Multiplying Fractions and Mixed Numbers Worksheet

Let’s solve each problem step by step.

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**Problem 1:
1/6 × 5/9 = ?**

Multiply numerators: 1 × 5 = 5
Multiply denominators: 6 × 9 = 54
Answer: 5/54

Check if it can be simplified — 5 and 54 have no common factors other than 1 → already simplest form.

✔ Final for #1: 5/54

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**Problem 2:
2/5 × 7/8 = ?**

Numerators: 2 × 7 = 14
Denominators: 5 × 8 = 40
→ 14/40

Simplify: divide numerator and denominator by 2 → 7/20

✔ Final for #2: 7/20

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**Problem 3:
6/7 × 2/9 = ?**

Numerators: 6 × 2 = 12
Denominators: 7 × 9 = 63
→ 12/63

Simplify: GCF of 12 and 63 is 3 → 12÷3=4, 63÷3=21 → 4/21

✔ Final for #3: 4/21

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**Problem 4:
18 × 5/6 = ?**

Write 18 as fraction: 18/1
Now multiply: (18/1) × (5/6) = (18×5)/(1×6) = 90/6

Simplify: 90 ÷ 6 = 15 → but wait! The instruction says: “Mixed numbers should be written as improper fractions.” But 15 is a whole number — that’s fine. However, let’s check if we can simplify before multiplying.

Better way: Cancel 18 and 6 first.

18 ÷ 6 = 3 → so now it’s 3 × 5 / 1 = 15/1? Wait — actually:

(18/1) × (5/6) → cancel 18 and 6 → 18÷6=3, 6÷6=1 → becomes (3/1) × (5/1) = 15/1 → which is 15.

But the instructions say to write answers in simplest form, and mixed numbers as improper fractions. Since 15 is an integer, we can write it as 15/1? Or just 15?

Looking at example: “Ex. 9/2” — they want improper fractions even if it's a whole number? Actually, 15 is fine as 15, but to match format, maybe write as 15/1? Let me re-read.

“Write answers in simplest form. Mixed numbers should be written as improper fractions.”

It doesn’t say whole numbers must be written as fractions. So 15 is acceptable.

But let’s see problem 4 again: 18 × 5/6

We can do: 18 × 5 = 90, divided by 6 = 15 → yes.

Alternatively: 18 ÷ 6 = 3, then 3 × 5 = 15.

So answer is 15

But to be safe, since all others are fractions, and example shows 9/2, perhaps they expect 15/1? No — 15 is simpler. I think 15 is correct.

Wait — let me check problem 4 again: 18 × 5/6

Yes, 18 * 5 / 6 = 90 / 6 = 15 → so 15

✔ Final for #4: 15

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**Problem 5:
5/24 × 8/15 = ?**

Numerators: 5 × 8 = 40
Denominators: 24 × 15 = 360
→ 40/360

Simplify: divide numerator and denominator by 40 → 1/9? Wait, better to cancel before multiplying.

Look: 5 and 15 → 5÷5=1, 15÷5=3
8 and 24 → 8÷8=1, 24÷8=3

So: (5/24) × (8/15) = (1/3) × (1/3) = 1/9

Wait — let me write it clearly:

After canceling:

5 and 15 → 5 goes into 5 once, into 15 three times → so 1 and 3
8 and 24 → 8 goes into 8 once, into 24 three times → so 1 and 3

So now: (1/3) × (1/3) = 1/9

✔ Final for #5: 1/9

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**Problem 6:
16/7 × 21/8 = ?**

Cancel before multiplying.

16 and 8 → 16÷8=2, 8÷8=1
21 and 7 → 21÷7=3, 7÷7=1

So now: (2/1) × (3/1) = 6/1 = 6

✔ Final for #6: 6

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**Problem 7:
2 11/12 × 2/5 = ?**

First, convert mixed number to improper fraction.

2 11/12 = (2×12 + 11)/12 = (24+11)/12 = 35/12

Now multiply: 35/12 × 2/5

Cancel: 35 and 5 → 35÷5=7, 5÷5=1
2 and 12 → 2÷2=1, 12÷2=6

So: (7/6) × (1/1) = 7/6

✔ Final for #7: 7/6

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**Problem 8:
1 3/4 × 20/21 = ?**

Convert 1 3/4 to improper: (1×4 + 3)/4 = 7/4

Now: 7/4 × 20/21

Cancel: 7 and 21 → 7÷7=1, 21÷7=3
20 and 4 → 20÷4=5, 4÷4=1

So: (1/1) × (5/3) = 5/3

✔ Final for #8: 5/3

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**Problem 9:
4 9/10 × 1 1/7 = ?**

Convert both to improper fractions.

4 9/10 = (4×10 + 9)/10 = 49/10
1 1/7 = (1×7 + 1)/7 = 8/7

Now multiply: 49/10 × 8/7

Cancel: 49 and 7 → 49÷7=7, 7÷7=1
8 and 10 → 8÷2=4, 10÷2=5

So: (7/5) × (4/1) = 28/5

✔ Final for #9: 28/5

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**Problem 10:
8 1/3 × 4 1/2 = ?**

Convert to improper:

8 1/3 = (8×3 + 1)/3 = 25/3
4 1/2 = (4×2 + 1)/2 = 9/2

Multiply: 25/3 × 9/2

Cancel: 9 and 3 → 9÷3=3, 3÷3=1

So: 25/1 × 3/2 = 75/2

✔ Final for #10: 75/2

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Final Answers:

1. 5/54
2. 7/20
3. 4/21
4. 15
5. 1/9
6. 6
7. 7/6
8. 5/3
9. 28/5
10. 75/2

Note: For problems 4 and 6, the answers are whole numbers. Since the instruction says "mixed numbers should be written as improper fractions", but doesn't require whole numbers to be written as fractions, writing them as integers is acceptable. However, to strictly follow "improper fractions" for any non-mixed result, we could write 15 as 15/1 and 6 as 6/1, but that seems unnecessary. Looking back at the example: "Ex. 9/2" — that’s an improper fraction from a mixed number. In our case, 15 and 6 are not mixed numbers, so they’re fine as is.

But let me double-check problem 4: 18 × 5/6 = 15 — yes. Problem 6: 16/7 × 21/8 = 6 — yes.

I think it’s okay.

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}