Question

the equivalent ratios are $8: \frac{1}{3}$, d $4:\frac{1}{6}$ $\boldsymbol{\checkmark}$ , e $6:\frac{1}{4}$ $\boldsymbol{\checkmark}$ , and f $\square:\square$ .

Explanation:

Step1: Simplify the base ratio

First, simplify $8:\frac{1}{3}$ by converting it to a fraction:
$$8\div\frac{1}{3}=8\times3=24$$
So the ratio simplifies to $24:1$ (meaning the first term is 24 times the second term).

Step2: Verify given equivalent ratios

For $4:\frac{1}{6}$:
$$4\div\frac{1}{6}=4\times6=24$$
For $6:\frac{1}{4}$:
$$6\div\frac{1}{4}=6\times4=24$$
Both equal 24, confirming the ratio rule.

Step3: Find a new equivalent ratio

Choose a value for the second term, e.g., $\frac{1}{2}$. Calculate the first term:
$$24\times\frac{1}{2}=12$$
So the ratio is $12:\frac{1}{2}$.

Answer:

$12:\frac{1}{2}$ (Note: Any ratio where the first term is 24 times the second term is valid, e.g., $24:1$, $12:\frac{1}{2}$, $3:\frac{1}{8}$)