Question

which of the following expressions is equivalent to $\frac{1}{49}$? $\frac{11}{7}cdot\frac{7}{11}$, $\frac{2}{7}cdot\frac{7}{2}$, $\frac{3}{7}cdot\frac{7}{3}$, $\frac{4}{7}cdot\frac{7}{4}$, $\frac{5}{7}cdot\frac{7}{5}$

Explanation:

Step1: Recall fraction - division rule

Dividing by a fraction is equivalent to multiplying by its reciprocal. So $\frac{1}{7}\div\frac{4}{7}=\frac{1}{7}\times\frac{7}{4}$.

Step2: Multiply the fractions

When multiplying fractions $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$. Here, $a = 1$, $b = 7$, $c = 7$, $d = 4$, so $\frac{1}{7}\times\frac{7}{4}=\frac{1\times7}{7\times4}=\frac{7}{28}=\frac{1}{4}$.
Let's check each option:

• Option 1: $\frac{3}{7}\div\frac{2}{7}=\frac{3}{7}\times\frac{7}{2}=\frac{3}{2}$.
• Option 2: $\frac{4}{7}\div\frac{7}{4}=\frac{4}{7}\times\frac{4}{7}=\frac{16}{49}$.
• Option 3: $\frac{5}{7}\div\frac{1}{7}=\frac{5}{7}\times\frac{7}{1}=5$.
• Option 4: $\frac{6}{7}\div\frac{3}{7}=\frac{6}{7}\times\frac{7}{3}=2$.
• Option 5: $\frac{11}{7}\div\frac{2}{7}=\frac{11}{7}\times\frac{7}{2}=\frac{11}{2}$.

Since there is no correct - looking option in the provided ones, if we assume there is a calculation error in writing the options and we focus on the rule of fraction - division:
The general rule for $\frac{a}{b}\div\frac{c}{b}=\frac{a}{b}\times\frac{b}{c}=\frac{a}{c}$. If we want an equivalent of $\frac{1}{7}\div\frac{4}{7}$, we should have something like $\frac{1}{x}\div\frac{4}{x}$ (where $x
eq0$).

If we rewrite the problem in a more standard way, we know that $\frac{1}{7}\div\frac{4}{7}=\frac{1}{4}$.

Answer:

There seems to be an error in the provided options as none of them is equivalent to $\frac{1}{7}\div\frac{4}{7}=\frac{1}{4}$.