Chapter 4.4, Problem 81E

Solution

To order the number from least to greatest.

  $\frac{7}{20},\frac{3}{8},\frac{5}{12}$ .

Option F:

Given information: $\frac{2}{9},\frac{1}{6},\frac{4}{25}$

Formula Used: Factorisation

Calculation:

Convert these fractions to equivalent fractions with common denominator in order to compare them more easily.

LCM of 9,6 and 25 is 450

So , denominator of both fractions 450.

  $\frac{2\times 50}{9\times 50}=\frac{100}{450}$

  $\frac{1\times 75}{6\times 75}=\frac{75}{450}$

  $\frac{4\times 18}{25\times 18}=\frac{72}{450}$

  $\frac{100}{450}>\frac{75}{450}>\frac{72}{450}$

  $\frac{2}{9}>\frac{1}{6}>\frac{4}{25}$

Option G:

Given information: $\frac{3}{7},\frac{11}{24},\frac{9}{21}$

Formula Used: Factorisation

Calculation:

We need to convert these fractions to equivalent fractions with common denominator in order to compare them more easily.

LCM of 7,24 and 21 is 168

So we have to made denominator of both fractions 168.

  $\frac{3\times 24}{7\times 24}=\frac{72}{168}$

  $\frac{11\times 7}{24\times 7}=\frac{77}{168}$

  $\frac{9\times 8}{21\times 8}=\frac{72}{168}$

  $\frac{72}{168}<\frac{77}{168}>\frac{72}{168}$

  $\frac{3}{7}<\frac{11}{24}>\frac{9}{21}$

Option H:

Given information: $\frac{7}{20},\frac{3}{8},\frac{5}{12}$

Formula Used: Factorisation

Calculation:

We need to convert these fractions to equivalent fractions with common denominator in order to compare them more easily.

LCM of 20,8 and 12 is 120

So we have to made denominator of both fractions 120.

  $\frac{7\times 6}{20\times 6}=\frac{42}{120}$

  $\frac{3\times 15}{8\times 15}=\frac{45}{120}$

  $\frac{5\times 10}{12\times 10}=\frac{50}{120}$

  $\frac{42}{120}<\frac{45}{120}<\frac{50}{120}$

  $\frac{7}{20}<\frac{3}{8}<\frac{5}{12}$

Option I:

Given information: $\frac{2}{5},\frac{19}{40},\frac{21}{45}$

Formula Used: Factorisation

Calculation:

We need to convert these fractions to equivalent fractions with common denominator in order to compare them more easily.

LCM of 5,40 and 45 is 360

So we have to made denominator of both fractions 360.

  $\frac{2\times 72}{5\times 72}=\frac{144}{360}$

  $\frac{19\times 9}{40\times 9}=\frac{171}{360}$

  $\frac{21\times 8}{45\times 8}=\frac{168}{360}$

  $\frac{144}{360}<\frac{171}{360}>\frac{168}{360}$

  $\frac{2}{5}<\frac{19}{40}>\frac{21}{45}$