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  • Arrange the fractions \frac{6}{7},\frac{7}{8},\frac{4}{5}\; and\; \frac{3}{4} in descending order.

Arrange the fractions \frac{6}{7},\frac{7}{8},\frac{4}{5}\; and\; \frac{3}{4} in descending order.

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Given number \frac{6}{7},\frac{7}{8},\frac{4}{5}\; and\; \frac{3}{4}

By prime factorization method LCM of 4,5,7,8

4 = 2 x 2

5 =  1x 5

7 =  1x 7 

8 = 2 x 2 x 2 

LCM of 4,5,7,8 = 2 x 2 x 2 x 5 x 7 = 280

\begin{aligned} &\frac{6}{7}=\frac{6 \times 40}{7 \times 40}=\frac{240}{280} \\ &\frac{7}{8}=\frac{7 \times 35}{8 \times 35}=\frac{245}{280} \end{aligned}

\\ \frac{4}{5}=\frac{4 \times 56}{5 \times 56}=\frac{224}{280} \\\\ \frac{3}{4}=\frac{3 \times 70}{4 \times 70}=\frac{210}{280}

\\ \because \frac{245}{280}>\frac{240}{280}>\frac{224}{280}>\frac{210}{280} \\ \\ \therefore \frac{7}{8}>\frac{6}{7}>\frac{4}{5}>\frac{3}{4}

 

Posted by

Ravindra Pindel

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