Chidi is making a necklace using red beads and blue beads in the ratio 2:3. He uses 10 red beads. How many blue beads does he need?
(2)
3
The diagram shows a grid of 20 squares (4 rows of 5). 8 squares are shaded grey and the rest are unshaded white. Write the ratio of shaded squares to unshaded squares in its simplest form.
(2)
4
A recipe for 8 flapjacks needs 150g of oats and 90g of butter. Sofia wants to make 20 flapjacks using the same recipe.
(a)Work out how many grams of oats she needs.(2)
(b)Work out how many grams of butter she needs.(1)
5
Priya and Jack share 45 sweets in the ratio 4:5. How many sweets does Jack get?
(2)
6
The ages of three sisters, Amara, Zara and Ellie, are in the ratio 2:3:4. The sum of their ages is 54. Find each sister's age.
(3)
7
Tomasz is comparing two bags of the same pasta. A 400g bag costs GBP1.60. A 600g bag costs GBP2.16. Which bag is better value for money? Show working to justify your answer.
(2)
8
Declan buys 3 identical toy cars for a total of GBP7.20. Work out the cost of 8 of these toy cars.
(3)
9
Liam is looking at a map with a scale of 1:25000. The distance between two villages on the map is 6cm. Work out the real distance between the villages in kilometres.
(2)
10
Rhys measures out 750ml of orange squash concentrate and 2 litres of water. Write the ratio of concentrate to water in its simplest form.
(2)
11
Mei's family drive 180km in 3 hours at a constant speed. Work out how far they would travel in 5 hours at the same speed.
(3)
12
In Ben's school choir, the ratio of boys to girls is 3:7. There are 12 boys in the choir. How many children are in the choir altogether?
(2)
13
Marcus scored 18 out of 24 in a spelling test. Write his score as a fraction in its simplest form, then write it as a percentage.
(2)
14
Nadia makes a fruit drink by mixing orange juice and lemonade in the ratio 2:5. She makes 700ml of the drink, then adds a further 100ml of lemonade. Work out the new ratio of orange juice to lemonade in its simplest form.
(3)
15
Callum says, 'If I double both numbers in a ratio, the ratio stays the same.' Is Callum correct? Explain your answer using an example.
(2)
16
Show that the ratios 4:6 and 10:15 are equivalent.
(3)
17
Fatima enlarges a photograph measuring 10cm by 15cm by scale factor 3. Work out the dimensions of the enlarged photograph.
(2)
18
Two numbers are in the ratio 5:8. The smaller number can be written as 5n and the larger number as 8n, where n is a whole number. When the smaller number is increased by 12 and the larger number is decreased by 3, the two new numbers are equal. Form an equation and solve it to find the two original numbers.
(4)
19
At Ivy Lane Primary School, the ratio of Year 5 to Year 6 pupils is 4:5. The ratio of Year 6 to Year 7 pupils is 3:2. Find the ratio of Year 5 to Year 6 to Year 7 pupils in its simplest form.
(3)
20
Aisha is comparing two packs of pens. A pack of 6 pens costs GBP2.70. A pack of 10 pens of the same type costs GBP4.20. Which pack is better value, and by how much is the price per pen cheaper for that pack compared with the other pack?
(3)
Mark scheme · KS2.M-R3 Reasoning: Ratio and Proportion
Question 1
B1 9:15 circled; cao
Answer: 9:15
Question 2
M1 10 / 2 = 5 (finds the scale factor) oe
A1 15 cao
Answer: 15 blue beads
Question 3
M1 identifies 8:12 oe
A1 2:3 oe cao (simplest form)
Answer: 2:3
Question 4
(a) M1 scale factor = 20 / 8 = 2.5 oe
(a) A1 375g cao
(a) Answer: 375g
(b) A1 225g ft from their scale factor in part (a)
(b) Answer: 225g
Question 5
M1 45 / 9 = 5 (value of one part) oe
A1 25 cao
Answer: 25 sweets
Question 6
M1 54 / 9 = 6 (value of one part) oe
A1 Amara = 12 and Zara = 18 cao
A1 Ellie = 24 cao
Answer: Amara = 12, Zara = 18, Ellie = 24
Question 7
M1 finds a unit price for each bag, e.g. 0.4p per g and 0.36p per g (or 40p and 36p per 100g) oe
A1 correct conclusion: 600g bag is better value oe, cao
Answer: 600g bag (36p per 100g compared with 40p per 100g)
Question 8
M1 unit cost = 720p / 3 = 240p oe
dM1 240p x 8, dependent on M1
A1 GBP19.20 cao
Answer: GBP19.20
Question 9
M1 6 x 25000 = 150000cm oe
A1 1.5km cao
Answer: 1.5km
Question 10
M1 converts 2 litres to 2000ml oe
A1 3:8 oe cao (simplest form)
Answer: 3:8
Question 11
M1 speed = 180 / 3 = 60km/h oe
dM1 60 x 5, dependent on M1
A1 300km cao
Answer: 300km
Question 12
M1 scale factor = 12 / 3 = 4, so girls = 7 x 4 = 28 oe
A1 40 cao
Answer: 40 children
Question 13
A1 3/4 oe
A1 75% cao
Answer: 3/4 = 75%
Question 14
M1 one part = 700 / 7 = 100ml oe
M1 orange = 200ml and new lemonade = 500 + 100 = 600ml oe
A1 1:3 oe cao (simplest form)
Answer: 1:3
Question 15
B1 correct judgement that Callum is correct oe
B1 valid example showing an equivalent ratio, e.g. 2:3 doubled is 4:6, which simplifies back to 2:3 oe
Answer: Callum is correct; doubling both parts of a ratio gives an equivalent ratio, e.g. 2:3 becomes 4:6, which simplifies back to 2:3.
Question 16
M1 simplifies 4:6 to 2:3 oe
M1 simplifies 10:15 to 2:3 oe
A1 cso; states both ratios simplify to 2:3 so are equivalent (answer printed, working must be shown)
Answer: 4:6 = 2:3 and 10:15 = 2:3, so the ratios are equivalent.
Question 17
M1 one correct dimension, e.g. 30cm oe
A1 30cm by 45cm cao (both dimensions correct)
Answer: 30cm by 45cm
Question 18
M1 forms equation 5n + 12 = 8n - 3 oe
M1 solves to n = 5 oe
A1 smaller number = 25 cao
A1 larger number = 40 cao
Answer: 25 and 40
Question 19
M1 identifies common multiple of 5 and 3 for the Year 6 term, e.g. 15 oe
M1 scales both ratios to a shared Year 6 value: 12:15 and 15:10 oe
A1 12:15:10 oe cao (cannot be simplified further)
Answer: 12:15:10
Question 20
M1 unit price of pack of 6 = 270p / 6 = 45p per pen oe
M1 unit price of pack of 10 = 420p / 10 = 42p per pen oe
A1 pack of 10 is better value, cheaper by 3p per pen cao
Answer: Pack of 10 is better value; it is cheaper by 3p per pen (42p compared with 45p).