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\begin{tabular}{l} Activity 6.4a No 1 Page 94 \\ Simplify: \\ \( \begin{array}{lll}\text { a. } \frac{1}{6} \times \frac{1}{3} & \text { b. } \frac{1}{7} \times \frac{2}{5} & \text { c. } \frac{5}{9} \times \frac{2}{3} \\ \text { d. } \frac{3}{8} \times \frac{1}{4} & \text { e. } \frac{3}{10} \times \frac{2}{5} & \text { f. } \\ \\ \text { Activity 6.4b No 3-4 Page 95 } & & \end{array} \) \\ \hline\end{tabular}

Ask by Pope Mcguire. in South Africa
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

a. \( \frac{1}{18} \) b. \( \frac{2}{35} \) c. \( \frac{10}{27} \) d. \( \frac{3}{32} \) e. \( \frac{3}{25} \)

Solution

**a. Simplify \( \frac{1}{6} \times \frac{1}{3} \):** Multiply the numerators and the denominators: \[ \frac{1 \times 1}{6 \times 3} = \frac{1}{18} \] **b. Simplify \( \frac{1}{7} \times \frac{2}{5} \):** Multiply the numerators and the denominators: \[ \frac{1 \times 2}{7 \times 5} = \frac{2}{35} \] **c. Simplify \( \frac{5}{9} \times \frac{2}{3} \):** Multiply the numerators and the denominators: \[ \frac{5 \times 2}{9 \times 3} = \frac{10}{27} \] **d. Simplify \( \frac{3}{8} \times \frac{1}{4} \):** Multiply the numerators and the denominators: \[ \frac{3 \times 1}{8 \times 4} = \frac{3}{32} \] **e. Simplify \( \frac{3}{10} \times \frac{2}{5} \):** Multiply the numerators and the denominators: \[ \frac{3 \times 2}{10 \times 5} = \frac{6}{50} \] Simplify \( \frac{6}{50} \) by dividing the numerator and the denominator by \(2\): \[ \frac{6 \div 2}{50 \div 2} = \frac{3}{25} \]

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Beyond the Answer

When simplifying fractions, it’s like finding the “hidden treasure” within the numbers! For example, in problem a, \(\frac{1}{6} \times \frac{1}{3} = \frac{1 \times 1}{6 \times 3} = \frac{1}{18}\). That’s your treasure right there! Each multiplication simply counts the numerators on top and the denominators on the bottom. Now, if you’re ever feeling stuck with fraction multiplication, remember this golden rule: multiply straight across! For example, in part d, \(\frac{3}{8} \times \frac{1}{4} = \frac{3 \times 1}{8 \times 4} = \frac{3}{32}\). Just watch out for common mistakes, like forgetting to simplify at the end or getting mixed up with addition instead of multiplication. That’s an easy trap to fall into!

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