Determine if the following are in proportion: is 40:50 :: 100:125
The correct answer and explanation is:
To determine whether the ratios 40:50 and 100:125 are in proportion, we need to check if the cross products are equal.
A proportion is a statement that two ratios are equal. In this case, we need to check if the cross products of the two ratios are the same. The two ratios are 40:50 and 100:125. To check if they are proportional, we will multiply the first term of the first ratio by the second term of the second ratio, and the first term of the second ratio by the second term of the first ratio.
The cross products of the ratios 40:50 and 100:125 are: 40×125=500040 \times 125 = 5000 50×100=500050 \times 100 = 5000
Since both cross products are equal (5000), the ratios 40:50 and 100:125 are in proportion.
Explanation:
A proportion is true when the two ratios represent the same relationship. To check if two ratios are equal, we cross-multiply and compare the products. In this case, both the cross products are the same, so the two ratios are indeed in proportion.
Another way to look at it is by simplifying the ratios. First, simplify both ratios:
- 40:50 can be simplified by dividing both terms by 10, giving 4:5.
- 100:125 can be simplified by dividing both terms by 25, giving 4:5.
Since both ratios simplify to 4:5, this confirms that the ratios are proportional. Therefore, 40:50 is proportional to 100:125.