Did you know?
Did you know that cross products can be used to determine if a pair of ratios can form a proportion? For example, let's consider the ratios 1/3 x 3/9, 2/3 x 4/9, 2/3 x 4/6, and 1/3 x 2/6. To determine which pairs cannot form a proportion, we can follow these steps:
1. Take the first ratio and multiply its numerator by the denominator of the second ratio: (1/3) x 9 = 3.
2. Next, multiply the denominator of the first ratio by the numerator of the second ratio: 3 x 4 = 12.
3. Compare the results of steps 1 and 2. If the values are equal, the ratios form a proportion. If they are not equal, the ratios do not form a proportion.
By performing these steps, we find that the cross products for the given ratios are as follows:
- 1/3 x 3/9: 3 x 9 = 27 and 3 x 3 = 9. Since 27 and 9 are not equal, this pair of ratios cannot form a proportion.
- 2/3 x 4/9: 2 x 9 = 18 and 3 x 4 = 12. These values are not equal, so this pair of ratios cannot form a proportion.
- 2/3 x 4/6: 2 x 6 = 12 and 3 x 4 = 12. Since these values are equal, this pair of ratios can form a proportion.
- 1/3 x 2/6: 1 x 6 = 6 and 3 x 2 = 6. These values are equal, so this pair of ratios can form a proportion.
In summary, the pairs of ratios 1/3 x 3/9 and 2/3 x 4/9 cannot form proportions, while the pairs 2/3 x 4/6 and 1/3 x 2/6 can form proportions.
