Question

Chad bought a box of raisins. He gave 1/6 of it to one brother, 1/4 to another brother, & he kept the rest for himself. What fraction did he keep?

Answer 1

Fraction, that he gave to his brothers = 1/6 + 1/4 = 5/12

So, Fraction he kept for himself, 1 - 5/12 = 7/12

Answer 2

He keeps 7/12 of the box of raisins

Explanation:

First of all you should know what fraction of the total he distributed among his brothers. For that, you must add
`(1)/(6)` and
`(1)/(4)`. You can see that both fractions have different denominators. So, to add, the first thing to do is put a common denominator. One of the easiest ways to get this denominator is just multiply the denominators of the two fractions:

6*4=24

Then the denominator in both fractions will be 24. But if you modified the denominator, the numerator. That is: if in fraction 1/6 you multiplied 6 by 4 to reach denominator 24, then numerator 1 must also be multiplied by 4. Then:

`(1)/(6)=(4)/(24)`

Similarly: if in the 1/4 fraction you multiplied the 4 by 6 to reach the denominator 20, then the numerator 1 must also be multiplied by 6. Then:

`(1)/(4) =(6)/(24)`

As now the 2 fractions have the same denominator, to add you leave the same denominator, which is 24, and add the numerators:

`(4)/(24)+(6)/(24)  =(4+6)/(20) =(10)/(24)`

This fraction can be reduced, that is, express it in a simpler way. For that you divide the numerator and denominator by the same number. In this case, you can choose to divide the numerator and denominator by 2 and you get
`(5)/(12)`

So
`(1)/(6) +(1)/(4)` is
`(5)/(12)`. Then Chad gives his brothers
`(5)/(12)`. To obtain the portion he keeps, 1 minus
`(5)/(12)` is subtracted, 1 being the total. Taking into account that 1 =
`(1)/(1)` and that the subtraction is done in a similar way to the sum previously explained, you get

`1-(5)/(12) =(1)/(1)-(5)/(12)  =(12)/(12) -(5)/(12) =(12-5)/(12) =(7)/(12)`

So, he keeps 7/12 of the box.