Question

How would you compare two ratios given in words?

Answer 1

To compare two ratios given in words, follow these steps:

1. **Understand the Ratios**: First, clarify each ratio. For example, if you have "the ratio of apples to oranges is 3 to 5" and "the ratio of bananas to apples is 2 to 3", you need to express these ratios in numeric form.

2. **Convert to Fractional Form**: Convert each ratio into a fraction. For instance:
- The ratio of apples to oranges (3:5) can be represented as \( \frac{3}{5} \).
- The ratio of bananas to apples (2:3) can be expressed as \( \frac{2}{3} \).

3. **Cross-Multiply**: To compare the two fractions, use cross-multiplication. For \( \frac{3}{5} \) and \( \frac{2}{3} \):
- Multiply the numerator of the first by the denominator of the second: \( 3 \times 3 = 9 \).
- Multiply the denominator of the first by the numerator of the second: \( 5 \times 2 = 10 \).

4. **Compare the Results**: Now, compare the two products:
- Since \( 9 < 10 \), we conclude that \( \frac{3}{5} < \frac{2}{3} \), or that the ratio of apples to oranges is less than the ratio of bananas to apples.

5. **Interpretation**: Finally, interpret what this comparison means in context. For example, you could say, "The proportion of apples to oranges is smaller than the proportion of bananas to apples."

By methodically converting ratios to fractions and using cross-multiplication, you can clearly compare any two ratios expressed in words.