Fill in the blanks with the correct symbol out of $>, <$ and $=$ :-
$\frac{- 2}{3} . . . . \frac{5}{- 8}$

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Solution

The given numbers are, $\frac{- 2}{3}$ and $\frac{5}{- 8}$

First we have to write each of the given numbers with a positive denominator.
$∴ \frac{5}{- 8}$ $= \frac{5 \times (- 1)}{- 8 \times (- 1)}$ $= \frac{- 5}{8}$

The $L C M$ of the denominators $3$ and $8$ is $24$
$∴ \frac{- 2}{3} = \frac{(- 2 \times 8)}{(3 \times 8)} = \frac{- 16}{24}$
and $\frac{- 5}{8} = \frac{(- 5 \times 3)}{(8 \times 3)} = \frac{- 15}{24}$

Now, $- 16 < - 15$
$\Rightarrow \frac{- 16}{24} < \frac{- 15}{24}$
$\Rightarrow \frac{- 2}{3} < \frac{- 5}{8}$

Hence, $\frac{- 2}{3} < \frac{5}{- 8}$

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Question 8 (i)

Fill in the boxes with the correct symbol out of <, > and =:
$\frac{- 5}{7}$ ____ $\frac{2}{3}$

Fill in the blanks with the correct symbol out of $>, =$ and $<:$
(i) $- \frac{3}{7} \dots \dots - \frac{6}{13}$

(ii) $\frac{5}{- 13} \dots \dots - \frac{35}{91}$

(iii) $- 2 \dots \dots - \frac{13}{5}$

(iv) $- \frac{2}{3} \dots \dots \frac{- 5}{8}$

(v) $0 \dots \dots \frac{- 3}{- 5}$

(vi) $- \frac{8}{9} \dots \dots \frac{- 9}{10}$

Question 35

In the following question, fill in the blanks with correct symbol >, < or =.

$\frac{8}{8}$ ___ $\frac{2}{2}$

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