Question

$2\frac{3}{5}+4\frac{1}{15}=K$

$\text{If}"K"\text{is a mixed number, then find the}\text{difference between its whole number part and}\text{its fractional part.}$

• A. $6\frac{1}{3}$
• B. $5\frac{1}{3}$
• C. $6\frac{2}{3}$
• D. $5\frac{2}{3}$

Answer 1

The correct option is B $5\frac{1}{3}$

$2\frac{3}{5}+4\frac{1}{15}=K$

$⟹K=\frac{(2\times 5)+3}{5}+\frac{(4\times 15)+1}{15}$

$=\frac{13}{5}+\frac{61}{15}$

$=\frac{13\times 3}{5\times 3}+\frac{61}{15}$

$=\frac{39}{15}+\frac{61}{15}$

$=\frac{100}{15}$

$\text{To express this as a mixed number,}\text{we follow the rule:}$

$MixedNumber=Quotient\frac{Remainder}{Divisor}$

$⟹\frac{100}{15}=6\frac{10}{15}=6\frac{2}{3}$

$\therefore K=6\frac{2}{3}$

$\text{Hence,}$

$\text{Whole number part of}K=6$

$\text{Fractional part of}K=\frac{2}{3}$

$⟹\text{Difference between the whole}$ $\text{number and fractional parts}$

$=6-\frac{2}{3}$

$=\frac{6}{1}-\frac{2}{3}$

$=\frac{6\times 3}{1\times 3}-\frac{2}{3}$

$=\frac{18}{3}-\frac{2}{3}$

$=\frac{16}{3}$

$=5\frac{1}{3}$