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Conversion between Fractions and Decimals

Simplify : 2/...

Question

Simplify $:$ $($ $\frac{2}{7}$ $+$ $\frac{1}{5}$ $)$ $\div$ $\frac{2}{21}$ of $($ $\frac{5}{7}$ $-$ $\frac{1}{3}$ $)$

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Solution

Step 1 : Simplifying the first bracket
$\frac{2}{7}$ $+$ $\frac{1}{5}$
Step 2: The bottom numbers are different, To make it same take the L.C.M of 7 and 5
L.C.M of $7$ and $5$ is $35$
Step 3: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator
$\frac{2}{7}$ $=$ $\frac{2 \times 5}{7 \times 5}$ $=$ $\frac{10}{35}$
$\frac{1}{5}$ $=$ $\frac{1 \times 7}{5 \times 7}$ $=$ $\frac{7}{35}$
Step 4: Add the numerators and put the answer over the denominator
$\frac{10}{35}$ $+$ $\frac{7}{35}$ $=$ $\frac{17}{35}$
Step 5 : Simplifying the second bracket
$\frac{5}{7}$ $-$ $\frac{1}{3}$
Step 6: The bottom numbers are different, To make it same take the L.C.M of 7 and 3

L.C.M of $7$ and $3$ is $21$
Step 7: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator
$\frac{5}{7}$ $=$ $\frac{5 \times 3}{7 \times 3}$ $=$ $\frac{15}{21}$
$\frac{1}{3}$ $=$ $\frac{1 \times 7}{3 \times 7}$ $=$ $\frac{7}{21}$
Step 8: Subtract the numerators and put the answer over the denominator
$\frac{15}{21}$ $-$ $\frac{7}{21}$ $=$ $\frac{8}{21}$
$($ $\frac{2}{7}$ $+$ $\frac{1}{5}$ $)$ $\div$ $\frac{2}{21}$ of $($ $\frac{5}{7}$ $-$ $\frac{1}{3}$ $)$ $=$ $($ $\frac{17}{35}$ $)$ $\div$ $\frac{2}{21}$ of $\frac{8}{21}$
Step 9 : Replace the word ‘ of ’ with the symbol ‘ x ’ and do multiplication
$\frac{2}{21}$ $\times$ $\frac{8}{21}$ $=$ $\frac{2 \times 8}{21 \times 21}$ $=$ $\frac{16}{441}$
$($ $\frac{17}{35}$ $)$ $\div$ $\frac{2}{21}$ of $\frac{8}{21}$ $=$ $($ $\frac{17}{35}$ $)$ $\div$ $\frac{16}{441}$
Step 10: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication
$\frac{17}{35}$ $\times$ $\frac{441}{16}$ $=$ $\frac{7497}{560}$
Step11: Simplify the fraction
Divide numerator $7497$ by the denominator $560$

$\frac{7497}{560}$ $=$ $13 \frac{217}{560}$
Here $\frac{217}{560}$ $=$ $\frac{217 \div 7}{560 \div 7}$ $=$ $\frac{31}{80}$
$13 \frac{217}{560}$ $=$ $13 \frac{31}{80}$
Hence $,$ $($ $\frac{2}{7}$ $+$ $\frac{1}{5}$ $)$ $\div$ $\frac{2}{21}$ of $($ $\frac{5}{7}$ $-$ $\frac{1}{3}$ $)$ $=$ $13 \frac{31}{80}$ .

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