Which ratios form a proportion? Use equivalent ratios to test each pair.
Ratios form a proportion when they are equivalent, meaning that they have the same value. To test if two ratios form a proportion, you can cross-multiply and check if the products are equal.
For example, let's consider the ratios 2:3 and 4:6. To test if they form a proportion, we cross-multiply:
2 * 6 = 12
3 * 4 = 12
Since the products are equal, the ratios 2:3 and 4:6 form a proportion.
Here are a few more examples:
1. 3:4 and 6:8
Cross-multiplying:
3 * 8 = 24
4 * 6 = 24
Since the products are equal, the ratios 3:4 and 6:8 form a proportion.
2. 5:7 and 10:14
Cross-multiplying:
5 * 14 = 70
7 * 10 = 70
Since the products are equal, the ratios 5:7 and 10:14 form a proportion.
3. 2:5 and 8:20
Cross-multiplying:
2 * 20 = 40
5 * 8 = 40
Since the products are equal, the ratios 2:5 and 8:20 form a proportion.
In conclusion, ratios form a proportion when you can cross-multiply and obtain equal products.
To determine if two ratios form a proportion, we can check if the ratios are equivalent. Two ratios are equivalent if they have the same value.
To test if two ratios are equivalent, we can cross-multiply and see if the products are equal. If the cross-products are equal, then the ratios are in proportion.
For example, let's test the following pairs of ratios:
1) 2:4 and 3:6
To check if these ratios are in proportion, we cross-multiply:
2 x 6 = 12
4 x 3 = 12
Since the cross-products are equal, the ratios 2:4 and 3:6 are in proportion.
2) 5:8 and 10:16
Cross-multiplying:
5 x 16 = 80
8 x 10 = 80
Since the cross-products are equal, the ratios 5:8 and 10:16 are in proportion.
3) 7:3 and 21:9
Cross-multiplying:
7 x 9 = 63
3 x 21 = 63
Again, the cross-products are equal, so the ratios 7:3 and 21:9 are in proportion.
In conclusion, the ratios 2:4 and 3:6, 5:8 and 10:16, and 7:3 and 21:9 form proportions.