To determine whether any of the given sets of ratios form a proportion, we can use the cross-multiplication method. A proportion states that two ratios are equal. Specifically, if we have \( \frac{a}{b} = \frac{c}{d} \), then cross-multiplying gives us \( a \cdot d = b \cdot c \).
Let's evaluate each set of ratios:
-
For \( 2.2510 = 940 \):
- The ratio is \( \frac{2.25}{10} = \frac{9}{40} \).
- Cross-multiplication:
- \( 2.25 \cdot 40 = 90 \)
- \( 10 \cdot 9 = 90 \)
- Since \( 90 = 90 \), this ratio is a proportion.
-
For \( 2.510 = 9040 \):
- The ratio is \( \frac{2.5}{10} = \frac{90}{40} \).
- Cross-multiplication:
- \( 2.5 \cdot 40 = 100 \)
- \( 10 \cdot 90 = 900 \)
- Since \( 100 \neq 900 \), this ratio is not a proportion.
-
For \( 2.2512 = 9040 \):
- The ratio is \( \frac{2.25}{12} = \frac{90}{40} \).
- Cross-multiplication:
- \( 2.25 \cdot 40 = 90 \)
- \( 12 \cdot 90 = 1080 \)
- Since \( 90 \neq 1080 \), this ratio is not a proportion.
In conclusion, the only set of ratios that is a proportion is:
2.2510 = 940 (or \( \frac{2.25}{10} = \frac{9}{40} \)).
So the response would be:
2.2510=940 Start Fraction 2.25 over 10 End Fraction equals Start Fraction 9 over 40 End Fraction.
1 answer