5-6- 7-8- 3-4- 4-5 arranged in ascending order would be - A 3-4 4-5 - 5-6 - 7-8C 3-4 - 4-5 - 5-6 - 7-8D 4-5 - 3-4 - 5-6 - 7-8-1-

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Arranging like Fractions

5/6, 7/8, 3/4...

Question

$\frac{5}{6}$ , $\frac{7}{8}$ , $\frac{3}{4}$ , $\frac{4}{5}$ arranged in ascending order would be :
(A) $\frac{3}{4}$ < $\frac{5}{6}$ < $\frac{4}{5}$ < $\frac{7}{8}$
(B) $\frac{3}{4}$ > $\frac{4}{5}$ > $\frac{5}{6}$ > $\frac{7}{8}$
(C) $\frac{3}{4}$ < $\frac{4}{5}$ < $\frac{5}{6}$ < $\frac{7}{8}$
(D) $\frac{4}{5}$ < $\frac{3}{4}$ < $\frac{5}{6}$ < $\frac{7}{8}$
$[1]$

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Solution

To arrange the given numbers in ascending order we will have to first make the Denominators equal by finding the LCM.

LCM of 6, 8, 4 and 5 is 120

Calculating these numbers converting denominator to 120 we get :

$\frac{5 \times 20}{6 \times 20}$ , $\frac{7 \times 15}{8 \times 15}$ , $\frac{3 \times 30}{4 \times 30}$ , $\frac{4 \times 24}{5 \times 24}$

$\Rightarrow$ $\frac{100}{120}$ , $\frac{105}{120}$ , $\frac{90}{120}$ , $\frac{96}{120}$

Arranging them in ascending order we get,

$\frac{90}{120}$ < $\frac{96}{120}$ < $\frac{100}{120}$ < $\frac{105}{120}$

$\Rightarrow$ $\frac{3}{4}$ < $\frac{4}{5}$ < $\frac{5}{6}$ < $\frac{7}{8}$

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Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

$\frac{5}{6}$ , $\frac{7}{8}$ , $\frac{3}{4}$ , $\frac{4}{5}$ arranged in ascending order would be :

Q. Verify:

\frac{3}{4} + (\frac{- 5}{6} + \frac{7}{8}) = (\frac{3}{4} + \frac{- 5}{6}) + \frac{7}{8}

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56, 78, 34, 45 arranged in ascending order would be : (A) 34 < 56 < 45 < 78 (B) 34 > 45 > 56 > 78 (C) 34 < 45 < 56 < 78 (D) 45 < 34 < 56 < 78 [1]