Question

Find which of the following pairs are equal by writing them in their simplest form.

• A. $\frac{1}{4}$ and $\frac{28}{184}$
• B. $\frac{1}{5}$ and $\frac{48}{480}$
• C. $\frac{2}{3}$ and $\frac{150}{225}$
• D. $\frac{3}{4}$ and $\frac{38}{164}$

Answer 1

The correct option is C $\frac{2}{3}$ and $\frac{150}{225}$

We have $\frac{28}{184}=\frac{28÷4}{184÷4}=\frac{7}{46}$, the simplest form of $\frac{28}{184}$ and $\frac{7}{46}\ne \frac{1}{4}⟹\frac{28}{184}\ne \frac{1}{4}.$
Similarly, $\frac{48}{480}=\frac{48÷48}{480÷48}=\frac{1}{10}$, not equal to $\frac{1}{5}.$
Next, $\frac{150}{225}=\frac{150÷75}{225÷75}=\frac{2}{3}.$
And, $\frac{38}{164}=\frac{38÷2}{164÷2}\frac{19}{82}$, not equal to $\frac{3}{4}.$