Sure! Let’s solve each of the 18 mixed multiplication problems from the worksheet. These involve multiplying
mixed numbers (like 6⅗) and
whole numbers with
fractions.
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💡 Key Strategy:
To multiply mixed numbers:
1. Convert the mixed number to an
improper fraction.
2. Multiply the fractions (numerator × numerator, denominator × denominator).
3. Simplify the result, and convert back to a
mixed number if needed.
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##
✔ Problem-by-Problem Solutions:
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1. 6⅗ × 12
→ Convert 6⅗ = (6×5 + 3)/5 = 33/5
→ 33/5 × 12 = (33 × 12)/5 = 396/5
→ Convert to mixed: 396 ÷ 5 = 79 with remainder 1 →
79⅕
✔ Answer: 79⅕
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2. 4⅓ × 11⁷⁄₁₂
→ 4⅓ = 13/3; 11⁷⁄₁₂ = (11×12 + 7)/12 = 139/12
→ 13/3 × 139/12 = (13 × 139)/(3 × 12) = 1807 / 36
→ Simplify: 1807 ÷ 36 = 50 with remainder 7 →
50⁷⁄₃₆
→ ⁷⁄₃₆ is already simplified.
✔ Answer: 50⁷⁄₃₆
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3. 3⅔ × 1⅓
→ 3⅔ = 11/3; 1⅓ = 4/3
→ 11/3 × 4/3 = 44/9
→ 44 ÷ 9 = 4 with remainder 8 →
4⁸⁄₉
✔ Answer: 4⁸⁄₉
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4. ⁷⁄₈ × 6⅖
→ 6⅖ = 32/5
→ ⁷⁄₈ × 32/5 = (7 × 32)/(8 × 5) = 224 / 40
→ Simplify: Divide numerator and denominator by 8 → 28/5
→ 28 ÷ 5 = 5 with remainder 3 →
5⅗
✔ Answer: 5⅗
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5. ⁴⁄₅ × 6¾
→ 6¾ = 27/4
→ ⁴⁄₅ × 27/4 = (4 × 27)/(5 × 4) = 108 / 20
→ Cancel 4: 27/5
→ 27 ÷ 5 = 5 with remainder 2 →
5⅖
✔ Answer: 5⅖
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6. ⁴⁄₁₀ × 4⅓
→ 4⅓ = 13/3; ⁴⁄₁₀ = ²⁄₅ (simplified)
→ ²⁄₅ × 13/3 = 26/15
→ 26 ÷ 15 = 1 with remainder 11 →
1¹¹⁄₁₅
✔ Answer: 1¹¹⁄₁₅
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7. ⁵⁄₈ × ⁴³⁄₇
→ ⁵⁄₈ × ⁴³⁄₇ = (5 × 43)/(8 × 7) = 215 / 56
→ 215 ÷ 56 = 3 with remainder 47 →
3⁴⁷⁄₅₆
✔ Answer: 3⁴⁷⁄₅₆
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8. ⁴⁄₁₂ × ¹⁹⁄₃
→ ⁴⁄₁₂ = ¹⁄₃
→ ¹⁄₃ × ¹⁹⁄₃ = 19/9
→ 19 ÷ 9 = 2 with remainder 1 →
2¹⁄₉
✔ Answer: 2¹⁄₉
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9. ²⁄₅ × ¹⁹⁄₄
→ (2 × 19)/(5 × 4) = 38 / 20 = 19/10
→ 19 ÷ 10 = 1 with remainder 9 →
1⁹⁄₁₀
✔ Answer: 1⁹⁄₁₀
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10. ¹⁄₄ × 9
→ ¹⁄₄ × 9 = 9/4
→ 9 ÷ 4 = 2 with remainder 1 →
2¼
✔ Answer: 2¼
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11. ⁸⁄₁₁ × 6
→ ⁸⁄₁₁ × 6 = 48/11
→ 48 ÷ 11 = 4 with remainder 4 →
4⁴⁄₁₁
✔ Answer: 4⁴⁄₁₁
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12. ⁸⁄₉ × 11
→ ⁸⁄₉ × 11 = 88/9
→ 88 ÷ 9 = 9 with remainder 7 →
9⁷⁄₉
✔ Answer: 9⁷⁄₉
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13. ⁷⁄₈ × ⁸⁄₁₁ × 6
→ First, ⁷⁄₈ × ⁸⁄₁₁ = (7×8)/(8×11) = 56/88 → simplify by 8 → 7/11
→ Then 7/11 × 6 = 42/11
→ 42 ÷ 11 = 3 with remainder 9 →
3⁹⁄₁₁
✔ Answer: 3⁹⁄₁₁
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14. 2½ × 8
→ 2½ = 5/2
→ 5/2 × 8 = 40/2 =
20
✔ Answer: 20
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15. 7⅓ × 5
→ 7⅓ = 22/3
→ 22/3 × 5 = 110/3
→ 110 ÷ 3 = 36 with remainder 2 →
36⅔
✔ Answer: 36⅔
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16. 6 × 2
→ Simple multiplication:
12
✔ Answer: 12
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17. 15 × 2
→
30
✔ Answer: 30
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18. 9 × 14
→ 9 × 14 =
126
✔ Answer: 126
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## 🎯 Final Answers Summary:
1.
79⅕
2.
50⁷⁄₃₆
3.
4⁸⁄₉
4.
5⅗
5.
5⅖
6.
1¹¹⁄₁₅
7.
3⁴⁷⁄₅₆
8.
2¹⁄₉
9.
1⁹⁄₁₀
10.
2¼
11.
4⁴⁄₁₁
12.
9⁷⁄₉
13.
3⁹⁄₁₁
14.
20
15.
36⅔
16.
12
17.
30
18.
126
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Let me know if you’d like step-by-step work shown for any specific problem — or if you want to check your own answers! 😊
Parent Tip: Review the logic above to help your child master the concept of year 6 fractions worksheet.
