Multiply Mixed Numbers Worksheet (examples, answers, videos ... - Free Printable

Let’s solve each problem step by step.

We’re multiplying mixed numbers. The rule is:
1. Convert each mixed number to an improper fraction.
2. Multiply the numerators together and denominators together.
3. Simplify if possible (cancel before multiplying if you can).
4. If needed, convert back to a mixed number — but since the instructions don’t say to, we’ll leave as improper or simplified fraction unless it’s whole number.

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Problem 1: $4 \frac{2}{5} \times 2 \frac{1}{2}$

Convert:
- $4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{22}{5}$
- $2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$

Multiply:
$\frac{22}{5} \times \frac{5}{2} = \frac{22 \times 5}{5 \times 2}$

Cancel 5s: $\frac{22}{2} = 11$

✔ Answer: 11

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Problem 2: $2 \frac{1}{4} \times 3 \frac{1}{3}$

Convert:
- $2 \frac{1}{4} = \frac{9}{4}$
- $3 \frac{1}{3} = \frac{10}{3}$

Multiply:
$\frac{9}{4} \times \frac{10}{3} = \frac{90}{12}$

Simplify: divide numerator and denominator by 6 → $\frac{15}{2}$

Or as mixed number: $7 \frac{1}{2}$ — but again, not required. We’ll keep as simplified fraction unless specified.

Wait — let’s check cancellation first:

$\frac{9}{4} \times \frac{10}{3}$ → 9 and 3 cancel (divide both by 3): 9÷3=3, 3÷3=1
→ $\frac{3}{4} \times \frac{10}{1} = \frac{30}{4} = \frac{15}{2}$

Same result.

✔ Answer: $\frac{15}{2}$ or 7.5, but better as fraction: $\frac{15}{2}$

But looking at other problems, maybe they want mixed numbers? Let’s see… Actually, the instruction says “multiply” and doesn’t specify form. But in school, often they want mixed number if answer >1. However, since original were mixed, and no instruction to convert back, I think improper is fine. But let’s check consistency.

Actually, let me re-read: “Convert the mixed numbers to improper fractions and multiply.” It doesn’t say to convert back. So we can leave as improper or simplify.

But for clarity, perhaps we should give simplified fraction or mixed number? Since the user might expect same format... Hmm.

Looking at problem 1: got 11 — that’s whole number.

Problem 2: $\frac{15}{2} = 7 \frac{1}{2}$ — maybe write as mixed? But again, not instructed.

I think safest is to simplify fraction and if it’s improper, leave it unless told otherwise. But let’s proceed and see.

Actually, let’s do all and then decide. For now, I’ll write simplified fraction.

But wait — in many worksheets, they expect mixed number if answer is greater than 1. To be safe, I’ll convert to mixed number when applicable.

Re-do Problem 2: $\frac{15}{2} = 7 \frac{1}{2}$

Okay, let’s adopt: if final answer is improper fraction, convert to mixed number.

So:

Problem 1: 11 → already whole → 11

Problem 2: $\frac{15}{2} = 7 \frac{1}{2}$ → $7 \frac{1}{2}$

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Problem 3: $4 \frac{2}{5} \times 4 \frac{3}{4}$

Convert:
- $4 \frac{2}{5} = \frac{22}{5}$
- $4 \frac{3}{4} = \frac{19}{4}$

Multiply: $\frac{22}{5} \times \frac{19}{4} = \frac{418}{20}$

Simplify: divide numerator and denominator by 2 → $\frac{209}{10}$

As mixed number: $20 \frac{9}{10}$

✔ Answer: $20 \frac{9}{10}$

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Problem 4: $4 \frac{1}{3} \times 2 \frac{1}{2}$

Convert:
- $4 \frac{1}{3} = \frac{13}{3}$
- $2 \frac{1}{2} = \frac{5}{2}$

Multiply: $\frac{13}{3} \times \frac{5}{2} = \frac{65}{6}$

Mixed number: $10 \frac{5}{6}$

✔ Answer: $10 \frac{5}{6}$

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Problem 5: $2 \frac{2}{5} \times 3 \frac{1}{3}$

Convert:
- $2 \frac{2}{5} = \frac{12}{5}$
- $3 \frac{1}{3} = \frac{10}{3}$

Multiply: $\frac{12}{5} \times \frac{10}{3}$

Cancel: 12 and 3 → 12÷3=4, 3÷3=1; 10 and 5 → 10÷5=2, 5÷5=1

So: $\frac{4}{1} \times \frac{2}{1} = 8$

✔ Answer: 8

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Problem 6: $2 \frac{1}{2} \times 2 \frac{2}{3}$

Convert:
- $2 \frac{1}{2} = \frac{5}{2}$
- $2 \frac{2}{3} = \frac{8}{3}$

Multiply: $\frac{5}{2} \times \frac{8}{3} = \frac{40}{6}$

Simplify: divide by 2 → $\frac{20}{3}$

Mixed number: $6 \frac{2}{3}$

✔ Answer: $6 \frac{2}{3}$

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Problem 7: $2 \frac{2}{5} \times 2 \frac{1}{3}$

Convert:
- $2 \frac{2}{5} = \frac{12}{5}$
- $2 \frac{1}{3} = \frac{7}{3}$

Multiply: $\frac{12}{5} \times \frac{7}{3} = \frac{84}{15}$

Simplify: divide by 3 → $\frac{28}{5}$

Mixed number: $5 \frac{3}{5}$

✔ Answer: $5 \frac{3}{5}$

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Problem 8: $4 \frac{3}{4} \times 4 \frac{2}{3}$

Convert:
- $4 \frac{3}{4} = \frac{19}{4}$
- $4 \frac{2}{3} = \frac{14}{3}$

Multiply: $\frac{19}{4} \times \frac{14}{3} = \frac{266}{12}$

Simplify: divide by 2 → $\frac{133}{6}$

Mixed number: $22 \frac{1}{6}$ (since 6×22=132, remainder 1)

✔ Answer: $22 \frac{1}{6}$

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Now, compiling all answers:

1. $4 \frac{2}{5} \times 2 \frac{1}{2} = 11$
2. $2 \frac{1}{4} \times 3 \frac{1}{3} = 7 \frac{1}{2}$
3. $4 \frac{2}{5} \times 4 \frac{3}{4} = 20 \frac{9}{10}$
4. $4 \frac{1}{3} \times 2 \frac{1}{2} = 10 \frac{5}{6}$
5. $2 \frac{2}{5} \times 3 \frac{1}{3} = 8$
6. $2 \frac{1}{2} \times 2 \frac{2}{3} = 6 \frac{2}{3}$
7. $2 \frac{2}{5} \times 2 \frac{1}{3} = 5 \frac{3}{5}$
8. $4 \frac{3}{4} \times 4 \frac{2}{3} = 22 \frac{1}{6}$

All checked. Calculations verified with cancellation where possible.

Final Answer:
11, $7 \frac{1}{2}$, $20 \frac{9}{10}$, $10 \frac{5}{6}$, 8, $6 \frac{2}{3}$, $5 \frac{3}{5}$, $22 \frac{1}{6}$