Sure! Let’s solve each problem step by step. The task is to
multiply mixed numbers and whole numbers.
General Strategy:
1.
Convert the mixed number to an improper fraction.
2.
Write the whole number as a fraction (over 1).
3.
Multiply the two fractions (numerator × numerator, denominator × denominator).
4.
Simplify the result, and convert back to a mixed number if needed.
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Let’s go one by one:
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1) 6 ²⁄₃ × 9
- Convert 6 ²⁄₃ → (6×3 + 2)/3 = 20/3
- 9 = 9/1
- Multiply: (20/3) × (9/1) = (20 × 9)/(3 × 1) = 180/3 =
60
✔ Answer: 60
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2) 7 × 1 ²⁄₉
- 7 = 7/1
- 1 ²⁄₉ = (9×1 + 2)/9 = 11/9
- Multiply: (7/1) × (11/9) = 77/9
- Convert to mixed number: 77 ÷ 9 = 8 with remainder 5 →
8 ⁵⁄₉
✔ Answer: 8 ⁵⁄₉
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3) 11 × 2 ²⁄₇
- 11 = 11/1
- 2 ²⁄₇ = (7×2 + 2)/7 = 16/7
- Multiply: (11/1) × (16/7) = 176/7
- 176 ÷ 7 = 25 with remainder 1 →
25 ¹⁄₇
✔ Answer: 25 ¹⁄₇
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4) 2 ¹⁄₄ × 8
- 2 ¹⁄₄ = (4×2 + 1)/4 = 9/4
- 8 = 8/1
- Multiply: (9/4) × (8/1) = 72/4 =
18
✔ Answer: 18
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5) 10 ⁹⁄₁₀ × 10
- 10 ⁹⁄₁₀ = (10×10 + 9)/10 = 109/10
- 10 = 10/1
- Multiply: (109/10) × (10/1) = 1090/10 =
109
✔ Answer: 109
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6) 6 × 1 ⁷⁄₁₂
- 6 = 6/1
- 1 ⁷⁄₁₂ = (12×1 + 7)/12 = 19/12
- Multiply: (6/1) × (19/12) = 114/12
- Simplify: divide numerator and denominator by 6 → 19/2 =
9 ¹⁄₂
✔ Answer: 9 ¹⁄₂
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7) 2 × 3 ²⁄₉
- 2 = 2/1
- 3 ²⁄₉ = (9×3 + 2)/9 = 29/9
- Multiply: (2/1) × (29/9) = 58/9
- 58 ÷ 9 = 6 with remainder 4 →
6 ⁴⁄₉
✔ Answer: 6 ⁴⁄₉
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8) 2 ³⁄₅ × 15
- 2 ³⁄₅ = (5×2 + 3)/5 = 13/5
- 15 = 15/1
- Multiply: (13/5) × (15/1) = 195/5 =
39
✔ Answer: 39
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9) 2 ⁵⁄₆ × 12
- 2 ⁵⁄₆ = (6×2 + 5)/6 = 17/6
- 12 = 12/1
- Multiply: (17/6) × (12/1) = 204/6 =
34
✔ Answer: 34
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10) 4 × 7 ¹⁄₂
- 4 = 4/1
- 7 ¹⁄₂ = (2×7 + 1)/2 = 15/2
- Multiply: (4/1) × (15/2) = 60/2 =
30
✔ Answer: 30
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11) 5 × 3 ⁷⁄₈
- 5 = 5/1
- 3 ⁷⁄₈ = (8×3 + 7)/8 = 31/8
- Multiply: (5/1) × (31/8) = 155/8
- 155 ÷ 8 = 19 with remainder 3 →
19 ³⁄₈
✔ Answer: 19 ³⁄₈
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12) 1 ¹⁰⁄₁₁ × 2
- 1 ¹⁰⁄₁₁ = (11×1 + 10)/11 = 21/11
- 2 = 2/1
- Multiply: (21/11) × (2/1) = 42/11
- 42 ÷ 11 = 3 with remainder 9 →
3 ⁹⁄₁₁
✔ Answer: 3 ⁹⁄₁₁
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##
✔ Final Answers:
1)
60
2)
8 ⁵⁄₉
3)
25 ¹⁄₇
4)
18
5)
109
6)
9 ¹⁄₂
7)
6 ⁴⁄₉
8)
39
9)
34
10)
30
11)
19 ³⁄₈
12)
3 ⁹⁄₁₁
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Let me know if you’d like to see any step explained in more detail!
Parent Tip: Review the logic above to help your child master the concept of multiplying mixed fractions worksheet.
