Let’s solve each problem step by step. We’re multiplying a whole number by a mixed fraction. The trick is to turn the mixed fraction into an improper fraction first, then multiply.
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1. 2 × 2 1/3
First, convert 2 1/3 to an improper fraction:
2 1/3 = (2×3 + 1)/3 = 7/3
Now multiply:
2 × 7/3 = 14/3
Convert back to mixed number:
14 ÷ 3 = 4 with remainder 2 →
4 2/3
*(Note: The example in the worksheet shows 2×2 + 2×1/3 = 4 + 2/3 = 4 2/3 — same answer!)*
✔ Answer:
4 2/3
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2. 3 × 5 2/9
Convert 5 2/9 to improper:
(5×9 + 2)/9 = 47/9
Multiply:
3 × 47/9 = 141/9
Simplify: divide numerator and denominator by 3 → 47/3
Convert to mixed: 47 ÷ 3 = 15 R2 →
15 2/3
✔ Answer:
15 2/3
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3. 4 × 3 1/15
Convert: (3×15 + 1)/15 = 46/15
Multiply: 4 × 46/15 = 184/15
Divide: 184 ÷ 15 = 12 R4 →
12 4/15
✔ Answer:
12 4/15
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4. 7 × 8 1/10
Convert: (8×10 + 1)/10 = 81/10
Multiply: 7 × 81/10 = 567/10
Divide: 567 ÷ 10 = 56 R7 →
56 7/10
✔ Answer:
56 7/10
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5. 6 × 10 2/21
Convert: (10×21 + 2)/21 = 212/21
Multiply: 6 × 212/21 = 1272/21
Simplify: Divide numerator and denominator by 3 → 424/7
Divide: 424 ÷ 7 = 60 R4 →
60 4/7
Wait — let me double-check that division:
7 × 60 = 420 → 424 - 420 = 4 → yes,
60 4/7
But wait — maybe we can simplify earlier? Let’s try again:
6 × 212 / 21 = (6/21) × 212 = (2/7) × 212 = 424/7 → same thing.
✔ Answer:
60 4/7
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6. 2 × 2 2/3
Convert: (2×3 + 2)/3 = 8/3
Multiply: 2 × 8/3 = 16/3
Divide: 16 ÷ 3 = 5 R1 →
5 1/3
✔ Answer:
5 1/3
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7. 3 × 4/9
This one is simple — no mixed number!
3 × 4/9 = 12/9 = 4/3 (divide top and bottom by 3)
Convert to mixed: 4 ÷ 3 = 1 R1 →
1 1/3
✔ Answer:
1 1/3
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8. 4 × 3 7/15
Convert: (3×15 + 7)/15 = 52/15
Multiply: 4 × 52/15 = 208/15
Divide: 208 ÷ 15 = 13 R13 →
13 13/15
Check: 15×13=195, 208-195=13 → correct.
✔ Answer:
13 13/15
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9. 7 × 8 3/10
Convert: (8×10 + 3)/10 = 83/10
Multiply: 7 × 83/10 = 581/10
Divide: 581 ÷ 10 = 58 R1 →
58 1/10
✔ Answer:
58 1/10
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10. 6 × 10 2/21
Same as #5 but with 6 instead of 6? Wait — actually, this is identical to #5? No — #5 was also 6 × 10 2/21. Oh, it’s repeated? Or typo? Anyway, same calculation.
We already did: 6 × 212/21 = 1272/21 = 424/7 = 60 4/7
✔ Answer:
60 4/7
Wait — looking back at the original list, problem #5 and #10 are both “6 × 10 2/21”. So they should have the same answer.
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Final Answers List:
1. 4 2/3
2. 15 2/3
3. 12 4/15
4. 56 7/10
5. 60 4/7
6. 5 1/3
7. 1 1/3
8. 13 13/15
9. 58 1/10
10. 60 4/7
All checked and verified.
Final Answer:
1. 4 2/3
2. 15 2/3
3. 12 4/15
4. 56 7/10
5. 60 4/7
6. 5 1/3
7. 1 1/3
8. 13 13/15
9. 58 1/10
10. 60 4/7
Parent Tip: Review the logic above to help your child master the concept of multiplying mixed fractions worksheet.
