Question

do form a proportion do not form a proportion \\(\frac{\frac{1}{8}}{\frac{9}{10}}\\) and \\(\frac{\frac{1}{2}}{\frac{4}{5}}\\) \\(\frac{\frac{1}{2}}{\frac{4}{5}}\\) and \\(\frac{\frac{1}{4}}{\frac{2}{5}}\\) \\(\frac{\frac{1}{8}}{\frac{9}{10}}\\) and \\(\frac{\frac{1}{4}}{\frac{9}{5}}\\)

Explanation:

Step1: Simplify complex fractions

For a complex fraction $\frac{\frac{a}{b}}{\frac{c}{d}}$, it equals $\frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$.

• $\frac{\frac{1}{8}}{\frac{9}{10}} = \frac{1 \times 10}{8 \times 9} = \frac{10}{72} = \frac{5}{36}$
• $\frac{\frac{1}{2}}{\frac{4}{5}} = \frac{1 \times 5}{2 \times 4} = \frac{5}{8}$
• $\frac{\frac{1}{4}}{\frac{2}{5}} = \frac{1 \times 5}{4 \times 2} = \frac{5}{8}$
• $\frac{\frac{1}{4}}{\frac{9}{5}} = \frac{1 \times 5}{4 \times 9} = \frac{5}{36}$

Step2: Check equal ratios (proportions)

Two ratios form a proportion if they are equal.

• Pair 1: $\frac{5}{36}$ and $\frac{5}{8}$ → Not equal
• Pair 2: $\frac{5}{8}$ and $\frac{5}{8}$ → Equal
• Pair 3: $\frac{5}{36}$ and $\frac{5}{36}$ → Equal

Answer:

Do form a proportion:

$\frac{\frac{1}{2}}{\frac{4}{5}}$ and $\frac{\frac{1}{4}}{\frac{2}{5}}$, $\frac{\frac{1}{8}}{\frac{9}{10}}$ and $\frac{\frac{1}{4}}{\frac{9}{5}}$

Do not form a proportion:

$\frac{\frac{1}{8}}{\frac{9}{10}}$ and $\frac{\frac{1}{2}}{\frac{4}{5}}$