Question

Write these ratios in their simplest form.
a. 20:32
b. 16:40

Answer 1

The simplest form of the ratios 20:32 and 16:40 are 5:8 and 2:5 respectively, after dividing both terms of each ratio by their greatest common divisor (GCD). A proportion typically compares two related ratios, so these simplifications do not directly lead to a meaningful proportion between the two.

Step-by-step explanation:

To simplify the ratios 20:32 and 16:40, we need to find the greatest common divisor (GCD) for each pair of numbers and then divide both terms of the ratio by their GCD.

For 20:32, the GCD is 4. So we divide both 20 and 32 by 4 to get the simplest form:

1. 20 ÷ 4 = 5
2. 32 ÷ 4 = 8

Therefore, the simplest form of 20:32 is 5:8.

For 16:40, the GCD is 8. So we divide both 16 and 40 by 8 to get the simplest form:

1. 16 ÷ 8 = 2
2. 40 ÷ 8 = 5

Therefore, the simplest form of 16:40 is 2:5.

Now, if we want to write a proportion, we could compare the two simplified ratios by setting them equal to each other. However, since they are unrelated and represent different things, we can't directly create a meaningful proportion between them.