Question

write the following fraction in an ascending order .3/4,3/2,2/3,1/5,18/7​

Answer 1

★ How to do :-

Here, we are given with five fractions. Some of them are proper fractions and some of them are improper fractions. We are asked to arrange all those five fractions in ascending order i.e, from smallest number of biggest number. We can see that all the fractions have a different denominators. So, first we should make their denominators as same by taking their equivalent fractions. The concept of LCM is used to find their common multiple and then make their denominators as same. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{3}{4} ; \dfrac{3}{2} ; \dfrac{2}{3} ; \dfrac{1}{5} ; \dfrac{18}{7}}$

Convert them into like fractions by taking the LCM of the denominators i.e, 4, 2, 3, 5 and 7.

LCM of 4, 2, 3, 5 and 7 is 420.

${\tt \leadsto \dfrac{3 \times 105}{4 \times 105} ; \dfrac{3 \times 210}{2 \times 210} ; \dfrac{2 \times 140}{3 \times 140} ; \dfrac{1 \times 84}{5 \times 84} ; \dfrac{18 \times 60}{7 \times 60}}$

Multiply all the numerators and denominators to get their equivalent fractions.

${\tt \leadsto \dfrac{315}{420} ; \dfrac{630}{420} ; \dfrac{280}{420} ; \dfrac{84}{420} ; \dfrac{1080}{420}}$

Now, find out which is smaller and greater and arrange them from smallest to biggest.

${\tt \leadsto \dfrac{84}{420} < \dfrac{280}{420} < \dfrac{315}{420} < \dfrac{630}{420} < \dfrac{1080}{420}}$

Now, write their lowest form which were given at first, which will be the final answer.

${\tt \leadsto \pink{ \boxed{\tt \dfrac{1}{5} < \dfrac{2}{3} < \dfrac{3}{4} < \dfrac{3}{2} < \dfrac{18}{7}}}}$

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Hence solved !!