B4 — divide 12 into 3 equal groups and count one group
C36 — multiply 12 by 3
D1 — because the numerator of 1/3 is 1
To find 1/3 of 12, divide 12 into 3 equal groups: 12 ÷ 3 = 4 per group. Then take 1 group: 4. The denominator (3) tells you how many equal groups to make; the numerator (1) tells you how many groups to count. Option A confuses the denominator with the answer itself.
Question 2 Multiple Choice
A student finds 3/4 of 20 and gets the answer 5. What step did the student complete, but then stop before finishing?
AThe student divided 20 by 3 instead of 4
BThe student correctly found 1/4 of 20 = 5, but forgot to multiply by 3 to count three groups
CThe student multiplied 3 × 4 = 12 and then divided 20 by 12
DThe student added 3 + 4 = 7 and divided 20 by 7
3/4 of 20: step 1, divide into 4 groups → 20 ÷ 4 = 5 per group. Step 2, count 3 groups → 5 × 3 = 15. Getting 5 means the student completed step 1 but stopped there. The correct answer is 15. Missing step 2 is the most common error with non-unit fractions of a set.
Question 3 True / False
Finding 1/4 of a number gives the same result as dividing that number by 4.
TTrue
FFalse
Answer: True
True. The denominator tells you how many equal groups to divide into. 1/4 of a number means splitting it into 4 equal groups and taking 1 group — which is exactly division by 4. The fraction bar is literally a division symbol, and unit fractions directly correspond to division.
Question 4 True / False
To find 2/3 of 18, you should divide 18 by 2 first, then multiply by 3.
TTrue
FFalse
Answer: False
False. Always divide by the denominator first, then multiply by the numerator. Divide 18 by 3 (the denominator) to find the size of one group: 18 ÷ 3 = 6. Then multiply 6 × 2 (the numerator) = 12. Dividing by 2 first (giving 9) and multiplying by 3 yields 27 — larger than the original set, which makes no sense for a fraction of a set.
Question 5 Short Answer
Explain the two-step process for finding 3/4 of a set. Why do you divide before you multiply?
Think about your answer, then reveal below.
Model answer: Step 1: Divide the total by the denominator (4) to find the size of one equal group. Step 2: Multiply by the numerator (3) to count that many groups. You divide first because the denominator defines how many equal groups to create — you must make the groups before you can select some of them.
Fractions of a set are about making equal groups (division by the denominator) and then selecting the right number of those groups (multiplication by the numerator). The denominator is always the divisor because it names how many parts the whole is split into.