Answer:
He keeps 7/12 of the box of raisins
Step-by-step explanation:
First of all you should know what fraction of the total he distributed among his brothers. For that, you must add \(\frac{1}{6}\) and \(\frac{1}{4}\). 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:
\(\frac{1}{6}=\frac{4}{24}\)
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:
\(\frac{1}{4} =\frac{6}{24}\)
As now the 2 fractions have the same denominator, to add you leave the same denominator, which is 24, and add the numerators:
\(\frac{4}{24}+\frac{6}{24} =\frac{4+6}{20} =\frac{10}{24}\)
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 \(\frac{5}{12}\)
So \(\frac{1}{6} +\frac{1}{4}\) is \(\frac{5}{12}\). Then Chad gives his brothers \(\frac{5}{12}\). To obtain the portion he keeps, 1 minus \(\frac{5}{12}\) is subtracted, 1 being the total. Taking into account that 1 = \(\frac{1}{1}\) and that the subtraction is done in a similar way to the sum previously explained, you get
\(1-\frac{5}{12} =\frac{1}{1}-\frac{5}{12} =\frac{12}{12} -\frac{5}{12} =\frac{12-5}{12} =\frac{7}{12}\)
So, he keeps 7/12 of the box.
