Which of the following numbers is proportional to start fraction 84 over 108 end fraction?
start fraction 86 over 110 end fraction
start fraction 98 over 126 end fraction
start fraction 64 over 72 end fraction
start fraction 91 over 104 end fraction
To determine which of the given fractions is proportional to the fraction 84/108, we can simplify the fraction 84/108 and then simplify each of the given options to see if any of them have the same simplest form.
First, simplify 84/108:
The greatest common divisor (GCD) of 84 and 108 is 12.
Dividing both the numerator and denominator by 12, we get:
84 ÷ 12 = 7
108 ÷ 12 = 9
So, 84/108 simplifies to 7/9.
Now, we need to check each of the given options to see if any of them simplify to 7/9.
1. 86/110
GCD of 86 and 110 is 2.
86 ÷ 2 = 43
110 ÷ 2 = 55
This fraction does not simplify to 7/9.
2. 98/126
GCD of 98 and 126 is 14.
98 ÷ 14 = 7
126 ÷ 14 = 9
This fraction simplifies to 7/9, so 98/126 is proportional to 84/108.
3. 64/72
GCD of 64 and 72 is 8.
64 ÷ 8 = 8
72 ÷ 8 = 9
This fraction does not simplify to 7/9.
4. 91/104
There is no common divisor (other than 1) of 91 and 104 that will simplify this fraction to 7/9.
Thus, the only fraction from the given options that is proportional to 84/108 is 98/126.