Write of the following, Option 1 or Option 2, is a proportion?
Option 1: 7:8 = 20/22
Option 2: 7:8 = 21/24
Option __ is a proportion.
Option 1
To determine which option is a proportion, we need to check if the two ratios are equal.
Let's first simplify both ratios:
Option 1: 7:8 = 20/22 simplified = 10/11
Option 2: 7:8 = 21/24 simplified = 7/8
Now we can compare the simplified ratios:
Option 1: 10/11
Option 2: 7/8
Since the simplified ratios are not equal, Option 1 is not a proportion. On the other hand, Option 2 is a proportion since the simplified ratio 7/8 is equal to the given ratio 7:8.
To determine which option is a proportion, we need to check if the two ratios are equal. A proportion is defined as two ratios that are equivalent to each other.
Let's start by simplifying the ratios:
Option 1: 7:8 = 20/22
To simplify this ratio, we can find the greatest common divisor (GCD) of 20 and 22, which is 2. Dividing both the numerator and denominator by 2, we get:
7:8 = 10/11
Option 2: 7:8 = 21/24
Again, let's find the GCD of 21 and 24, which is 3. Dividing both the numerator and denominator by 3, we get:
7:8 = 7/8
Comparing the simplified ratios, we see that Option 1 is 7:8 = 10/11, and Option 2 is 7:8 = 7/8.
Since Option 2 is already in the simplified form, where the numerator and denominator have no common factors, we can say that Option 2 is a proportion.
Therefore, Option 2 is a proportion.