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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 183. (page 53)

Add or Subtract Fraction.
$\frac{x}{3} + \frac{1}{4}$

Short Answer

Expert verified

The value of the given fraction is $\frac{4 x + 3}{12}$ .

Step by step solution

01

Step 1. Given information

Consider the expression.

$\frac{x}{3} + \frac{1}{4}$

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 $3$ and $4$ .

$\begin{array}{rcl} 3 & = & 3 路 1 \\ 4 & = & 2 路 2 \\ 鈬� & L C M = 3 路 2 路 2 \\ 鈬� & L C M = 12 \end{array}$

03

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

$\begin{array}{rcl} \frac{x}{3} + \frac{1}{4} & = & \frac{x 路 4}{3 路 4} + \frac{1 路 3}{4 路 3} \\ = & \frac{4 x}{12} + \frac{3}{12} \end{array}$

04

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

$\frac{x}{3} + \frac{1}{4} = \frac{4 x + 3}{12}$

Hence, the value is $\frac{4 x + 3}{12}$ .

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