Multiplying Fractions & Mixed Numbers Worksheet - Practice Problems for Math Students

Let’s solve each problem step by step, multiplying the fractions and mixed numbers as instructed. Remember:
→ Multiply numerators together.
→ Multiply denominators together.
→ Simplify the answer to simplest form.
→ If the result is a mixed number, write it as an improper fraction (like 9/2).

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Problem 1:
$\frac{1}{6} \times \frac{5}{9}$
Multiply numerators: $1 \times 5 = 5$
Multiply denominators: $6 \times 9 = 54$
Answer: $\frac{5}{54}$ — already in simplest form.

✔ Final for #1: $\frac{5}{54}$

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Problem 2:
$\frac{2}{5} \times \frac{7}{8}$
Numerators: $2 \times 7 = 14$
Denominators: $5 \times 8 = 40$
Simplify $\frac{14}{40}$ → divide numerator and denominator by 2 → $\frac{7}{20}$

✔ Final for #2: $\frac{7}{20}$

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Problem 3:
$\frac{6}{7} \times \frac{2}{9}$
Numerators: $6 \times 2 = 12$
Denominators: $7 \times 9 = 63$
Simplify $\frac{12}{63}$ → divide by 3 → $\frac{4}{21}$

✔ Final for #3: $\frac{4}{21}$

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Problem 4:
$18 \times \frac{5}{6}$
Write 18 as $\frac{18}{1}$
$\frac{18}{1} \times \frac{5}{6} = \frac{18 \times 5}{1 \times 6} = \frac{90}{6} = 15$
But wait — 15 is a whole number. The instructions say if you get a mixed number, write as improper fraction. But 15 is just 15/1? Actually, let’s check:
$\frac{90}{6} = 15$, which is an integer. But since the instruction says “mixed numbers should be written as improper fractions”, and 15 is not a mixed number, we can leave it as 15 or write as 15/1? Let’s see — actually, 15 is fine as is, but to match format, maybe write as $\frac{15}{1}$? No — that’s unnecessary. Looking at example: “Ex. 9/2” — so they want improper fractions only when there’s a mixed number result. Since 15 is whole, we can write 15. But let’s double-check calculation:

Actually, better to simplify before multiplying:
$\frac{18}{1} \times \frac{5}{6}$ → 18 and 6 share factor 6 → 18÷6=3, 6÷6=1 → becomes $\frac{3}{1} \times \frac{5}{1} = 15$

So answer is 15. But since the worksheet says “write answers in simplest form. Mixed numbers should be written as improper fractions.” — 15 is not a mixed number, so 15 is acceptable. However, to be safe and consistent with fraction format, perhaps write as $\frac{15}{1}$? But that’s odd. Let me check other problems — problem 4 is likely expecting 15. But let’s see: 18 × 5/6 = (18×5)/6 = 90/6 = 15. So final answer is 15.

Wait — actually, looking back at the instruction: “Mixed numbers should be written as improper fractions.” It doesn’t say whole numbers must be written as fractions. So 15 is fine.

But let’s confirm with problem 5 — it will give a fraction. For now, I’ll go with 15.

Actually, no — let’s think again. In math worksheets like this, even whole numbers are sometimes left as is. But to be precise, since 15 = 15/1, and it’s an improper fraction? Well, 15/1 is technically an improper fraction, but usually we don’t write it that way. I think 15 is acceptable.

But let’s look at problem 4 again: 18 × 5/6. We can also think: 18 divided by 6 is 3, times 5 is 15. Yes.

I’ll write 15.

But wait — the example given is “Ex. 9/2” — which is an improper fraction. So perhaps they want all answers as fractions, even whole numbers? That would be unusual. Let me check online or standard practice — actually, no, typically whole numbers are written as whole numbers unless specified otherwise.

To avoid confusion, let’s calculate exactly:

$\frac{18}{1} \times \frac{5}{6} = \frac{90}{6} = 15$

And 15 is the simplified form. So I’ll put 15.

But let’s see problem 7 — it has mixed numbers, so those will become improper fractions. For now, I’ll proceed.

Actually, I recall that in some curricula, they expect whole numbers to be written as fractions over 1, but that’s rare. I think 15 is fine.

Let me move on and come back.

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Problem 5:
$\frac{5}{24} \times \frac{8}{15}$
Numerators: $5 \times 8 = 40$
Denominators: $24 \times 15 = 360$
So $\frac{40}{360}$
Simplify: divide numerator and denominator by 40 → $\frac{1}{9}$? Wait, 40÷40=1, 360÷40=9? 40×9=360, yes. So $\frac{1}{9}$

Or better, simplify before multiplying:
5 and 15 share 5 → 5÷5=1, 15÷5=3
8 and 24 share 8 → 8÷8=1, 24÷8=3
So now: $\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Yes, easier.

✔ Final for #5: $\frac{1}{9}$

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Problem 6:
$\frac{16}{7} \times \frac{21}{8}$
Numerators: $16 \times 21 = 336$
Denominators: $7 \times 8 = 56$
$\frac{336}{56} = 6$? Let’s divide: 56×6=336, yes. So 6.

Simplify before:
16 and 8 share 8 → 16÷8=2, 8÷8=1
21 and 7 share 7 → 21÷7=3, 7÷7=1
So $\frac{2}{1} \times \frac{3}{1} = 6$

✔ Final for #6: 6

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Problem 7:
$2 \frac{11}{12} \times \frac{2}{5}$
First, convert mixed number to improper fraction:
$2 \frac{11}{12} = \frac{2 \times 12 + 11}{12} = \frac{24 + 11}{12} = \frac{35}{12}$
Now multiply: $\frac{35}{12} \times \frac{2}{5}$
Numerators: $35 \times 2 = 70$
Denominators: $12 \times 5 = 60$
$\frac{70}{60}$
Simplify: divide by 10 → $\frac{7}{6}$
Or simplify before: 35 and 5 share 5 → 35÷5=7, 5÷5=1
2 and 12 share 2 → 2÷2=1, 12÷2=6
So $\frac{7}{6} \times \frac{1}{1} = \frac{7}{6}$

✔ Final for #7: $\frac{7}{6}$

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Problem 8:
$1 \frac{3}{4} \times \frac{20}{21}$
Convert mixed number: $1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$
Now: $\frac{7}{4} \times \frac{20}{21}$
Simplify before multiplying:
7 and 21 share 7 → 7÷7=1, 21÷7=3
20 and 4 share 4 → 20÷4=5, 4÷4=1
So $\frac{1}{1} \times \frac{5}{3} = \frac{5}{3}$

✔ Final for #8: $\frac{5}{3}$

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Problem 9:
$4 \frac{9}{10} \times 1 \frac{1}{7}$
Convert both to improper fractions:
$4 \frac{9}{10} = \frac{4 \times 10 + 9}{10} = \frac{49}{10}$
$1 \frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{8}{7}$
Now multiply: $\frac{49}{10} \times \frac{8}{7}$
Simplify: 49 and 7 share 7 → 49÷7=7, 7÷7=1
8 and 10 share 2 → 8÷2=4, 10÷2=5
So $\frac{7}{5} \times \frac{4}{1} = \frac{28}{5}$

✔ Final for #9: $\frac{28}{5}$

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Problem 10:
$8 \frac{1}{3} \times 4 \frac{1}{2}$
Convert to improper fractions:
$8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{25}{3}$
$4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$
Multiply: $\frac{25}{3} \times \frac{9}{2}$
Simplify: 9 and 3 share 3 → 9÷3=3, 3÷3=1
So $\frac{25}{1} \times \frac{3}{2} = \frac{75}{2}$

✔ Final for #10: $\frac{75}{2}$

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Now, back to Problem 4: $18 \times \frac{5}{6} = 15$
Since 15 is a whole number, and the instruction says "mixed numbers should be written as improper fractions", but 15 is not a mixed number, I think it's acceptable to write 15. However, to be consistent with the format of other answers (which are fractions), and since 15 can be written as $\frac{15}{1}$, but that seems forced. Looking at the example "Ex. 9/2", it's an improper fraction, but 15 is also an improper fraction if written as 15/1, but typically we don't do that.

I recall that in many worksheets, whole numbers are left as is. For example, if the answer is 5, they write 5, not 5/1. So I'll go with 15.

But let me double-check the calculation for #4:
18 × 5/6 = (18/1) × (5/6) = (18×5)/(1×6) = 90/6 = 15. Yes.

So final answers:

1. $\frac{5}{54}$
2. $\frac{7}{20}$
3. $\frac{4}{21}$
4. $15$
5. $\frac{1}{9}$
6. $6$
7. $\frac{7}{6}$
8. $\frac{5}{3}$
9. $\frac{28}{5}$
10. $\frac{75}{2}$

For problems 4 and 6, the answers are whole numbers. Since the instruction specifies "mixed numbers should be written as improper fractions", and these are not mixed numbers, writing them as whole numbers is appropriate. If the teacher expects fractions, they might want 15/1 and 6/1, but that is not standard. I think 15 and 6 are fine.

To confirm, let's see if any other problem gives a whole number — only 4 and 6 do. And in the context, it's clear.

So I'll proceed.

Final Answer:
1. $\frac{5}{54}$
2. $\frac{7}{20}$
3. $\frac{4}{21}$
4. $15$
5. $\frac{1}{9}$
6. $6$
7. $\frac{7}{6}$
8. $\frac{5}{3}$
9. $\frac{28}{5}$
10. $\frac{75}{2}$

But the response format requires a single "Final Answer" section. Since there are 10 problems, I need to list all answers.

Looking back at the user's request: "Solve the problem accurately." and "Provide only the final correct answer" — but there are 10 problems. So I should list all 10 answers.

In the structure, it says "Final Answer: [Provide only the final correct answer]" — but for multiple problems, it should be the list.

I think it's fine to list them.

So:

Final Answer:
1. $\frac{5}{54}$
2. $\frac{7}{20}$
3. $\frac{4}{21}$
4. $15$
5. $\frac{1}{9}$
6. $6$
7. $\frac{7}{6}$
8. $\frac{5}{3}$
9. $\frac{28}{5}$
10. $\frac{75}{2}$

But to make it clean, perhaps write as a list.

Since the instruction says "ONLY THEN provide the final answer", and "provide only the final correct answer", I'll present it clearly.

Also, for problem 4 and 6, I'll keep as whole numbers.

One more thing: in problem 4, 18 × 5/6, if we write it as fraction, it's 90/6 which simplifies to 15, and 15 is the simplest form. Similarly for 6.

I think it's correct.

So here is the final answer.