Question

Arrange these rational number in asending order -7upon10 5upon-8 2upon-3 -1upon4 -3upon5

Answer 1

First write the rational numbers with positive denominator so it becomes - 7 / 10, - 5 / 8 , - 2 / 3 .

Find the LCM of denominators ( LCM of 10, 8, 3 is 120 )

- 7 / 10 = ( -7 x 12 ) / (10 x 12 ) = - 84 / 120

-5 / 8 = ( -5 x 15) / ( 8 x 15 ) = - 75 / 120

- 2 / 3 = ( 2 x 40 ) / ( 3 x 40 ) = - 80 / 120

Comparing the numerators of these numbers, we get

- 84 < - 80 < - 75

∴ - 84 / 120 < - 80 / 120 < - 75 / 120 ⇒ -7 / 10 < 2 / -3 < 5 / -8
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Answer 2

$\frac{ - 7}{10} \: \: \frac{5}{ - 8} \: \: \frac{2}{ - 3 } \: \: \frac{ - 1}{4} \: \: \frac{ - 3}{5} \\ \\ first \: of \: all \: make \: denominator \: of \\ \: each \: rational \: number \: positive \\ \\ i.e \\ \frac{ - 7}{10} \: \: \frac{ - 5}{8} \: \: \frac{ - 2}{3} \: \: \frac{ - 1}{4} \: \: \frac{ - 3}{5} \\ \\ now \:by \: taking \: lcm \: of \: there \: denominators \\ \\ lcm = 2 \times 2 \times 2 \times 3 \times 5 \\ \: \: \: \: \: \: \: \: = 120 \\ \\ \frac{ - 7 \times 12}{10 \times 12} \: \: \frac{ - 5 \times 15}{8 \times 15} \: \: \frac{ - 2 \times 40}{3 \times 40} \: \: \frac{ - 1 \times 30}{4 \times 30} \: \: \frac{ - 3 \times 24}{5 \times 24} \\ \\ \frac{ - 84}{120} \: \: \frac{ - 75}{120} \: \: \frac{ - 80}{120} \: \: \frac{ - 30}{120} \: \: \frac{ - 72}{120} \\ \\ since \: they \: are \: having \: negative \: sign \\ \\ now \: arrange \: them \: ascending \: order \\ \\ \frac{ - 84}{120} < \frac{ - 80}{120} < \frac{ - 75}{120} < \frac{ - 72 }{120} < \frac{ - 30}{120} \\ \\ i.e \\ \frac{ - 7}{10} < \frac{2}{ - 3} < \frac{5}{ - 8} < \frac{ - 3}{5} < \frac{ - 1}{4}$