Question

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

27 : 54
□ : 18
3 : □
□ : 2

Explanation:

Step1: Simplify the base ratio

First, simplify $27:54$ by dividing both terms by 27:
$\frac{27}{27}:\frac{54}{27} = 1:2$
This is the simplest equivalent ratio.

Step2: Find first missing value

We have $\square:18$, and know the simplified ratio is $1:2$. Let the missing value be $x$. Set up the proportion:
$\frac{x}{18} = \frac{1}{2}$
Solve for $x$: $x = \frac{18}{2} = 9$

Step3: Find second missing value

We have $3:\square$, let the missing value be $y$. Use the simplified ratio $1:2$:
$\frac{3}{y} = \frac{1}{2}$
Solve for $y$: $y = 3\times2 = 6$

Step4: Find third missing value

We have $\square:2$, let the missing value be $z$. Use the simplified ratio $1:2$:
$\frac{z}{2} = \frac{1}{2}$
Solve for $z$: $z = 1$

Answer:

The filled-in ratios are:
$9:18$
$3:6$
$1:2$