Let’s solve each problem step by step. We’re multiplying whole numbers by mixed numbers (or sometimes just fractions). The easiest way is to turn the mixed number into an improper fraction, multiply, then simplify if needed — or convert back to a mixed number.
We’ll go one by one:
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1a. 4 1/4 × 6
→ Turn 4 1/4 into improper fraction: (4×4 + 1)/4 = 17/4
→ Multiply: 17/4 × 6 = (17×6)/4 = 102/4
→ Simplify: 102 ÷ 2 = 51, 4 ÷ 2 = 2 → 51/2
→ Convert to mixed number: 51 ÷ 2 = 25 remainder 1 →
25 1/2
1b. 1 5/6 × 6
→ Improper fraction: (1×6 + 5)/6 = 11/6
→ Multiply: 11/6 × 6 = (11×6)/6 = 66/6 =
11
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2a. 5 × 9 3/8
→ 9 3/8 = (9×8 + 3)/8 = 75/8
→ 5 × 75/8 = 375/8
→ 375 ÷ 8 = 46 remainder 7 →
46 7/8
2b. 6 × 6 2/3
→ 6 2/3 = (6×3 + 2)/3 = 20/3
→ 6 × 20/3 = 120/3 =
40
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3a. 10 2/6 × 3
→ First, simplify 2/6 to 1/3 → so 10 1/3
→ 10 1/3 = (10×3 + 1)/3 = 31/3
→ 31/3 × 3 = 93/3 =
31
*(Note: You could also do 10×3 = 30 and 1/3×3 = 1 → total 31)*
3b. 4 × 3 2/6
→ Simplify 2/6 to 1/3 → 3 1/3
→ 3 1/3 = 10/3
→ 4 × 10/3 = 40/3 = 13 remainder 1 →
13 1/3
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4a. 1 1/2 × 4
→ 1 1/2 = 3/2
→ 3/2 × 4 = 12/2 =
6
4b. 6 × 1 3/4
→ 1 3/4 = 7/4
→ 6 × 7/4 = 42/4 = 21/2 =
10 1/2
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5a. 2 × 6 4/8
→ Simplify 4/8 to 1/2 → 6 1/2
→ 6 1/2 = 13/2
→ 2 × 13/2 = 26/2 =
13
5b. 9 5/6 × 4
→ 9 5/6 = (9×6 + 5)/6 = 59/6
→ 59/6 × 4 = 236/6
→ Simplify: divide numerator and denominator by 2 → 118/3
→ 118 ÷ 3 = 39 remainder 1 →
39 1/3
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6a. 3 2/4 × 5
→ Simplify 2/4 to 1/2 → 3 1/2
→ 3 1/2 = 7/2
→ 7/2 × 5 = 35/2 =
17 1/2
6b. 2 × 11 1/2
→ 11 1/2 = 23/2
→ 2 × 23/2 = 46/2 =
23
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7a. 5 × 1 5/8
→ 1 5/8 = 13/8
→ 5 × 13/8 = 65/8
→ 65 ÷ 8 = 8 remainder 1 →
8 1/8
7b. 4 × 7 4/6
→ Simplify 4/6 to 2/3 → 7 2/3
→ 7 2/3 = (7×3 + 2)/3 = 23/3
→ 4 × 23/3 = 92/3
→ 92 ÷ 3 = 30 remainder 2 →
30 2/3
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8a. 4 4/6 × 5
→ Simplify 4/6 to 2/3 → 4 2/3
→ 4 2/3 = (4×3 + 2)/3 = 14/3
→ 14/3 × 5 = 70/3
→ 70 ÷ 3 = 23 remainder 1 →
23 1/3
8b. 6 1/8 × 6
→ 6 1/8 = (6×8 + 1)/8 = 49/8
→ 49/8 × 6 = 294/8
→ Simplify: divide numerator and denominator by 2 → 147/4
→ 147 ÷ 4 = 36 remainder 3 →
36 3/4
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Final Answer:
1a. 25 1/2
1b. 11
2a. 46 7/8
2b. 40
3a. 31
3b. 13 1/3
4a. 6
4b. 10 1/2
5a. 13
5b. 39 1/3
6a. 17 1/2
6b. 23
7a. 8 1/8
7b. 30 2/3
8a. 23 1/3
8b. 36 3/4
Parent Tip: Review the logic above to help your child master the concept of multiplying fractions and whole numbers worksheet.
