Add the following rational numbers-v 31-4 and -58

Given : nbsp;31 4 and 58 ∴31 4 + 58 = 314 + 58 LCM of denominators nbsp; 4 and 8 =8 Expressing each of the given rational number with 8 as common denomi ...

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Standard IX

Mathematics

Operations on Rational and Irrational Numbers

Add the follo...

Question

Add the following rational numbers:

(v) $\frac{31}{- 4} and \frac{- 5}{8}$

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Solution

Given : $\frac{31}{- 4} and \frac{- 5}{8}$

$∴ \frac{31}{- 4} + \frac{- 5}{8} = \frac{- 31}{4} + \frac{- 5}{8}$
LCM of denominators $4$ and $8 = 8$
Expressing each of the given rational number with $8$ as common denominator.
$\Rightarrow \frac{- 31}{4} = \frac{- 31 \times 2}{4 \times 2} = \frac{- 62}{8}$

Now, $\frac{- 31}{4} + \frac{- 5}{8} = \frac{- 62}{8} + \frac{- 5}{8}$

$= \frac{- 62 - 5}{8} = \frac{- 67}{8}$

Hence, the sum of $\frac{31}{- 4} and \frac{- 5}{8}$ is $\frac{- 67}{8}$

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Operations on Rational and Irrational Numbers

Standard IX Mathematics

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Add the following rational numbers:​ (v) 31−4 and −58

Given : 31−4 and −58 ∴31−4+−58=−314+−58 LCM of denominators 4 and 8=8 Expressing each of the given rational number with 8 as common denominator. ⇒−314=−31×24×2=−628 Now, −314+−58=−628+−58 =−62−58=−678 Hence, the sum of 31−4 and −58 is −678

Add the following rational numbers:

(v) $\frac{31}{- 4} and \frac{- 5}{8}$