Question

Select all ratios equivalent to 15:12.
25:20
10:32
11:2

Answer 1

To determine which ratios are equivalent to \(15:12\), we can simplify \(15:12\) by finding the greatest common divisor (GCD) of 15 and 12.

The GCD of 15 and 12 is 3.

Now, we can simplify \(15:12\):

\[
\frac{15}{3} : \frac{12}{3} = 5:4
\]

Now, we will simplify the given ratios and check for equivalence to \(5:4\).

1. **For \(25:20\)**:
\[
\text{GCD of 25 and 20 is 5.}
\]
\[
\frac{25}{5} : \frac{20}{5} = 5:4
\]
So, \(25:20\) is equivalent to \(15:12\).

2. **For \(10:32\)**:
\[
\text{GCD of 10 and 32 is 2.}
\]
\[
\frac{10}{2} : \frac{32}{2} = 5:16
\]
So, \(10:32\) is not equivalent to \(15:12\).

3. **For \(11:2\)**:
The ratio \(11:2\) is already in its simplest form, and it cannot be simplified to \(5:4\).

Thus, \(11:2\) is also not equivalent to \(15:12\).

**Conclusion:** The only ratio equivalent to \(15:12\) is \(25:20\).