Share 10 pounds between Maya and Noah in the ratio 1:1. Write down how much each person receives.
(2)
2
Share 15 apples between Priya and Kwame in the ratio 2:1. How many apples does each person get?
(2)
3
Share 14 biscuits between Erin and Yusuf in the ratio 3:4. How many biscuits does each person receive?
(2)
4
Share 18 pounds between Callum and Amelia in the ratio 2:1. State each share in pounds.
(2)
5
Share 21 sweets between three friends in the ratio 1:1:1. How many sweets does each friend get?
(2)
6
Share 30 marbles between A, B and C in the ratio 1:2:3. Find how many marbles C receives.
(3)
7
A total of 56 centimetres is shared between two pieces in the ratio 3:5. Find the length of the smaller piece.
(2)
8
A:B = 4:1 and A + B = 25. Find the value of A.
(2)
9
Simplify the ratio 8:12 to its lowest terms.
(1)
10
A packet of 40 sweets is shared between Ben and Zara in the ratio 3:5. Ben gives 6 of his sweets to Zara. Find the new ratio of Ben:Zara.
(3)
11
Write the ratio 120 g : 80 g in its simplest form.
(1)
12
A total of 55 pens are shared between two students in the ratio 4:7. How many pens does each student get?
(2)
13
Share 48 centimetres in the ratio 3:2:1. What is the smallest share?
(2)
14
A length of ribbon 81 cm is shared in the ratio 4:5. Find the two lengths.
(2)
15
Given that a:b = 5:2 and a = 35, find b.
(2)
16
Share 84 pounds between three siblings in the ratio 3:4:5. Find the largest share.
(2)
17
Stretch. A and B share some money in the ratio 2:3. A gives 6 pounds to B. After this transfer the ratio of A:B becomes 1:2. Find the initial total amount of money shared.
(4)
18
Stretch. A, B and C share 110 pounds in the ratio 2:3:5. C then gives 10 pounds to A. Find the new ratio A:B:C in simplest form.
(4)
Mark scheme · KS3.M-R3 Sharing in a Given Ratio
Question 1
M1 divide 10 into 2 equal parts, 10/2 = 5
A1 5 pounds and 5 pounds cao
Answer: 5 pounds, 5 pounds
Question 2
M1 find one unit: 15 divided by (2+1) = 15/3 = 5
A1 Priya 10, Kwame 5 cao
Answer: Priya 10, Kwame 5
Question 3
M1 one unit = 14 / (3+4) = 14/7 = 2
A1 3 units = 6 and 4 units = 8 cao
Answer: Erin 6, Yusuf 8
Question 4
M1 one unit = 18 / (2+1) = 6
A1 2 units = 12 and 1 unit = 6 cao
Answer: 12 pounds, 6 pounds
Question 5
M1 one unit = 21 / (1+1+1) = 7
A1 each friend gets 7 sweets cao
Answer: 7, 7, 7
Question 6
M1 find total units 1+2+3 = 6 and one unit = 30/6 = 5
M1 method to get C's share: 3 units = 3 x 5
A1 C receives 15 marbles cao
Answer: 15
Question 7
M1 one unit = 56 / (3+5) = 56/8 = 7
A1 smaller piece = 3 x 7 = 21 cm cao
Answer: 21 cm
Question 8
M1 one unit = 25 / (4+1) = 5
A1 A = 4 x 5 = 20 cao
Answer: 20
Question 9
B1 2:3 cao (common factor 4 used)
Answer: 2:3
Question 10
M1 find initial shares: total units 3+5=8, one unit = 40/8 = 5, so Ben = 15, Zara = 25
M1 Ben gives 6 so Ben = 15-6 = 9 and Zara = 25+6 = 31
A1 new ratio Ben:Zara = 9:31 cao
Answer: 9:31
Question 11
B1 3:2 cao (divide both by 40)
Answer: 3:2
Question 12
M1 one unit = 55 / (4+7) = 55/11 = 5
A1 4 units = 20 and 7 units = 35 cao
Answer: 20, 35
Question 13
M1 total units 3+2+1 = 6 so one unit = 48/6 = 8
A1 smallest share = 1 x 8 = 8 cm cao
Answer: 8 cm
Question 14
M1 one unit = 81 / (4+5) = 81/9 = 9
A1 4 units = 36 and 5 units = 45 cao
Answer: 36 cm, 45 cm
Question 15
M1 unit value: a = 5 units, so one unit = 35/5 = 7
A1 b = 2 x 7 = 14 cao
Answer: 14
Question 16
M1 total units 3+4+5 = 12 so one unit = 84/12 = 7
A1 largest share = 5 x 7 = 35 pounds cao
Answer: 35 pounds
Question 17
M1 let initial shares be 2k and 3k; set up equation for after transfer (2k - 6)/(3k + 6) = 1/2
M1 clear fraction and form linear equation: 2(2k - 6) = 3k + 6
M1 solve for k: 4k - 12 = 3k + 6 so k = 18
A1 initial total = 5k = 5 x 18 = 90 pounds cao
Answer: 90 pounds
Question 18
M1 find one unit: total units = 2+3+5 = 10 so one unit = 110/10 = 11
M1 initial shares: A = 2x11 = 22, B = 3x11 = 33, C = 5x11 = 55
M1 after transfer A = 22+10 = 32 and C = 55-10 = 45
A1 new ratio A:B:C = 32:33:45 cao (already in simplest integer terms)