Answer. Write the answer in simplest form.
1. [tex]\frac{1}{6} \times \frac{5}{9}=[/tex]
2. [tex]\frac{2}{5} \times \frac{7}{8}=[/tex]
3. [tex]\frac{6}{7} \times \frac{2}{9}=[/tex]
4. [tex]18 \times \frac{5}{6}=[/tex]
5. [tex]\frac{5}{24} \times \frac{8}{15}=[/tex]
6. [tex]\frac{16}{7} \times \frac{21}{8}=[/tex]
7. [tex]2 \frac{11}{12} \times \frac{2}{5}=[/tex]
8. [tex]1 \frac{3}{4} \times \frac{20}{21}=[/tex]
9. [tex]4 \frac{9}{10} \times 1 \frac{1}{7}=[/tex]
10. [tex]8 \frac{1}{3} \times 4 \frac{1}{2}=[/tex]
Answer (2)
The products of the given multiplications involving fractions and mixed numbers have been calculated, resulting in specific simplified answers for each problem. A systematic approach, including properly multiplying fractions and converting mixed numbers, was used to achieve these results.
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Multiply the fractions directly: 6 1 × 9 5 = 54 5 , 5 2 × 8 7 = 20 7 , 7 6 × 9 2 = 21 4 , 24 5 × 15 8 = 9 1 .
Multiply the whole number by the fraction: 18 × 6 5 = 15 .
Convert mixed numbers to improper fractions and multiply: 2 12 11 × 5 2 = 6 7 , 1 4 3 × 21 20 = 3 5 , 4 10 9 × 1 7 1 = 5 28 , 8 3 1 × 4 2 1 = 2 75 .
Simplify each resulting fraction to its simplest form.
The final answers are: 54 5 , 20 7 , 21 4 , 15 , 9 1 , 6 , 6 7 , 3 5 , 5 28 , 2 75
Explanation
Understanding the Problem We are given 10 multiplication problems involving fractions and mixed numbers. Our goal is to find the product in simplest form for each problem.
Problem 1
6 1 × 9 5 = 6 × 9 1 × 5 = 54 5
Problem 2
5 2 × 8 7 = 5 × 8 2 × 7 = 40 14 = 20 7
Problem 3
7 6 × 9 2 = 7 × 9 6 × 2 = 63 12 = 21 4
Problem 4
18 × 6 5 = 1 18 × 6 5 = 1 × 6 18 × 5 = 6 90 = 15
Problem 5
24 5 × 15 8 = 24 × 15 5 × 8 = 360 40 = 9 1
Problem 6
7 16 × 8 21 = 7 × 8 16 × 21 = 56 336 = 6
Problem 7
2 12 11 × 5 2 = 12 2 × 12 + 11 × 5 2 = 12 35 × 5 2 = 12 × 5 35 × 2 = 60 70 = 6 7
Problem 8
1 4 3 × 21 20 = 4 1 × 4 + 3 × 21 20 = 4 7 × 21 20 = 4 × 21 7 × 20 = 84 140 = 3 5
Problem 9
4 10 9 × 1 7 1 = 10 4 × 10 + 9 × 7 1 × 7 + 1 = 10 49 × 7 8 = 10 × 7 49 × 8 = 70 392 = 5 28
Problem 10
8 3 1 × 4 2 1 = 3 8 × 3 + 1 × 2 4 × 2 + 1 = 3 25 × 2 9 = 3 × 2 25 × 9 = 6 225 = 2 75
Final Answer The answers to the 10 multiplication problems are: 54 5 , 20 7 , 21 4 , 15 , 9 1 , 6 , 6 7 , 3 5 , 5 28 , and 2 75 .
Examples
Understanding fraction multiplication is crucial in many real-life scenarios. For instance, when you're baking and need to halve a recipe, you're essentially multiplying fractions. If a recipe calls for 3 2 cup of flour and you want to make half the recipe, you multiply 3 2 by 2 1 to find out you need 3 1 cup of flour. Similarly, in construction or engineering, calculating proportions and scaling dimensions often involves multiplying fractions to ensure accuracy and proper scaling.
