Which of the following, Option 1 or Option 2, is a proportion?
Option 1: 7/8=20/22
Option 2: 7/8=21/24
Both Option 1 and Option 2 are proportions.
To determine whether Option 1 or Option 2 is a proportion, we need to check if the two fractions are equal. Let's evaluate both options.
Option 1: 7/8 = 20/22
Cross multiplying:
7 * 22 = 8 * 20
154 = 160
Option 2: 7/8 = 21/24
Cross multiplying:
7 * 24 = 8 * 21
168 = 168
By cross multiplying, we can see that in Option 1, the two fractions are not equal since 154 is not equal to 160. However, in Option 2, the two fractions are equal since 168 is equal to 168.
Therefore, Option 2: 7/8 = 21/24 is a proportion.
To determine which of the given options is a proportion, we need to check if the ratios on both sides of the equal sign are equal. Let's break down the options:
Option 1: 7/8 = 20/22
Option 2: 7/8 = 21/24
For Option 1, we can simplify both ratios. The fraction 20/22 can be reduced by dividing both the numerator (20) and denominator (22) by their greatest common divisor, which is 2. This gives us 10/11.
Comparing 7/8 and 10/11, we see that both ratios are equal. Therefore, Option 1 is a proportion.
Now, let's check Option 2. We can simplify the fraction 21/24 by dividing both the numerator (21) and denominator (24) by their greatest common divisor, which is 3. This results in 7/8.
Since 7/8 on both sides of the equal sign are equal, Option 2 is also a proportion.
In summary, both Option 1 and Option 2 are proportions.