The problem asks us to simplify the given ratios: $5:8$, $12:32$, $18:45$, and $33:44$. We need to find the simplified form of each ratio.

1. Problem Description

The problem asks us to simplify the given ratios: $5:8$, $12:32$, $18:45$, and $33:44$. We need to find the simplified form of each ratio.

2. Solution Steps

We will simplify each ratio by dividing both numbers in the ratio by their greatest common divisor (GCD).

Ratio 1: $5:8$

The GCD of 5 and 8 is

1. Thus, the simplified ratio is $5:8$.

Ratio 2: $12:32$

The GCD of 12 and 32 is

4. Divide both numbers by 4:

$12 / 4 = 3$

$32 / 4 = 8$

So, the simplified ratio is $3:8$.

Ratio 3: $18:45$

The GCD of 18 and 45 is

9. Divide both numbers by 9:

$18 / 9 = 2$

$45 / 9 = 5$

So, the simplified ratio is $2:5$.

Ratio 4: $33:44$

The GCD of 33 and 44 is

1

1. Divide both numbers by 11:

$33 / 11 = 3$

$44 / 11 = 4$

So, the simplified ratio is $3:4$.

3. Final Answer

$5:8 = 5:8$

$12:32 = 3:8$

$18:45 = 2:5$

$33:44 = 3:4$