Chapter MH, Problem 18PP

Solution

a)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{11}{10}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

There must be a common denominator between two fractions before the number are added together.

The least common multiple of the two denominators is used to identify common denominators.

The given operation is $\frac{2}{3}+\frac{3}{4}$ .

The least common multiple of $3$ and $4$ is $12$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{2}{3}+\frac{3}{4}=\left(\frac{2}{3}\times \frac{4}{4}\right)+\left(\frac{3}{4}\times \frac{3}{3}\right)\\ =\frac{8}{12}+\frac{9}{12}\\ =\frac{17}{12}\end{array}$

b)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{11}{10}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

There must be a common denominator between two fractions before the number are added together.

The least common multiple of the two denominators is used to identify common denominators.

The given operation is $\frac{4}{5}+\frac{3}{10}$ .

The least common multiple of $5$ and $10$ is $10$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{4}{5}+\frac{3}{10}=\left(\frac{4}{5}\times \frac{2}{2}\right)+\left(\frac{3}{10}\times \frac{1}{1}\right)\\ =\frac{8}{10}+\frac{3}{10}\\ =\frac{11}{10}\end{array}$

c)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{1}{12}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

There must be a common denominator between two fractions before the numbers are subtracted.

The least common multiple of the two denominators is used to identify common denominators.

The given operation is $\frac{1}{4}-\frac{1}{6}$ .

The least common multiple of $6$ and $4$ is $12$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{1}{4}-\frac{1}{6}=\left(\frac{1}{4}\times \frac{3}{3}\right)+\left(\frac{1}{6}\times \frac{2}{2}\right)\\ =\frac{3}{12}-\frac{2}{12}\\ =\frac{1}{12}\end{array}$

d)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{1}{24}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

There must be a common denominator between two fractions before the numbers are subtracted.

The least common multiple of the two denominators is used to identify common denominators.

The given operation is $\frac{7}{8}-\frac{5}{6}$ .

The least common multiple of $6$ and $8$ is $24$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{7}{8}-\frac{5}{6}=\left(\frac{7}{8}\times \frac{3}{3}\right)+\left(\frac{5}{6}\times \frac{4}{4}\right)\\ =\frac{21}{24}-\frac{20}{24}\\ =\frac{1}{24}\end{array}$

e)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{1}{4}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

The numerators and denominators are multiplied together when multiplying fractions.

The given operation is $\frac{1}{3}\times \frac{3}{4}$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{1}{3}\times \frac{3}{4}=\frac{1}{\cancel{3}}\times \frac{\cancel{3}}{4}\\ =\frac{1}{4}\end{array}$

f)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{6}{35}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

The numerators and denominators are multiplied together when multiplying fractions.

The given operation is $\frac{3}{5}\times \frac{2}{7}$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{3}{5}\times \frac{2}{7}=\frac{3\times 2}{5\times 7}\\ =\frac{6}{35}\end{array}$

g)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{5}{2}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

When dividing fractions, the dividend is multiplied by the divisor, which is then inverted.

The given operation is $\frac{5}{8}÷\frac{1}{4}$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{5}{8}÷\frac{1}{4}=\frac{5}{8}\times \frac{4}{1}\\ =\frac{5}{2}\end{array}$

h)

Interpretation : The indicated operation is to be performed.

Concept Introduction : The same types of operations apply to fractions as they do to other numbers. A fraction is a mathematical value that illustrates the components of a whole.

The answer to performed operation is $\frac{32}{27}$ .

A fraction's numerator is the number at the top, and its denominator is the number at the bottom.

The numerators and denominators are multiplied together when multiplying fractions.

The given operation is $\frac{4}{9}÷\frac{3}{8}$ .

The operation is performed as follows:

  $\begin{array}{c}\frac{4}{9}÷\frac{3}{8}=\frac{4}{9}\times \frac{8}{3}\\ =\frac{32}{27}\end{array}$