Question
Let's multiply. \( \begin{array}{lllll}\text { a) } 3 \times \frac{1}{5} & \text { b) } 8 \times \frac{2}{7} & \text { c) } \frac{5}{9} \times 2 & \text { d) } \frac{2}{3} \times 9 & \text { e) } \frac{5}{6} \times 24 \\ \begin{array}{lllll}10 \times \frac{7}{8} & \text { g) } 18 \times \frac{2}{15} & \text { h) } \frac{2}{3} \times \frac{4}{5} & \text { i] } \frac{3}{4} \times \frac{5}{8} & \text { j) } \frac{4}{7} \times \frac{7}{8} \\ \text { k) } \frac{5}{8} \times \frac{8}{15} & \text { l) } \frac{5}{6} \times \frac{8}{15} & \text { m) } \frac{15}{16} \times \frac{12}{25} & \text { n) } 1 \frac{1}{2} \times 1 \frac{1}{3} & \text { o) } 4 \frac{3}{8} \times 1 \frac{1}{15}\end{array} \\ \text { el's divide. }\end{array} \)
Ask by Ward Mccarthy. in Nepal
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**a)**
\( 3 \times \frac{1}{5} = \frac{3}{5} \)
**b)**
\( 8 \times \frac{2}{7} = \frac{16}{7} \)
**c)**
\( \frac{5}{9} \times 2 = \frac{10}{9} \)
**d)**
\( \frac{2}{3} \times 9 = 6 \)
**e)**
\( \frac{5}{6} \times 24 = 20 \)
**f)**
\( 10 \times \frac{7}{8} = 8\frac{3}{4} \)
**g)**
\( 18 \times \frac{2}{15} = 2\frac{2}{5} \)
**h)**
\( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \)
**i)**
\( \frac{3}{4} \times \frac{5}{8} = \frac{15}{32} \)
**j)**
\( \frac{4}{7} \times \frac{7}{8} = \frac{1}{2} \)
**k)**
\( \frac{5}{8} \times \frac{8}{15} = \frac{1}{3} \)
**l)**
\( \frac{5}{6} \times \frac{8}{15} = \frac{4}{9} \)
**m)**
\( \frac{15}{16} \times \frac{12}{25} = \frac{9}{20} \)
**n)**
\( 1\frac{1}{2} \times 1\frac{1}{3} = 2 \)
**o)**
\( 4\frac{3}{8} \times 1\frac{1}{15} = 4\frac{2}{3} \)
Solution
**a)**
\( 3 \times \frac{1}{5} = \frac{3}{5} \)
---
**b)**
\( 8 \times \frac{2}{7} = \frac{16}{7} \)
---
**c)**
\( \frac{5}{9} \times 2 = \frac{5 \times 2}{9} = \frac{10}{9} \)
---
**d)**
\( \frac{2}{3} \times 9 = \frac{2 \times 9}{3} = \frac{18}{3} = 6 \)
---
**e)**
\( \frac{5}{6} \times 24 = \frac{5 \times 24}{6} = \frac{120}{6} = 20 \)
---
**f)**
\( 10 \times \frac{7}{8} = \frac{10 \times 7}{8} = \frac{70}{8} = \frac{35}{4} = 8\frac{3}{4} \)
---
**g)**
\( 18 \times \frac{2}{15} = \frac{18 \times 2}{15} = \frac{36}{15} = \frac{12}{5} = 2\frac{2}{5} \)
---
**h)**
\( \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \)
---
**i)**
\( \frac{3}{4} \times \frac{5}{8} = \frac{3 \times 5}{4 \times 8} = \frac{15}{32} \)
---
**j)**
\( \frac{4}{7} \times \frac{7}{8} = \frac{4 \times 7}{7 \times 8} = \frac{28}{56} = \frac{1}{2} \)
---
**k)**
\( \frac{5}{8} \times \frac{8}{15} = \frac{5 \times 8}{8 \times 15} \)
Cancel the common factor \(8\):
\( = \frac{5}{15} = \frac{1}{3} \)
---
**l)**
\( \frac{5}{6} \times \frac{8}{15} = \frac{5 \times 8}{6 \times 15} = \frac{40}{90} \)
Divide numerator and denominator by \(10\):
\( = \frac{4}{9} \)
---
**m)**
\( \frac{15}{16} \times \frac{12}{25} = \frac{15 \times 12}{16 \times 25} = \frac{180}{400} \)
Divide numerator and denominator by \(20\):
\( = \frac{9}{20} \)
---
**n)**
Convert mixed numbers to improper fractions:
\( 1\frac{1}{2} = \frac{3}{2} \) and \( 1\frac{1}{3} = \frac{4}{3} \)
Multiply:
\( \frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2 \)
---
**o)**
Convert mixed numbers:
\( 4\frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{35}{8} \) and \( 1\frac{1}{15} = \frac{1 \times 15 + 1}{15} = \frac{16}{15} \)
Multiply:
\( \frac{35}{8} \times \frac{16}{15} = \frac{35 \times 16}{8 \times 15} \)
Since \( \frac{16}{8} = 2 \), this becomes:
\( = \frac{35 \times 2}{15} = \frac{70}{15} = \frac{14}{3} = 4\frac{2}{3} \)
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Simplify this solution Extra Insights
When multiplying fractions, simply multiply the numerators together for your new numerator and the denominators together for your new denominator. For example, \( \frac{2}{3} \times \frac{4}{5} \) equals \( \frac{8}{15} \). It's a snap! Now, don't forget to simplify your answers if possible. For instance, \( \frac{5}{8} \times \frac{8}{15} \) simplifies to \( \frac{1}{15} \) as the 8’s can cancel each other out, making your math life a bit easier and keeping your answers neat!
