Question

The least among the ratio 5:6,7:8,2:3 and 9:17 is

Answer 1

Answer:

9:17 is the answer

hope it will help u

Answer 2

The least among the ratio 5:6,7:8,2:3 and 9:17 is 9 : 17

Solution:

Given, set of ratios are 5 : 6, 7 : 8, 2 : 3, and 9 : 17.

We have to find smallest ratio among the given ratios.

Now, given ratios can be written as $\frac{5}{6}, \frac{7}{8}, \frac{2}{3}, \text { and } \frac{9}{17}$

For comparisons we have to convert the denominators as same.

So, now we have to find L.C.M of denominators = L.C.M of (6, 8, 3, 17)

Write the numbers as multiplication of prime factors

$\begin{array}{l}{6 \rightarrow 2 \times 3} \\ {8 \rightarrow 2 \times 2 \times 2} \\ {3 \rightarrow 3} \\ {17 \rightarrow 17}\end{array}$

Now L.C.M is given as $=2 \times 2 \times 2 \times 3 \times 17=408$

Now, multiply each ratio with $\frac{408 \times \text { denominator }}{408 \times \text { denominator }}$

$\text { So, ratios are } \frac{5}{6} \times \frac{408 \times 6}{408 \times 6}, \frac{7}{8} \times \frac{408 \times 8}{408 \times 8}, \frac{2}{3} \times \frac{408 \times 3}{408 \times 3}, \text { and } \frac{9}{17} \times \frac{408 \times 17}{408 \times 17}$

$\rightarrow \frac{5 \times 68}{408}, \frac{7 \times 51}{408}, \frac{2 \times 136}{408}, \text { and } \frac{9 \times 24}{408}$

Now, as denominators are same, we can compare numerators.

Numerators are, 5 x 68, 7 x 51, 2 x 136, 9 x 24 → 340, 357, 272, 216.

Here, least number is 216.  

Hence, least ratio is 9 : 17.