Question

1. complete the patterns of equivalent ratios by filling in the gaps.

: 4
□ : 8
4 : 16
8 :

Explanation:

Step1: Find the ratio factor

From the pair $4:16$, the ratio simplifies to $\frac{4}{16}=\frac{1}{4}$, so the first value is $\frac{1}{4}$ of the second value, or the second value is $4$ times the first.

Step2: Fill first gap

Second value is 4, so first value is $\frac{4}{4}=1$

Step3: Verify middle gap

First value is 2 (since $8\times\frac{1}{4}=2$; correction: wait, using the factor: second value 8, first value is $8\times\frac{1}{4}=2$)

Step4: Fill last gap

First value is 8, so second value is $8\times4=32$

Answer:

First gap: $1$, Middle gap: $2$, Last gap: $32$
The completed ratios are:
$1:4$
$2:8$
$4:16$
$8:32$