Question

Compare the following pairs of rational numbers: -7/24 and 9/-20​

Answer 1

Answer:

Step-by-step explanation:

-7/24 and 9/-20

q should be positive  

so, 9 × -1 /-20 × -1

=  -9 / 20

now, find the L.C.M. of these positive denominators

The L.C.M. of 24 and 20 is 120

-7 × 5 / 24 × 5  =  -35 / 120

-9 × 6 / 20 × 6  =  -54 / 120

Clearly, -35 / 120  <  -54 /120

Hence, -7 / 24  <  9 /-2

Hope this will help u.

Answer 2

$\displaystyle \sf{ \frac{ - 7}{24} > \frac{9}{ - 20} }$

Given :

$\displaystyle \sf{ \frac{ - 7}{24} \: \: and \: \: \frac{9}{ - 20} }$

To find :

To compare the two rational numbers

Solution :

Step 1 of 3 :

Write down the given rational numbers

Here the given rational numbers are

$\displaystyle \sf{ \frac{ - 7}{24} \: \: and \: \: \frac{9}{ - 20} }$

Step 2 of 3 :

Convert the rational numbers with same denominators

$\displaystyle \sf{ \frac{ - 7}{24} = - \frac{7}{24} }$

$\displaystyle \sf{ \frac{9}{ - 20} = - \frac{9}{20} }$

The denominators of two rational numbers are 24 and 20

LCM of the denominators = 120

Thus we get

$\displaystyle \sf{ \frac{ - 7}{24} = - \frac{7}{24} = - \frac{7 \times 5}{24 \times 5} = - \frac{35}{120} }$

$\displaystyle \sf{ \frac{9}{ - 20} = - \frac{9}{20} = - \frac{9 \times 6}{20 \times 6} = - \frac{54}{120} }$

Step 3 of 3 :

Compare the two rational numbers

$\displaystyle \sf{ 35 < 54 }$

$\displaystyle \sf{ \implies - 35 > - 54}$

$\displaystyle \sf{ \implies - \frac{35}{120} > - \frac{54}{120} }$

$\displaystyle \sf{ \implies - \frac{ 7}{24} > - \frac{9}{ 20} }$

$\displaystyle \sf{ \implies \frac{ - 7}{24} > \frac{9}{ - 20} }$

$\boxed{ \: \: \displaystyle \sf{ \frac{ - 7}{24} > \frac{9}{ - 20} } \: \: }$

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