Question

Select all ratios equivalent to 48:15.
16:5
7:6
32:10

Answer 1

To determine which ratios are equivalent to \(48:15\), we can simplify \(48:15\) and then check each given ratio.

First, let's simplify \(48:15\):

1. Find the greatest common divisor (GCD) of 48 and 15.
- The GCD of 48 and 15 is 3.

2. Divide both numbers by their GCD:
\[
\frac{48}{3} : \frac{15}{3} = 16:5
\]

Now, we need to check the other ratios to see if they simplify to \(16:5\).

**Check \(16:5\):**
- This ratio is already in simplest form and matches \(16:5\).

**Check \(7:6\):**
- This ratio cannot be simplified further and does not equal \(16:5\).

**Check \(32:10\):**
1. Find the GCD of 32 and 10.
- The GCD of 32 and 10 is 2.

2. Divide both numbers by their GCD:
\[
\frac{32}{2} : \frac{10}{2} = 16:5
\]

Thus, the ratios that are equivalent to \(48:15\) are:
- \(16:5\)
- \(32:10\)

Final result: **The equivalent ratios are \(16:5\) and \(32:10\).**