Question

fill in the blanks using only \\(\frac{24}{35}\\), \\(\frac{6}{7}\\), and \\(\frac{4}{5}\\).
(a) \\(square\\) \\(\times\\) \\(square\\) \\(=\\) \\(square\\)
(b) \\(square\\) \\(\div\\) \\(square\\) \\(=\\) \\(square\\)

Explanation:

Step1: Multiply two smaller fractions

$\frac{6}{7} \times \frac{4}{5} = \frac{6 \times 4}{7 \times 5} = \frac{24}{35}$

Step2: Set up division with the product

$\frac{24}{35} \div \frac{6}{7} = \frac{24}{35} \times \frac{7}{6} = \frac{24 \times 7}{35 \times 6} = \frac{4}{5}$

Answer:

(a) $\boldsymbol{\frac{6}{7}} \times \boldsymbol{\frac{4}{5}} = \boldsymbol{\frac{24}{35}}$
(b) $\boldsymbol{\frac{24}{35}} \div \boldsymbol{\frac{6}{7}} = \boldsymbol{\frac{4}{5}}$

Note: For part (a), $\frac{4}{5} \times \frac{6}{7} = \frac{24}{35}$ is also valid. For part (b), other valid combinations include $\frac{24}{35} \div \frac{4}{5} = \frac{6}{7}$.