Question

fill in the blanks using only \\(\frac{8}{9}\\), \\(\frac{16}{63}\\), and \\(\frac{2}{7}\\).\
\\(\frac{8}{9}\\) \\(\frac{16}{63}\\) \\(\frac{2}{7}\\)\
(a) \\(\square \times \square = \square\\)\
(b) \\(\square \div \square = \square\\)

Explanation:

Step1: Multiply two given fractions

$\frac{8}{9} \times \frac{2}{7} = \frac{8 \times 2}{9 \times 7} = \frac{16}{63}$

Step2: Divide two given fractions

$\frac{16}{63} \div \frac{2}{7} = \frac{16}{63} \times \frac{7}{2} = \frac{16 \times 7}{63 \times 2} = \frac{8}{9}$

Answer:

(a) $\boldsymbol{\frac{8}{9}} \times \boldsymbol{\frac{2}{7}} = \boldsymbol{\frac{16}{63}}$
(b) $\boldsymbol{\frac{16}{63}} \div \boldsymbol{\frac{2}{7}} = \boldsymbol{\frac{8}{9}}$

Note: For part (b), valid alternative combinations include $\boldsymbol{\frac{16}{63}} \div \boldsymbol{\frac{8}{9}} = \boldsymbol{\frac{2}{7}}$ or $\boldsymbol{\frac{8}{9}} \div \boldsymbol{\frac{2}{7}} = \boldsymbol{\frac{28}{9}}$ (but this result is not in the given set, so the first two are the valid matches using only the provided fractions).