Question

Karen, James, Frank, and Dan were left an inheritance by their late grandfather. If Karen receives one-eighth of the inheritance, James receives one quarter of the inheritance, Frank receives three-eighths of the inheritance, and Dan receives the remainder, what fraction of the inheritance does Dan receive?

Answer 1

Count what fraction receive Karen, James and Frank in total:

since

Karen receives - $\frac{1}{8}$,

James receives - $\frac{1}{4}=\frac{2}{8}$,

Frank receives - $\frac{3}{8}$,

then $\frac{1}{8} +\frac{2}{8} +\frac{3}{8} =\frac{1+2+3}{8}=\frac{6}{8} =\frac{2\cdot 3}{2\cdot 4} =\frac{3}{4}$.

All inheritance is the whole 1, then for Dan remains $1-\frac{3}{4} =\frac{4}{4} -\frac{3}{4} =\frac{4-3}{4} =\frac{1}{4}$.

Answer: Dan receives one quarter of the inheritance.

Answer 2

The answer is  $\frac{1}{4}$

Explanation

$\frac{1}{8}+\frac{1}{4}+\frac{3}{8}$

$=\frac{1}{8}+\frac{2}{8}+\frac{3}{8}$

$=\frac{6}{8}=\frac{3}{4}$

$1-\frac{3}{4}=\frac{1}{4}$