Decimal Fraction

$$ = 0.4\overline {23} $$
$$ = \frac{{423 - 4}}{{990}}$$
$$ = \frac{{419}}{{990}}$$

Given expression :
= 293.48 - 141.27
= 152.21

Given expression :
$$ = \frac{{5.32 \times \left( {56 + 44} \right)}}{{\left( {7.66 + 2.34} \right)\left( {7.66 - 2.34} \right)}}$$
$$ = \frac{{5.32 \times 100}}{{10 \times 5.32}}$$
$$ = 10$$

$$ = 0.29\overline {56} $$
$$ = \frac{{2956 - 29}}{{9900}}$$
$$ = \frac{{2927}}{{9900}}$$

Given = 1599 ÷ 39.99 + $$\frac{4}{5}$$ × 2449 - 120.05
≈ 1600 ÷ 40 + $$\frac{4}{5}$$ × 2450 - 120
= 1600 ÷ 40 + 1960 - 120
= 40 + 1960 - 120
= 1880

Converting each of the given fractions into decimal form, we get:
$$\frac{9}{31}$$ = 0.29
$$\frac{3}{17}$$ = 0.176
$$\frac{6}{23}$$ = 0.26
$$\frac{4}{11}$$ = 0.363
$$\frac{7}{25}$$ = 0.28
Clearly, 0.363 > 0.29 > 0.28 > 0.26 > 0.176
So, $$\frac{4}{11}$$ > $$\frac{9}{31}$$ > $$\frac{7}{25}$$ > $$\frac{6}{23}$$ > $$\frac{3}{17}$$

Let original fraction be $$\frac{a}{b}$$
Now, according to the question,
$$ ⇒ \frac{{a - a \times \frac{{25}}{{100}}}}{{b + b \times \frac{{250}}{{100}}}} = \frac{6}{5}$$
$$ ⇒ \frac{{0.75a}}{{3.50b}} = \frac{6}{5}$$
$$ ⇒ \frac{a}{b} = \frac{6}{5} \times \frac{{3.50}}{{0.75}}$$
$$ ⇒ \frac{a}{b} = \frac{{6 \times 350 \times 100}}{{5 \times 75 \times 100}}$$
$$ ⇒ \frac{a}{b} = \frac{{28}}{5}$$

$$\frac{- 7}{10}$$ = - 0.7
$$\frac{5}{- 8}$$ = - $$\frac{5}{8}$$ = - 0.625,
$$\frac{2}{- 3}$$ = - $$\frac{2}{3}$$ = - 0.66
Since, -0.7 < -0.66 < -0.625
So, $$\frac{- 7}{10}$$ < $$\frac{2}{- 3}$$ < $$\frac{5}{- 8}$$

Given expression :
$$ = \frac{8 - 2.8}{1.3}$$
$$ = \frac{5.2}{1.3}$$
$$ = \frac{52}{13}$$
= 4