Question

Which of the rational numbers 4/9, -5/6,-7/12 and 11/-24. Is the smallest

Answer 1

Answer:

Hope this answer will help you.

Step-by-explanation:

LCM of 9,6,12,24 = 72

So, 4/9 = 24/72

-5/6 = -60/72

-7/12 = -42/72

-11/24 = -33/72

Now, -5/6 < -7/12 < -11/24 < 4/9

Therefore, -5/6 is the smallest rational number.

Answer 2

The smallest rational number is $-\frac{5}{6}$.

Given:

The rational numbers  $\frac{4}{9}, -\frac{5}{6}, -\frac{7}{12}, -\frac{11}{24}$ .

To Find:

We have to find the smallest rational number.

Solution:

This is a simple problem for fractions.

Let us tackle this question.

We can easily solve this question as follows.

According to the question,

The given rational numbers are  $\frac{4}{9}, -\frac{5}{6}, -\frac{7}{12}, -\frac{11}{24}$ .

Now,

LCM of the denominators of the given rational numbers

= LCM of 9, 6,12 and 24

=LCM (9,6,12,24)

= 72

So, we come to the next step now,

$\frac{4}{9}= \frac{4*8}{9*8} = \frac{32}{72}$

$-\frac{5}{6}=-\frac{5*12}{6*12} =-\frac{60}{72}$

$-\frac{7}{12}=-\frac{7*6}{12*6}=-\frac{42}{72}$

$-\frac{11}{24}=-\frac{11*3}{24*3} =-\frac{33}{72}$

Now,

We can easily see that,

$-\frac{60}{72} < -\frac{42}{72} < -\frac{33}{72} < \frac{32}{72}$

⇒$-\frac{5}{6} < -\frac{7}{12} < -\frac{11}{24} < \frac{4}{9}$

Hence, the smallest rational number is $-\frac{5}{6}$.

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