Fraction arithmetic

Algebra Level 1

The sum of 1 2 \frac{1}{2} , 4 5 \frac{4}{5} , and 21 10 \frac{21}{10} can be written as a b \frac{a}{b} , where a a and b b are coprime positive integers. What is the value of a + b a+b ?


The answer is 22.

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Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

We have,

1 3 + 4 5 + 31 15 = ( 1 3 ⋅ 5 5 ) + ( 4 5 ⋅ 3 3 ) + 31 15 = 5 15 + 12 15 + 31 15 = 5 + 12 + 31 15 = 48 15 = 16 5 \begin{aligned} \frac{1}{3} + \frac{4}{5} + \frac{31}{15} &= \left(\frac{1}{3}\cdot \frac{5}{5} \right) + \left(\frac{4}{5} \cdot \frac{3}{3} \right) + \frac{31}{15} \\ &= \frac{5}{15} + \frac{12}{15} + \frac{31}{15} \\ &= \frac{5 + 12 + 31}{15} \\ &= \frac{48}{15} \\ &= \frac{16}{5} \\ \end{aligned}

Hence a + b = 16 + 5 = 21 a + b = 16 + 5 = 21 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I think it is wrong. How did you get1/3 nd 31/15 Isn't it 1/2 and 21/10 And then the answer is simplified to 27/5 So the answer is 27+5=32 =32

Syed Hamza Khalid - 4 years, 1 month ago

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