Question

Put the given fractions in ascending order by making denominators equal : $\frac{5}{7},\frac{3}{8},\frac{9}{14}\text{and}\frac{20}{21}$

Answer 1

Step 1: Finding LCM of denominators of fractions : 7, 8, 14, 21:
L.C.M of 7, 8, 14 and 21:

LCM of 7, 8, 14 and 21 is = $2\times 2\times 2\times 3\times 7=168$

Bringing the fraction to same denominator 168 as follows:

By multiplying 24 in numerator and denominator in the $1^{\text{st}}$ fraction we get,

$\frac{5}{7}=\frac{5\times 24}{7\times 24}=\frac{120}{168}$

By multiplying 21 in numerator and denominator in the $2^{\text{nd}}$ fraction we get,

$\frac{3}{8}=\frac{3\times 21}{8\times 21}=\frac{63}{168}$

By multiplying 12 in numerator and denominator in the $3^{\text{rd}}$ fraction we get,

$\frac{9}{14}=\frac{9\times 12}{14\times 12}=\frac{108}{168}$

By multiplying 8 in numerator and denominator in the $4^{\text{th}}$ fraction we get,

$\frac{20}{21}=\frac{20\times 8}{21\times 8}=\frac{160}{168}$


Step 2: Comparing the like fractions
As denominators for the fractions are same, therefore, comparing the numerators of like decimals we get,
$63<108<120<160$
$\therefore \frac{63}{168}<\frac{108}{168}<\frac{120}{168}<\frac{160}{168}$

$\therefore$ Ascending order:

$\frac{3}{8}<\frac{9}{14}<\frac{5}{7}<\frac{20}{21}$