Question

Find the greater fraction: $\frac{6}{7}\text{and}\frac{5}{9}$

Answer 1

Step 1: Finding LCM of denominators 7 and 9:
​​Prime Factors of 7 = 7
Prime Factors of 9 = 3 $\times$ 3
Thus, LCM (7, 9) = $3\times 3\times 7=63$

Step 2: Converting into like Fractions:
Multiplying numerator and denominator of $1^{\text{st}}$ fraction by 9, we get,
$\frac{6}{7}=\frac{6\times 9}{7\times 9}$
$=\frac{54}{63}$

Multiplying numerator and denominator of $2^{\text{nd}}$ fraction by 7, we get,
$\frac{5}{9}=\frac{5\times 7}{9\times 7}$
$=\frac{35}{63}$

Step 3: Comparing the like fractions

Now comparing their numerator, we get
$35<54$
$\Rightarrow \frac{35}{63}<\frac{54}{63}$
$\Rightarrow \frac{5}{9}<\frac{6}{7}$
Hence $\frac{6}{7}$ is greater than $\frac{5}{9}$.