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)
To multiply fractions and mixed numbers, multiply the numerators and denominators, convert mixed numbers to improper fractions, and simplify if necessary. The final answers for the problems are: 54 5 , 20 7 , 21 4 , 15 , 9 1 , 6 , 6 7 , 3 5 , 5 28 , and 2 75 .
;
Multiply the fractions: b a × d c = b × d a × c .
Convert mixed numbers to improper fractions before multiplying.
Simplify the 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 of each problem in its simplest form.
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 35 × 5 2 = 12 × 5 35 × 2 = 60 70 = 6 7
Problem 8
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 49 × 7 8 = 10 × 7 49 × 8 = 70 392 = 5 28
Problem 10
8 3 1 × 4 2 1 = 3 25 × 2 9 = 3 × 2 25 × 9 = 6 225 = 2 75
Final Answers The answers to the multiplication problems, in simplest form, 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 baking, you might need to halve a recipe, which involves multiplying fractions. If a recipe calls for 3 2 cup of flour, and you only want half the recipe, you would calculate 2 1 × 3 2 = 3 1 cup of flour. Similarly, in construction or woodworking, calculating fractions of lengths is essential for accurate measurements and cuts. Knowing how to multiply and simplify fractions ensures precision and avoids waste in various practical applications.
