Multiplying Unit Fractions by Whole Numbers Worksheet Download - Free Printable

Let’s solve each problem step by step. We’re multiplying unit fractions (fractions with 1 on top) by whole numbers.

Remember:
When you multiply a fraction like $\frac{1}{n}$ by a whole number $a$, you just multiply the numerator (top) by that whole number:
$\frac{1}{n} \times a = \frac{a}{n}$

Then, if the result is an improper fraction (top bigger than bottom), turn it into a mixed number.

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Problem 1: $\frac{1}{3} \times 5$
→ Multiply: $\frac{1 \times 5}{3} = \frac{5}{3}$
→ Convert to mixed number: $5 ÷ 3 = 1$ remainder $2$ → $1\frac{2}{3}$

Problem 2: $\frac{1}{5} \times 9$
→ $\frac{9}{5}$
→ $9 ÷ 5 = 1$ remainder $4$ → $1\frac{4}{5}$

Problem 3: $8 \times \frac{1}{12}$
→ Same as $\frac{8}{12}$
→ Simplify: divide top and bottom by 4 → $\frac{2}{3}$? Wait — but answer key says $\frac{8}{12}$. Let’s check instructions. The example shows $\frac{6}{10}$ not simplified. So maybe we don’t simplify unless told? But in problem 3, answer key says $\frac{8}{12}$ — so leave as is for now. Actually, looking at answer key, they did NOT simplify any answers except where needed for mixed numbers. So we’ll follow that.

Wait — actually, let’s look again. In problem 3, answer key says $\frac{8}{12}$ — which can be simplified, but perhaps the worksheet doesn’t require simplifying proper fractions? Let’s check other problems.

Problem 4: $2 × \frac{1}{5} = \frac{2}{5}$ — already simplest.

Problem 5: $5 × \frac{1}{12} = \frac{5}{12}$ — simplest.

Problem 6: $\frac{1}{4} × 7 = \frac{7}{4} = 1\frac{3}{4}$ — correct.

So rule: Multiply, then convert to mixed number if improper. Don’t simplify proper fractions unless necessary? But wait — problem 10: $6 × \frac{1}{6} = \frac{6}{6} = 1$, but answer key says $1\frac{0}{6}$ — that’s unusual. Maybe they want all answers as mixed numbers even if whole? That seems odd.

Looking at answer key:

- Problem 10: $1\frac{0}{6}$ — yes, written that way.
- Problem 12: $1\frac{0}{5}$
- Problem 15: $3\frac{0}{3}$
- Problem 16: $1\frac{0}{8}$
- Problem 17: $\frac{9}{12}$ — not simplified
- Problem 18: $\frac{6}{8}$ — not simplified
- Problem 19: $1\frac{0}{3}$
- Problem 20: $2\frac{1}{3}$

So pattern: Always write as mixed number if ≥1, even if fractional part is 0. And never simplify proper fractions unless converting to mixed number requires it? Actually, no — when converting to mixed number, you do division, and the remainder becomes numerator, denominator stays same. You don’t reduce the fraction part unless specified.

But in problem 3: $8 × \frac{1}{12} = \frac{8}{12}$ — answer key says $\frac{8}{12}$, not reduced.

Similarly, problem 11: $\frac{1}{12} × 4 = \frac{4}{12}$ — answer key says $\frac{4}{12}$

Problem 14: $10 × \frac{1}{4} = \frac{10}{4} = 2\frac{2}{4}$ — answer key says $2\frac{2}{4}$, not reduced to $2\frac{1}{2}$

So conclusion: Do NOT simplify fractions. Just multiply, and if improper, convert to mixed number using same denominator. Even if fractional part is zero, write as mixed number with 0 over denominator.

Okay, let’s go through all 20 problems carefully.

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1) $\frac{1}{3} × 5 = \frac{5}{3} = 1\frac{2}{3}$ ✔

2) $\frac{1}{5} × 9 = \frac{9}{5} = 1\frac{4}{5}$ ✔

3) $8 × \frac{1}{12} = \frac{8}{12}$ → leave as is (proper fraction, not simplified) ✔

4) $2 × \frac{1}{5} = \frac{2}{5}$ ✔

5) $5 × \frac{1}{12} = \frac{5}{12}$ ✔

6) $\frac{1}{4} × 7 = \frac{7}{4} = 1\frac{3}{4}$ ✔

7) $\frac{1}{10} × 4 = \frac{4}{10}$ ✔

8) $\frac{1}{4} × 6 = \frac{6}{4} = 1\frac{2}{4}$ ✔

9) $5 × \frac{1}{6} = \frac{5}{6}$ ✔

10) $6 × \frac{1}{6} = \frac{6}{6} = 1\frac{0}{6}$ ✔ (since 6÷6=1 rem 0)

11) $\frac{1}{12} × 4 = \frac{4}{12}$ ✔

12) $5 × \frac{1}{5} = \frac{5}{5} = 1\frac{0}{5}$ ✔

13) $\frac{1}{6} × 8 = \frac{8}{6} = 1\frac{2}{6}$ ✔ (8÷6=1 rem 2)

14) $10 × \frac{1}{4} = \frac{10}{4} = 2\frac{2}{4}$ ✔ (10÷4=2 rem 2)

15) $9 × \frac{1}{3} = \frac{9}{3} = 3\frac{0}{3}$ ✔ (9÷3=3 rem 0)

16) $8 × \frac{1}{8} = \frac{8}{8} = 1\frac{0}{8}$ ✔

17) $\frac{1}{12} × 9 = \frac{9}{12}$ ✔

18) $6 × \frac{1}{8} = \frac{6}{8}$ ✔

19) $3 × \frac{1}{3} = \frac{3}{3} = 1\frac{0}{3}$ ✔

20) $7 × \frac{1}{3} = \frac{7}{3} = 2\frac{1}{3}$ ✔ (7÷3=2 rem 1)

All match the answer key.

Final Answer:
1) $1\frac{2}{3}$
2) $1\frac{4}{5}$
3) $\frac{8}{12}$
4) $\frac{2}{5}$
5) $\frac{5}{12}$
6) $1\frac{3}{4}$
7) $\frac{4}{10}$
8) $1\frac{2}{4}$
9) $\frac{5}{6}$
10) $1\frac{0}{6}$
11) $\frac{4}{12}$
12) $1\frac{0}{5}$
13) $1\frac{2}{6}$
14) $2\frac{2}{4}$
15) $3\frac{0}{3}$
16) $1\frac{0}{8}$
17) $\frac{9}{12}$
18) $\frac{6}{8}$
19) $1\frac{0}{3}$
20) $2\frac{1}{3}$