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)
We solved ten multiplication problems involving fractions and mixed numbers by multiplying numerators and denominators and simplifying where needed. The answers include fractions like 54 5 and mixed numbers like 37 2 1 . Understanding these operations is crucial for solving real-life problems involving proportionality and ratios.
;
Multiply the fractions by multiplying the numerators and the denominators.
Simplify the resulting fraction to its simplest form.
Convert mixed numbers to improper fractions before multiplying.
The answers are: 54 5 , 20 7 , 21 4 , 15 , 9 1 , 6 , 1 6 1 , 1 3 2 , 5 5 3 , 37 2 1 .
Explanation
Understanding the Problem We are given 10 multiplication problems involving fractions and mixed numbers. Our goal is to compute each product and express the answer in 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 2 × 12 + 11 × 5 2 = 12 35 × 5 2 = 12 × 5 35 × 2 = 60 70 = 6 7 = 1 6 1
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 = 1 3 2
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 = 5 5 3
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 = 37 2 1
Final Answers The answers to the multiplication problems, in simplest form, are:
54 5
20 7
21 4
15
9 1
6
1 6 1
1 3 2
5 5 3
37 2 1
Examples
Understanding fraction multiplication is essential in many real-life situations. For instance, when you're 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 to make half the recipe, you would multiply 2 1 × 3 2 to find out how much flour you need. This gives you 3 1 cup. Similarly, in construction or design, calculating areas often involves multiplying fractional dimensions.
