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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 178. (page 52)

Add or Subtract Fraction.
$- \frac{23}{30} + \frac{5}{48}$

Short Answer

Expert verified

The value of the given fraction is $\begin{array}{rcl} - \frac{53}{80} \end{array}$ .

Step by step solution

01

Step 1. Given information

The given expression is $- \frac{23}{30} + \frac{5}{48}$ .

02

Step 2. 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 $30$ and $48$ .

$\begin{array}{rcl} 30 & = & 2 路 3 路 5 \\ 48 & = & 2 路 2 路 2 路 2 路 3 \\ 鈬� & L C D = 2 路 2 路 2 路 2 路 3 路 5 \\ 鈬� & L C D = 240 \end{array}$

03

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 240.

$\begin{array}{rcl} - \frac{23}{30} + \frac{5}{48} & = & - \frac{23 路 8}{30 路 8} + \frac{5 路 5}{48 路 5} \\ = & - \frac{184}{240} + \frac{25}{240} \end{array}$

04

Step 4. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

$\begin{array}{rcl} - \frac{23}{30} + \frac{5}{48} & = & \frac{- 184 + 25}{240} \\ = & \frac{- 159}{240} \\ = & - \frac{53}{80} \end{array}$

Hence, the value is $\begin{array}{rcl} - \frac{53}{80} \end{array}$ .

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