Question

Convert the following fractions into equivalent like fractions :
$\left(i\right)\frac{7}{8},\frac{5}{14}$

$\left(ii\right)\frac{5}{6},\frac{7}{16}$
$\left(iii\right)\frac{3}{4}$ , $\frac{5}{6}$, $\frac{7}{8}$

Answer 1

(i) $\frac{7}{8},\frac{5}{14}$

The LCM of $8$ and $14$

2 8,14

2 4, 7

2 2, 7

7 1, 7

1, 1

$=2\times 2\times 2\times 7=56$

To write $\frac{7}{8}$ with denominator $56$, multiply the numerator and denominator by $7$

$=\frac{7\times 7}{8\times 7}=\frac{49}{56}$

Similarly, $\frac{5}{14}=\frac{5\times 4}{14\times 4}=\frac{20}{56}$

Thus, $\frac{7}{8},\frac{5}{14}$ can be written as $\frac{49}{56}$ and $\frac{20}{56}$ respectively which are equivalent like fractions.

$\left(ii\right)\frac{5}{6},\frac{7}{16}$

The LCM of $6$ and $16$

2 6 ,16

2 3, 8

2 3 , 4

2 3, 2

3 3, 1

1, 1

$=2\times 2\times 2\times \times 2\times 3=48$

To write $\frac{5}{6}$ with denominator $48$, multiply the numerator and denominator by $8$

$=\frac{5\times 8}{6\times 8}$ $=\frac{40}{48}$

Similarly, $\frac{7}{16}\Rightarrow \frac{7\times 3}{16\times 3}=\frac{21}{48}$

Thus $\frac{5}{6},\frac{7}{16}$ can be written as $\frac{40}{48},\frac{21}{48}$ respectively with equivalent like fractions.

$\left(iii\right)\frac{3}{4},\frac{5}{6},\frac{7}{8}$

The LCM of $4,6and8$

2 4,6,8

2 2,3,4

2 1,3,2

3 1,3,1

1,1,1

$=2\times 2\times 2\times 3=24$

To write $\frac{3}{4}$ with denominator $=24$ we need to multiply numerator and denominator by $6$

$=\frac{3}{4}\times \frac{6}{6}=\frac{18}{24}$

Similarly $\frac{5}{6}$ and $\frac{7}{8}$ can be written as

$\frac{5}{6}\times \frac{4}{4}=\frac{20}{24}$ and $\frac{7}{8}\times \frac{3}{3}=\frac{21}{24}$

Hence, $\frac{3}{4},\frac{5}{6},\frac{7}{8}$ can be written as $\frac{18}{24},\frac{20}{24},\frac{21}{24}respectively$.

Which are equivalent like terms.