Chapter 1.1, Problem 28E

(a)

To determine

To find: the simplest value of $\left(3+\frac{1}{4}\right)\left(1-\frac{4}{5}\right)$ .

Answer to Problem 28E

  $\left(3+\frac{1}{4}\right)\left(1-\frac{4}{5}\right)=\frac{11}{8}$

Explanation of Solution

Given information:

An expression is given as $\left(3+\frac{1}{4}\right)\left(1-\frac{4}{5}\right)$ .

Formula used:

Difference of two fraction $\frac{a}{b}$ and $\frac{c}{d}$ can be performed by

  $\frac{a}{b}-\frac{c}{d}=\frac{ab-cb}{bd}$

Product of two fraction $\frac{a}{b}$ and $\frac{c}{d}$ can be performed by

  $\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$

Calculation:

Consider the given expression.

  $\left(3+\frac{1}{4}\right)\left(1-\frac{4}{5}\right)$

Now, simplify the expression as shown:

  $\begin{array}{c}\left(3+\frac{1}{4}\right)\left(1-\frac{4}{5}\right)=\frac{3\cdot 4-1}{4}\cdot \frac{1\cdot 5-4}{2}\\ =\frac{12-1}{4}\cdot \frac{5-4}{2}\\ =\frac{11}{4}\cdot \frac{1}{2}\\ =\frac{11}{8}\end{array}$

Here, the simplified value is $\frac{11}{8}$ .

(b)

To determine

To find: the simplest value of $\left(\frac{1}{2}+\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{3}\right)$ .

Answer to Problem 28E

  $\left(\frac{1}{2}+\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{5}{36}$

Explanation of Solution

Given information:

An expression is given as $\left(\frac{1}{2}+\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{3}\right)$ .

Formula used:

Sum of two fraction $\frac{a}{b}$ and $\frac{c}{d}$ can be performed by

  $\frac{a}{b}+\frac{c}{d}=\frac{ab+cb}{bd}$

Difference of two fraction $\frac{a}{b}$ and $\frac{c}{d}$ can be performed by

  $\frac{a}{b}-\frac{c}{d}=\frac{ab-cb}{bd}$

Product of two fraction $\frac{a}{b}$ and $\frac{c}{d}$ can be performed by

  $\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$

Calculation:

Consider the given expression.

Now, simplify the expression as shown:

  $\begin{array}{c}\left(\frac{1}{2}+\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{3}\right)=\frac{1\cdot 3+1\cdot 2}{2\cdot 3}\cdot \frac{1\cdot 3-1\cdot 2}{2\cdot 3}\\ =\frac{3+2}{6}\cdot \frac{3-2}{6}\\ =\frac{5}{6}\cdot \frac{1}{6}\\ =\frac{5}{36}\end{array}$

Here, the simplified value is $\frac{5}{36}$ .