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

To find the fraction of senators who are Democrat or Republican, we add the fractions representing Democrats and Republicans. The fraction is $rac{49}{50}$.

Step-by-step explanation:

To find the fraction of senators who are Democrat or Republican, we need to add the fractions representing Democrats and Republicans. The fraction of senators who are Democrats is $rac{46}{100}$, and the fraction of senators who are Republicans is $rac{13}{25}$.

To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with denominators of 100. $rac{46}{100}$ is equivalent to $rac{46}{100} imes rac{1}{1}$, and $rac{13}{25}$ is equivalent to $rac{13}{25} imes rac{4}{4}$ (since $25 imes 4 = 100$).

Now we can add the fractions: $rac{46}{100} + rac{13}{25} = rac{46}{100} + rac{52}{100} = rac{98}{100}$.

So, $rac{98}{100}$ of the senators are Democrat or Republican, which simplifies to $rac{49}{50}$.

Answer 2

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