Question

Compare these three ratios using fractions.

3 to 2     5:6     8 to 12

Think about the steps you could take to compare the ratios using fractions.


The first step is to write the ratios as fractions.

The next step is to use a
to rewrite the fractions.
Finally, compare the
to help you order the ratios.

Answer 1

To compare the three ratios \(3:2\), \(5:6\), and \(8:12\) using fractions, we can follow the steps mentioned.

### Step 1: Write the Ratios as Fractions

1. \(3:2\) can be written as the fraction \(\frac{3}{2}\).
2. \(5:6\) can be written as the fraction \(\frac{5}{6}\).
3. \(8:12\) can be written as the fraction \(\frac{8}{12}\).

### Step 2: Use a Common Denominator to Rewrite the Fractions

The next step is to find a common denominator for the fractions. The denominators here are \(2\), \(6\), and \(12\). The least common multiple of these denominators is \(12\).

Now we can rewrite each fraction with a common denominator of \(12\):

- For \(\frac{3}{2}\):
\[
\frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12}
\]

- For \(\frac{5}{6}\):
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]

- For \(\frac{8}{12}\):
\[
\frac{8}{12} = \frac{8}{12} \quad \text{(already over a common denominator)}
\]

### Step 3: Compare the Numerators to Help Order the Ratios

Now we can compare the fractions:
- \(\frac{18}{12}\) (from \(3:2\))
- \(\frac{10}{12}\) (from \(5:6\))
- \(\frac{8}{12}\) (from \(8:12\))

By comparing the numerators:
1. \(\frac{18}{12} > \frac{10}{12} > \frac{8}{12}\)

### Final Order of Ratios
The order of the ratios from greatest to least is:
1. \(3:2\)
2. \(5:6\)
3. \(8:12\)

Thus, the complete answer would look like this:

The first step is to write the ratios as fractions.

The next step is to use a **common denominator** to rewrite the fractions.

Finally, compare the **numerators** to help you order the ratios.