Question

There are 100 senators in the 115th Congress. Democrats make up $\frac{46}{100}$ of the senators, and Republicans make up $\frac{13}{25}$ of the senators. The rest are Independents. What fraction of the senators are Democrat or Republican?

Answer 1

Answer: The fraction that makes up Democrats or Republicans is 49/50.

Step-by-step explanation: There are 100 senators in total. We have 46/100 representing the Democrats, and 13/25 representing the Republicans. The number representing the Republicans can be made into an equivalent fraction of the other simply by multiplying both numerator and denominator by 4 (in order to make the denominator the same, that is 100). Hence the fraction of Republicans is 52/100, while the rest are Independents. The independents are

Ind = 100 - (46/100 + 52/100)

Ind = 100 - 98/100

Ind = 2/100

{Total = 46/100 + 52/100 + 2/100}

{Total = 100/100}

However, the fraction of all senators that are Democrats or Republicans is derived as follows;

Dems = 46/100

Reps = 52/100

Total fraction = 46/100 + 52/100

Total fraction = 98/100

Total fraction = 49/50