Fraction Multiplication

Number Theory Level 1

If A is divided by B, the result is 2/3

If B is divided by C, the result is 4/7

The result when A is divided by C can be expressed as x y \frac x y , where x x and y y are coprime . What is x + y x+y ?


The answer is 29.

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Stewart Feasby by Stewart Feasby , 23, United Kingdom

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1 solution

Stewart Feasby
Oct 5, 2014

Firstly, it is good to notice that: A B × B C = A B B C = A C \frac { A }{ B } \times \frac { B }{ C } =\frac { AB }{ BC } =\frac { A }{ C } This means that: 2 3 × 4 7 = 2 × 4 3 × 7 = 8 21 \frac { 2 }{ 3 } \times \frac { 4 }{ 7 } =\frac { 2\times 4 }{ 3\times 7 } =\frac { 8 }{ 21 } This means we have x = 8 x=8 and y = 21 y=21 , therefore: x + y = 8 + 21 = 29 x+y=8+21=\boxed {29}

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21 and 8 are not a co prime numbers.

Palak Singh - 6 years, 6 months ago

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why are they not co-prime numbers?

Mehul Arora - 6 years, 6 months ago

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