Chapter 1.1, Problem 26E

(a)

To determine

To find: the simplest value of $\frac{2}{3}-\frac{3}{5}$ .

Answer to Problem 26E

  $\frac{2}{3}-\frac{3}{5}=\frac{1}{15}$

Explanation of Solution

Given information:

An expression is given as $\frac{2}{3}-\frac{3}{5}$ .

Formula used:

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

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

Calculation:

Consider the given expression.

  $\frac{2}{3}-\frac{3}{5}$

Now, simplify the expression as shown:

  $\begin{array}{c}\frac{2}{3}-\frac{3}{5}=\frac{2\cdot 5-3\cdot 3}{3\cdot 5}\\ =\frac{10-9}{15}\\ =\frac{1}{15}\end{array}$

Here, the simplified value is $\frac{1}{15}$ .

(b)

To determine

To find: the simplest value of $1+\frac{5}{8}-\frac{1}{6}$ .

Answer to Problem 26E

  $1+\frac{5}{8}-\frac{1}{6}=\frac{35}{24}$

Explanation of Solution

Given information:

An expression is given as $1+\frac{5}{8}-\frac{1}{6}$ .

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

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

Calculation:

Consider the given expression.

Now, simplify the expression as shown:

  $\begin{array}{c}1+\frac{5}{8}-\frac{1}{6}=1+\frac{5\cdot 6-1\cdot 8}{8\cdot 6}\\ =1+\frac{30-8}{48}\\ =1+\frac{22}{48}\\ =\frac{48+22}{48}\\ =\frac{70}{48}\\ =\frac{35}{24}\end{array}$

Here, the simplified value is $\frac{35}{24}$ .