Topics › KS3 › Ratio & proportion
Sharing in a ratio
-
£30 is shared in the ratio $2 : 3$. How much is the larger share?
A
Option A:
£15
B
Option B:
£18
C
Option C:
£12
D
Option D:
£90
Answer and misconceptions
A
Option A:
£15
✗
Shares equally, ignoring the ratioSplits £30 between two people as if the ratio were 1 : 1.
B
Option B:
£18
✓ Correct
C
Option C:
£12
✗
Gives the share for the first numberFinds one part (£6) correctly but multiplies by 2, assuming the first number gives the larger share.
D
Option D:
£90
✗
Multiplies the total by the ratio partWorks out £30 × 3 instead of dividing the total into 5 equal parts first.
-
In a class, boys : girls $= 3 : 5$. There are 40 pupils. How many are boys?
A
Option A:
24
B
Option B:
3
C
Option C:
15
D
Option D:
25
Answer and misconceptions
A
Option A:
24
✗
Treats the ratio 3 : 5 as the fraction 3/5Finds 3/5 of 40, using part : part as if it were part : whole (there are 8 parts in total).
B
Option B:
3
✗
Reads the ratio numbers as the actual amountsThinks the ratio 3 : 5 means there are exactly 3 boys.
C
Option C:
15
✓ Correct
D
Option D:
25
✗
Matches each part to the wrong groupUses the 5 parts for boys, finding the number of girls instead.
-
Ben and Cara share some sweets in the ratio $2 : 5$. Ben gets 8 sweets. How many sweets are there altogether?
A
Option A:
20
B
Option B:
56
C
Option C:
19
D
Option D:
28
Answer and misconceptions
A
Option A:
20
✗
Gives the other share instead of the totalFinds Cara's share (5 parts = 20) and stops, forgetting to add Ben's 8.
B
Option B:
56
✗
Treats the known share as one partMultiplies 8 by the 7 parts, not realising Ben's 8 sweets are 2 parts.
C
Option C:
19
✗
Uses addition instead of multiplyingAdds the difference in parts (5 − 2 = 3) to Ben's 8, so Cara gets 11 and the total is 19; ratio is multiplicative.
D
Option D:
28
✓ Correct
-
A bag has red and blue counters in the ratio red : blue $= 2 : 3$. What fraction of the counters are red?
A
Option A:
$\frac{2}{5}$
B
Option B:
$\frac{2}{3}$
C
Option C:
$\frac{2}{6}$
D
Option D:
$\frac{1}{2}$
Answer and misconceptions
A
Option A:
$\frac{2}{5}$
✓ Correct
B
Option B:
$\frac{2}{3}$
✗
Writes the ratio directly as a fractionTurns 2 : 3 into 2/3, using the blue part as the denominator instead of the total.
C
Option C:
$\frac{2}{6}$
✗
Multiplies the parts to find the totalThinks the total number of parts is 2 × 3 = 6 instead of 2 + 3 = 5.
D
Option D:
$\frac{1}{2}$
✗
Assumes two colours means half eachIgnores the ratio and thinks each colour must make up half.
-
£60 is shared in the ratio $1 : 2 : 3$. How much is the largest share?
A
Option A:
£10
B
Option B:
£20
C
Option C:
£30
D
Option D:
£180
Answer and misconceptions
A
Option A:
£10
✗
Stops after finding one partCorrectly finds one part (£60 ÷ 6 = £10) but does not multiply by 3.
B
Option B:
£20
✗
Divides by the number of peopleSplits £60 between three people equally, ignoring the ratio.
C
Option C:
£30
✓ Correct
D
Option D:
£180
✗
Multiplies the total by the ratio partWorks out £60 × 3 instead of first dividing £60 into 6 equal parts.