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
- \(3:2\) can be written as the fraction \(\frac{3}{2}\).
- \(5:6\) can be written as the fraction \(\frac{5}{6}\).
- \(8:12\) 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 \(12\):
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For \(\frac{3}{2}\): \[ \frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12} \]
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For \(\frac{5}{6}\): \[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]
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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:
- \(\frac{18}{12} > \frac{10}{12} > \frac{8}{12}\)
Final Order of Ratios
The order of the ratios from greatest to least is:
- \(3:2\)
- \(5:6\)
- \(8:12\)
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.
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