Question
Simplify:$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$
✓
Answer
We have:$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$
$=\frac{37}{6}-\frac{26}{5}+\frac{10}{3}$
$\begin{array}{c|c}2&6,5,3\\\hline3&3,5,3\\\hline5&1,5,1\\\hline&1,1,1\end{array}$
$L.C.M$. of $6, 5$ and $3 = (2 \times 5 \times 3) = 30$
$=\frac{(185-156+100)}{30}$
$\Big(\frac{30}{6}=5,5\times37=185\Big)$
$\Big(\frac{30}{5}=6,6\times26=156\Big)$ and
$\Big(\frac{30}{3}=10,10\times10=100\Big)$
$=\frac{(285-156)}{30}$
$=\frac{129}{30}$
$=\frac{43}{10}$
$=4\frac{3}{10}$
$=\frac{37}{6}-\frac{26}{5}+\frac{10}{3}$
$\begin{array}{c|c}2&6,5,3\\\hline3&3,5,3\\\hline5&1,5,1\\\hline&1,1,1\end{array}$
$L.C.M$. of $6, 5$ and $3 = (2 \times 5 \times 3) = 30$
$=\frac{(185-156+100)}{30}$
$\Big(\frac{30}{6}=5,5\times37=185\Big)$
$\Big(\frac{30}{5}=6,6\times26=156\Big)$ and
$\Big(\frac{30}{3}=10,10\times10=100\Big)$
$=\frac{(285-156)}{30}$
$=\frac{129}{30}$
$=\frac{43}{10}$
$=4\frac{3}{10}$
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