write the fraction.
6
FIn the ratio 2:5:3, what fraction of the total is the part shown by 3? Write the fraction.
7
PSIn the ratio 2:4, what fraction of the total is the part shown by 2? Write the fraction.
8
PSPriya and Jo share 75 pounds in the ratio 2:3. How much more money does Jo get than Priya, in pounds?
9
PSWrite the ratio 12:18 in its simplest form.
10
RSam says that in the ratio 2:3, the first part is 2/3 of the total. Is he right? Choose one: No, it is 2/5 of the total, Yes, it is 2/3 of the total or No, it is 2/3 of the second part only.
11
PSA school choir has 30 members. The ratio of sopranos to altos is 2:1, and there are no other voices. How many sopranos are there?
12
RExplain why a ratio of 1:2 means the second amount is twice the first.
13
PSTom and Ben share sweets in the ratio 4:5. Tom gets 24 sweets. How many sweets are there altogether?
14
PSA sum of money is split into 3 shares in the ratio 1:2:3. The largest share is 36 pounds. What is the total of the money, in pounds?
15
RWrite the fraction of the total that is the share for the middle person, in the ratio 1:2:3. Write the fraction in simplest form.
3.3

The unit method and percentages

Year 6
Use the unit method for proportion, including percentages of a whole (Year 5-6)
Video lesson: The unit method and percentagesComing soon
Story. Mr Cole is cooking rice for a school lunch. His recipe is for 4 people, and he needs to know how much rice to buy for 7 people. Later, a coat in the shop has been reduced, and his son wants to work out the price before the reduction.

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.
Worked example 3.3.1
A recipe for 4 people uses 300 g of pasta. How much pasta is needed for 7 people? Write the amount in g.

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

  1. Find the amount for one. 300 g is for 4, so one is 300 / 4.
    1 = 75 g
  2. Multiply for the new number. Multiply by 7.
    75 x 7 = 525
  3. 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.

Worked example 3.3.2
After 25% is taken off, a bike costs 60 pounds. What was the original price, in pounds?

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

  1. Work out 1 per cent. 60 pounds is 75% of the price, so 1% is 60 / 75.
    1% = 4/5
  2. Work out 100 per cent. The original price is 100%, so multiply 1% by 100.
    4/5 x 100 = 80
  3. 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.

Worked example 3.3.3
A recipe for 5 people uses 250 g of flour. How much flour is needed for 8 people? Write the amount in g.

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

  1. Find the amount for one. 250 g is for 5, so one is 250 / 5.
    1 = 50 g
  2. Multiply for the new number. Multiply by 8.
    50 x 8 = 400
  3. 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-calculator
1
FA recipe for 6 people uses 240 g of rice. How much rice is needed for 9 people? Write the amount in g.
2
FA recipe for 3 people uses 45 ml of juice. How much juice is needed for 8 people? Write the amount in ml.
3
FA recipe for 4 people uses 1200 ml of paint. How much paint is needed for 6 people? Write the amount in ml.
4
FA recipe for 5 people uses 350 g of oats. How much oats is needed for 12 people? Write the amount in g.
5
FAfter 20% is taken off, a coat costs 72 pounds. What was the original price, in pounds?
6
FAfter 40% is taken off, a game costs 45 pounds. What was the original price, in pounds?
7
PSA recipe for 8 people uses 200 g of butter. How much butter is needed for 12 people? Write the amount in g.
8
PSA taxi charges 6 pounds for 2 miles. How much does it charge for 7 miles, in pounds?
9
PSMia runs 3 km in 15 minutes at a steady speed. How far does she run in 40 minutes, in km?
10
RMax says that if 4 people need 2 pizzas, then 8 people need 4 pizzas. Is he right? Explain.
11
RAfter 20% is taken off, a boots costs 48 pounds. What was the original price, in pounds?
12
PSAfter 20% is taken off, a toy costs 36 pounds. What was the original price, in pounds?
13
RA school says a litre of juice costs 2 pounds, so half a litre costs 1 pound. Is this the unit method? Explain.
14
PSA recipe for 6 cakes uses 450 g of flour. How much flour is needed for 4 cakes, in grams?
3.4

Best value and fair comparisons

Year 6
Use proportional reasoning to compare prices and quantities, and explain why a comparison is or is not fair (Year 5-6)
Video lesson: Best value and fair comparisonsComing soon
Story. At the school shop, Pack A has 6 flapjacks for 240 pence, and Pack B has 4 flapjacks for 180 pence. The children argue about which is better value.

Rule

To compare prices, find the price of one item. The lower price for one item is the better value.

To compare results fairly, use the same basis. Compare percentages when the totals are different.

Key ideas

  • Price per item = total price / number of items.
  • A bigger pack is not always cheaper per item.
  • Compare percentages, not raw scores, when the number of tries is different.
Worked example 3.4.1
Pack A: 6 items cost 240p. Pack B: 4 items cost 180p. Which is better value for one item? Write the name.

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

  1. Work out the price of one item in Pack A. 240p / 6 = 40p.
    40p
  2. Work out the price of one item in Pack B. 180p / 4 = 45p.
    45p
  3. Compare the prices of one item. The cheaper one for one item is the better value.
    Pack A is cheaper for one item
  4. Write the answer.
    Pack A

Check. Pack A costs less for each item. ✓

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

Worked example 3.4.2
Team A scored 24 from 30 shots, and Team B scored 30 from 40 shots. Which had the better success rate? Write the name.

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

  1. Work out the percentage for Team A. 24 out of 30 is 24 / 30 x 100.
    80%
  2. Work out the percentage for Team B. 30 out of 40 is 30 / 40 x 100.
    75%
  3. Compare the two percentages. The higher percentage is the better result.
    Team A is higher
  4. Write the answer.
    Team A

Check. 80% and 75% are compared fairly. ✓

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

Worked example 3.4.3
Box X: 3 items cost 90p. Box Y: 5 items cost 175p. Which is better value for one item? Write the name.

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

  1. Work out the price of one item in Box X. 90p / 3 = 30p.
    30p
  2. Work out the price of one item in Box Y. 175p / 5 = 35p.
    35p
  3. Compare the prices of one item. The cheaper one for one item is the better value.
    Box X is cheaper for one item
  4. Write the answer.
    Box X

Check. Box X costs less for each item. ✓

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

Watch out

Watch out. Team B scored more goals in total, but they are not the better team if they had more attempts.

Exam tip

Practice guide. Put the same unit (pence per item, or percentage) on both sides before you compare.

Exercise 3D  Practice: best value and fair comparisons

Non-calculator
1
FBox X: 4 items cost 300p. Box Y: 6 items cost 390p. Which is better value for one item? Write the name.
2
FPacket A: 5 items cost 400p. Packet B: 8 items cost 600p. Which is better value for one item? Write the name.
3
FSam scored 18 from 20 shots, and Lou scored 21 from 30 shots. Which had the better success rate? Write the name.
4
FTeam Red scored 12 from 15 shots, and Team Blue scored 16 from 25 shots. Which had the better success rate? Write the name.
5
PSWhich is better value: 500 g of oats for 250 pence, or 750 g for 360 pence? Write the size of the better-value pack in grams.
6
PSA jar holds 1.5 litres for 2.10 pounds. Another jar holds 2 litres for 2.60 pounds. Which jar is cheaper per litre? Write 1.5 litres or 2 litres.
7
RWhich comparison is fair when two shops have different numbers of customers? Choose one: Compare the percentage of customers who bought something, Compare only the number of sales or Compare the number of shops.
8
RExplain why a bigger pack is not always better value.
9
PSRavi scored 15 from 20 shots, and Ben scored 36 from 50 shots. Which had the better success rate? Write the name.
10
RA cinema sold 180 tickets in one week, and 300 tickets in another week. Which week was the better week for sales, if the cinema had 300 seats in each week? Write the week, 1 or 2.
11
RBen says that 9 out of 10 is better than 19 out of 20, because 10 is less than 20. Explain why he is wrong.
3.5

Similar shapes and scale factors

Year 6
Solve problems involving similar shapes where the scale factor is known or can be found (Year 6)
Video lesson: Similar shapes and scale factorsComing soon
Story. Ruth has a photograph 4 cm wide. She enlarges it on a computer so that it is 12 cm wide. The photo is the same shape, so every length is enlarged in the same way.

Rule

Two shapes are similar when one is an enlargement of the other. All lengths are multiplied by the same scale factor.

Scale factor = new length / original length. Missing length = original length x scale factor.

Key ideas

  • Scale factor = new length / original length.
  • Every length is multiplied by the same scale factor.
  • Angles stay the same in similar shapes.
Worked example 3.5.1
A shape of length 4 cm is enlarged to 12 cm. What is the scale factor?

Method. Divide the new length by the original length.

  1. Write the scale factor as a division. The scale factor is the new length divided by the original.
    12 / 4
  2. Work it out. 12 / 4 = 3.
    3
  3. Write the answer.
    3

Check. 4 x 3 = 12. ✓

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

Worked example 3.5.2
A rectangle is enlarged by scale factor 2.5. One side of the original is 8 cm and the matching side of the enlarged rectangle is 20 cm. Another side of the original is 6 cm. How long is that side in the enlarged rectangle?

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

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

Check. 6 x 2.5 = 15, and 8 x 2.5 = 20. ✓

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

Worked example 3.5.3
A shape of length 5 cm is enlarged to 20 cm. What is the scale factor?

Method. Divide the new length by the original length.

  1. Write the scale factor as a division. The scale factor is the new length divided by the original.
    20 / 5
  2. Work it out. 20 / 5 = 4.
    4
  3. Write the answer.
    4

Check. 5 x 4 = 20. ✓

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

Watch out

Watch out. Find the scale factor from one pair of matching sides, then use it for every other length.

Exam tip

Practice guide. Write the scale factor next to the shape, so you can use it again.

Exercise 3E  Practice: similar shapes and scale factors

Non-calculator
1
FA shape of length 4 cm is enlarged to 10 cm. What is the scale factor?
2
FA shape of length 7 cm is enlarged to 21 cm. What is the scale factor?
3
FA rectangle is enlarged by scale factor 3. One side of the original is 4 cm and the matching side of the enlarged rectangle is 12 cm. Another side of the original is 5 cm. How long is that side in the enlarged rectangle?
4
FA rectangle is enlarged by scale factor 2. One side of the original is 6 cm and the matching side of the enlarged rectangle is 12 cm. Another side of the original is 7 cm. How long is that side in the enlarged rectangle?
5
FA rectangle is enlarged by scale factor 1.5. One side of the original is 10 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?
6
PSA photo is 12 cm wide and 8 cm high. It is enlarged so that the new width is 30 cm. What is the new height, in cm?
7
PSA model of a bus is built to a scale of 1:20. The model is 15 cm long. How long is the real bus, in cm?
8
FA line of length 3 cm becomes 9 cm in an enlargement. What is the scale factor? Choose one: 3, 6 or 1/3.
9
FTick the statements that are true for two similar shapes, where one is an enlargement of the other. Options: All the angles stay the same | All lengths are multiplied by the same scale factor | All the lengths stay the same | Corresponding lengths have different scale factors. Write the options you would tick, in the order given.
10
FA rectangle is 5 cm long and 3 cm wide. It is enlarged by a scale factor of 4. What is the new length, in cm?
11
RSam says that if a shape is enlarged by scale factor 2, its area is also doubled. Is he right? Explain.
12
PSTwo similar triangles have matching sides of 4 cm and 6 cm. The side of 10 cm is in the smaller triangle. How long is the matching side in the larger triangle?
13
RExplain how you know that two rectangles, one 2 cm by 3 cm and one 6 cm by 9 cm, are similar.
14
PSA garden plan has a scale of 1 cm to 2 metres. A path is 7 cm long on the plan. How long is the real path, in metres?

Chapter summary

SkillMethod
RatioCompares two amounts: a:b means a parts of one to b parts of the other.
Simplify a ratioDivide both parts by the same number, the highest common factor.
Missing amountFind the value of one part, then multiply by the number of parts.
SharingAdd the parts, divide the total by the parts, then multiply each part.
Unit methodFind the amount for one, then multiply.
PercentageFind 1% first, then multiply to get the percentage you want.
Best valueFind the price of one item and compare.
Scale factorNew length / original length. Multiply lengths by it.

Can you…?

  • I can simplify a ratio and find a missing amount in a ratio
  • I can share an amount in a given ratio and check the shares add up
  • I can use the unit method to scale a recipe or a rate
  • I can use a percentage to work out an original price
  • I can compare prices and results fairly
  • I can find a scale factor and use it to find a missing length

Key terms

ratio
a comparison of two or more amounts, written with a colon such as 3:5
equivalent ratio
a ratio that is the same as another after simplifying, such as 2:3 and 4:6
unit method
finding the amount for one, then multiplying to find the amount for more
scale factor
the number that every length in a shape is multiplied by in an enlargement
similar shapes
shapes with the same angles, where one is an enlargement of the other
unit price
the price of one item

Exercise 3Z  Check-up

Non-calculator
1
Write the ratio 28:35 in its simplest form.
2
The ratio of stars to circles is 3:8. There are 27 stars. How many circles are there?
3
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.
4
In the ratio 3:5, what fraction of the total is the part shown by 5? Write the fraction.
5
A recipe for 6 people uses 360 ml of milk. How much milk is needed for 10 people? Write the amount in ml.
6
After 10% is taken off, a hat costs 54 pounds. What was the original price, in pounds?
7
Pack P: 4 items cost 320p. Pack Q: 6 items cost 420p. Which is better value for one item? Write the name.
8
Ali scored 7 from 10 shots, and Jo scored 9 from 15 shots. Which had the better success rate? Write the name.
9
A shape of length 6 cm is enlarged to 15 cm. What is the scale factor?
10
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?

Total 19 marks. Allow about 19 minutes.

Exercise 3X  Practice test questions

Non-calculator
1
FWrite the ratio 18:27 in its simplest form.[1 mark]
2
FThe ratio of pens to pencils is 5:3. There are 21 pencils. How many pens are there?[1 mark]
3
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]
4
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]
5
PSTub A: 5 items cost 400p. Tub B: 3 items cost 228p. Which is better value for one item? Write the name.[2 marks]
6
PSAda scored 20 from 25 shots, and Ben scored 24 from 40 shots. Which had the better success rate? Write the name.[2 marks]
7
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]
8
RExplain why the ratio 4:8 is the same as the ratio 1:2.[2 marks]
9
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]
10
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]
11
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]
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