Let’s solve each problem step by step. Remember: to multiply mixed numbers, first turn them into improper fractions. Then multiply the numerators and denominators. Finally, simplify if needed — and if the answer is an improper fraction, turn it back into a mixed number.
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Problem 1:
3 ³⁄₅ × ⁵⁄
Step 1: Convert 3 ³⁄₅ to an improper fraction.
3 × 5 = 15, plus 3 = 18 → so ¹⁸⁄₅
Now multiply:
¹⁸⁄ × ⁵⁄₈ = (18 × 5) / (5 × 8) = 90 / 40
Simplify: divide numerator and denominator by 10 → 9/4
Convert to mixed number: 9 ÷ 4 = 2 with remainder 1 →
2 ¹⁄₄
✔ Check: 18×5=90, 5×8=40 → 90÷10=9, 40÷10=4 → 9/4 = 2¼ ✔️
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Problem 2:
2 ⁴⁄₉ × ³⁄₁₀
Convert 2 ⁴⁄₉: 2×9=18 + 4 = 22 → ²²⁄
Multiply: ²²⁄₉ × ³⁄₁₀ = (22×3)/(9×10) = 66 / 90
Simplify: divide by 6 → 11/15
✔ 66÷6=11, 90÷6=15 →
¹¹⁄₁₅
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Problem 3:
5 ³⁄₅ × ⁵⁄₁₆
Convert 5 ³⁄₅: 5×5=25 + 3 = 28 → ²⁸⁄
Multiply: ²⁸⁄₅ × ⁵⁄₁₆ = (28×5)/(5×16) = 140 / 80
Simplify: divide by 20 → 7/4
Convert to mixed: 7÷4 = 1 R3 →
1 ³⁄₄
✔ 140÷20=7, 80÷20=4 → 7/4 = 1¾ ✔️
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Problem 4:
2 ³⁄₁₄ × ²⁄₇
Convert 2 ³⁄₁₄: 2×14=28 + 3 = 31 → ³¹⁄₁₄
Multiply: ³¹⁄₁₄ × ²⁄₇ = (31×2)/(14×7) = 62 / 98
Simplify: divide by 2 → 31/49
✔ 62÷2=31, 98÷2=49 →
³¹⁄₄
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Problem 5:
3 ³⁄₄ × ¹⁶⁄₂₁
Convert 3 ³⁄₄: 3×4=12 + 3 = 15 → ¹⁵⁄₄
Multiply: ¹⁵⁄₄ × ¹⁶⁄₂₁ = (15×16)/(4×21) = 240 / 84
Simplify: divide by 12 → 20/7
Convert to mixed: 20÷7 = 2 R6 →
2 ⁶⁄
✔ 240÷12=20, 84÷12=7 → 20/7 = 2⁶⁄ ✔️
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Problem 6:
4 ⁵⁄ × ⁷₁₅
Convert 4 ⁵⁄₇: 4×7=28 + 5 = 33 → ³³⁄₇
Multiply: ³³⁄₇ × ⁷⁄₁₅ = (33×7)/(7×15) = 231 / 105
Cancel the 7s first! → 33/1 × 1/15 = 33/15
Simplify: divide by 3 → 11/5
Convert to mixed: 11÷5 = 2 R1 →
2 ¹⁄
✔ 33×7=231, 7×15=105 → cancel 7 → 33/15 → 11/5 = 2⅕ ✔️
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Problem 7:
2 ⁵⁄ × ¹⁴₁₅
Convert 2 ⁵⁄: 2×7=14 + 5 = 19 → ¹⁹⁄
Multiply: ¹⁹⁄ × ¹⁴₁₅ = (19×14)/(7×15)
Notice: 14 and 7 can cancel → 14÷7=2, 7÷7=1 → becomes (19×2)/(1×15) = 38/15
Convert to mixed: 38÷15 = 2 R8 →
2 ⁸⁄₁₅
✔ 19×14=266, 7×15=105 → but better to cancel first → 38/15 = 2⁸₁₅ ✔️
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Problem 8:
5 ²⁄₅ × ²⁄₉
Convert 5 ²⁄₅: 5×5=25 + 2 = 27 → ²⁷⁄₅
Multiply: ²⁷⁄₅ × ²⁄₉ = (27×2)/(5×9) = 54 / 45
Simplify: divide by 9 → 6/5
Convert to mixed: 6÷5 = 1 R1 →
1 ¹⁄₅
✔ 54÷9=6, 45÷9=5 → 6/5 = 1⅕ ✔️
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Final Answer:
1. 2 ¹⁄₄
2. ¹¹⁄₁₅
3. 1 ³⁄₄
4. ³¹⁄₄₉
5. 2 ⁶⁄₇
6. 2 ¹⁄₅
7. 2 ⁸⁄₁₅
8. 1 ¹⁄₅
Parent Tip: Review the logic above to help your child master the concept of multiplying mixed fractions printable.
