Topics › KS3 › Ratio & proportion
Simplifying ratio
-
Write $12 : 18$ in its simplest form.
A
Option A:
$4 : 6$
B
Option B:
$2 : 5$
C
Option C:
$3 : 2$
D
Option D:
$2 : 3$
Answer and misconceptions
A
Option A:
$4 : 6$
✗
Stops before the simplest formDivides both parts by 3 but does not notice that 4 and 6 still share a factor of 2.
B
Option B:
$2 : 5$
✗
Compares a part with the totalWrites 12 : 30 (part : whole) and simplifies, confusing a ratio with a fraction of the total.
C
Option C:
$3 : 2$
✗
Swaps the order of the partsSimplifies correctly but writes the parts in reverse order; order matters in a ratio.
D
Option D:
$2 : 3$
✓ Correct
-
Write 20 cm : 1 m in its simplest form.
A
Option A:
$20 : 1$
B
Option B:
$1 : 50$
C
Option C:
$1 : 5$
D
Option D:
$2 : 1$
Answer and misconceptions
A
Option A:
$20 : 1$
✗
Ignores the different unitsTreats 1 m as 1 without converting both quantities to the same unit (100 cm).
B
Option B:
$1 : 50$
✗
Thinks 1 m = 1000 cmConverts 1 m to 1000 cm, giving 20 : 1000 = 1 : 50.
C
Option C:
$1 : 5$
✓ Correct
D
Option D:
$2 : 1$
✗
Thinks 1 m = 10 cmConverts 1 m to 10 cm, giving 20 : 10 = 2 : 1.
-
Write $6 : 12 : 9$ in its simplest form.
A
Option A:
$2 : 4 : 3$
B
Option B:
$1 : 2 : 1$
C
Option C:
$2 : 3 : 4$
D
Option D:
$1 : 2 : 9$
Answer and misconceptions
A
Option A:
$2 : 4 : 3$
✓ Correct
B
Option B:
$1 : 2 : 1$
✗
Divides the parts by different numbersDivides 6 and 12 by 6 but 9 by 9; every part must be divided by the same number.
C
Option C:
$2 : 3 : 4$
✗
Rearranges the parts into size orderReorders to 6 : 9 : 12 before simplifying, so the parts no longer match their quantities.
D
Option D:
$1 : 2 : 9$
✗
Simplifies only the first two partsTreats 6 : 12 as the ratio to simplify and leaves the third part unchanged.
-
Write $0.5 : 2$ in its simplest form using whole numbers.
A
Option A:
$5 : 2$
B
Option B:
$1 : 4$
C
Option C:
$1 : 10$
D
Option D:
$1 : 2$
Answer and misconceptions
A
Option A:
$5 : 2$
✗
Removes the decimal point from one partTreats 0.5 as 5 without multiplying the other part by 10 as well.
B
Option B:
$1 : 4$
✓ Correct
C
Option C:
$1 : 10$
✗
Thinks 0.5 means one fifthReads 0.5 as 1/5 (0.2), so 0.2 : 2 becomes 1 : 10.
D
Option D:
$1 : 2$
✗
Doubles only one part of the ratioDoubles 0.5 to get 1 but leaves 2 unchanged; both parts must be multiplied by 2.
-
Write $4 : 10$ in the form $1 : n$.
A
Option A:
$1 : 7$
B
Option B:
$2 : 5$
C
Option C:
$1 : 0.4$
D
Option D:
$1 : 2.5$
Answer and misconceptions
A
Option A:
$1 : 7$
✗
Subtracts the same amount from each partTakes 3 from both parts to make the first part 1; ratios scale by dividing, not subtracting.
B
Option B:
$2 : 5$
✗
Gives whole-number simplest form insteadSimplifies to 2 : 5 but does not divide by the first part to make it 1.
C
Option C:
$1 : 0.4$
✗
Divides the first part by the secondWorks out 4 ÷ 10 = 0.4 for n instead of 10 ÷ 4.
D
Option D:
$1 : 2.5$
✓ Correct