Question

Arrange in decrasing order 2 upon 9, 2 upon 3, 8 upon 21

Answer 1

Given fractions are : $\frac{2}{9} \; , \; \frac{2}{3} \; , \; \frac{8}{21}$

We need to find the L.C.M of the denominators of these fractions to make the denominators same for every fractions. So we can find which fraction is big and which one is less.

So , LCM(9,3,21) = 63

Divide the L.C.M by each denominator to make the Denominator same.

$\Rightarrow \quad \frac{2}{9} = \frac{2}{9} \cdot \frac{7}{7} = \frac{14}{63} \\ \\ \Rightarrow \quad \frac{2}{3} = \frac{2}{3} \cdot \frac{21}{21} = \frac{42}{63} \\ \\ \Rightarrow \quad \frac{8}{21} = \frac{8}{21} \cdot \frac{3}{3} = \frac{24}{63}$

Hence, we can easily Identify which one is greater.

$\frac{42}{63} \; , \; \frac{24}{63} \; , \; \frac{14}{63} \\ \\ \mathtt{Or, \: We \: can \: write \: this \: as} \\ \\ \frac{2}{3} \; , \; \frac{8}{21} \; , \; \frac{2}{9}$