Question

Arrange in ascending order 1/4,3/8,5/12

Answer 1

Answer:

1/4<3/8<5/12

hope it helps

Answer 2

Given:

$\sf{The\:fractions\:\dfrac{1}{4},\:\dfrac{3}{8},\:\dfrac{5}{12}}$

To do:

$\sf{Arrange\:them\:in\:ascending\:order.}$

Solution:

→ To arrange the given fractions in ascending orders, we need to make them like fractions. This means that they should have the same denominators.

The current denominators of the fractions are 4, 8 and 12 respectively. Let's find their lowest common multiple.

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 4 , 8 , 12} \\ \cline{1-2} \tt 2 & \sf { 2 , 4 , 6} \\ \cline{1-2} \tt 2 & \sf{ 1 , 2 , 3} \\ \cline{1-2} \tt 3 & \sf{ 1 , 1 , 3} \\ \cline{1-2} & \sf{ 1 , 1 , 1} \end{array}}$

LCM =  2 x 2 x 2 x 3

        = 24

→ We find the number which should be multiplied by the denominator to get 24. We know that,

• 4 x 6 = 24
• 8 x 3 = 24
• 12 x 2 = 24

→ And now we multiply the numerators of the fractions with the same numbers we multiplied the denominators with to get 24.

So,

$\sf{\dfrac{1}{4}=\dfrac{1\times6}{4\times6},\:\dfrac{3}{8}=\dfrac{3\times3}{8\times3},\:\dfrac{5}{12}=\dfrac{5\times2}{12\times2}}$

$\sf{\dfrac{1}{4}=\dfrac{6}{24},\dfrac{3}{8}=\dfrac{9}{24},\dfrac{5}{12}=\dfrac{10}{24}}$

→ Now we can easily compare:

$\sf{\dfrac{6}{24}<\dfrac{9}{24}<\dfrac{10}{24}}$

$\boxed{\bf{Thus,\:\dfrac{1}{4}<\dfrac{3}{8}<\dfrac{5}{12}}}$

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