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18 April, 14:46

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?

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  1. 18 April, 17:55
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    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
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