Question
Find the sum: $2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$
✓
Answer
We have, $L.C.M$. of $4, 8$ and $16 = (2 \times 2 \times 2 \times 2) = 16$
$\begin{array}{c|c}2&4,8,16\\\hline2&2,4,8\\\hline2&1,2,4\\\hline2&1,1,2\\\hline&1,1,1\end{array}$
Therefore, $2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$
$=\frac{2}{1}+\frac{3}{4}+\frac{13}{8}+\frac{55}{16}$
$=\frac{(32+12+26+55)}{16}$
$\Big(\frac{16}{1}=16,6\times2=32\Big)$
$\Big(\frac{16}{4}=4,4\times3=12\Big)$
$\Big(\frac{16}{8}=2,2\times13=26\Big)$ and
$\Big(\frac{16}{16}=1,1\times55=55\Big)$
$=\frac{125}{16}$
$=7\frac{13}{16}$
$\begin{array}{c|c}2&4,8,16\\\hline2&2,4,8\\\hline2&1,2,4\\\hline2&1,1,2\\\hline&1,1,1\end{array}$
Therefore, $2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$
$=\frac{2}{1}+\frac{3}{4}+\frac{13}{8}+\frac{55}{16}$
$=\frac{(32+12+26+55)}{16}$
$\Big(\frac{16}{1}=16,6\times2=32\Big)$
$\Big(\frac{16}{4}=4,4\times3=12\Big)$
$\Big(\frac{16}{8}=2,2\times13=26\Big)$ and
$\Big(\frac{16}{16}=1,1\times55=55\Big)$
$=\frac{125}{16}$
$=7\frac{13}{16}$
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