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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 1: Q 192. (page 53)

Add or Subtract Fraction.
$a \frac{2 b}{5} + \frac{8}{15} b \frac{2 b}{5} 梅 \frac{8}{15}$

Short Answer

Expert verified

Part (a) The value of $\frac{2 b}{5} + \frac{8}{15}$ is $\frac{6 b + 8}{15}$ .

Part (b) The value of localid="1645593576717" $\frac{2 b}{5} 梅 \frac{8}{15}$ is $\frac{3 b}{4}$ .

Step by step solution

01

Part (a) Step 1. Given information

Consider the expression.

$a \frac{2 b}{5} + \frac{8}{15}$

02

Part (a) Step 2. Determine the operation.

The operation is addition.

03

Part (a) Step 3. Determine the whether the given fraction has the same denominator.

The given fraction does not have the same denominator.

So, find the least common denominator of $5$ and $15$ .

$\begin{array}{rcl} 5 & = & 5 路 3 \\ 15 & = & 5 路 3 \\ 鈬� & L C M = 5 路 3 \\ 鈬� & L C M = 15 \end{array}$

04

Part (a) Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 15.

$\begin{array}{rcl} \frac{2 b}{5} + \frac{8}{15} & = & \frac{2 b 路 3}{5 路 3} + \frac{8}{15} \\ = & \frac{6 b}{15} + \frac{8}{15} \end{array}$

05

Part (a) Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\frac{2 b}{5} + \frac{8}{15} = \frac{6 b + 8}{15}$

Thus, the value is $\frac{6 b + 8}{15}$ .

06

Part (b) Step 1. Now, consider the fraction.b2b5÷815Determine the operation.

The operation is division.

07

Part (b) Step 2. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

$\begin{array}{rcl} \frac{2 b}{5} 梅 \frac{8}{15} & = & \frac{2 b}{5} 路 \frac{15}{8} \\ = & \frac{2 b}{5} 路 \frac{5 路 3}{2 路 4} \\ = & \frac{3 b}{4} \end{array}$

Hence, the value is $\frac{3 b}{4}$ .

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