Which ratio is greater? $5 : 7 o r 9 : 14$

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Solution

Step 1: We can write $5 : 7 o r 9 : 14$ as $\frac{5}{7} o r \frac{9}{14}$
Step 2: We will have to equalise the denominators and then multiply by LCM of the denominators
Step 3: Firstly, Taking LCM of the denominators $7 a n d 14$
By prime factorisation method:
$7 = 7 \times 1$
$14 = 2 \times 7$
$L C M (7, 14) = 2 \times 7 = 14$
Step 4: Now, Multiplying the LCM in both terms:
$\frac{5}{7} \times 14 a n d \frac{9}{14} \times 14$
$5 \times 2 a n d 9 \times 1$
$10 a n d 9$
Since, $10 > 9$
Therefore, $\frac{5}{7} > \frac{9}{14}$ or $5 : 7 > 9 : 14$
Hence, $5 : 7$ is the greater ratio.

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