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Chapter 0: Problem 146

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{2}{3}$$

Short Answer

Expert verified
The sum of the fractions is \(\frac{7}{6}\).

Step by step solution

01

Set Up The Fractions

The two fractions are \(\frac{1}{2}\) and \(\frac{2}{3}\)
02

Find a Common Denominator

Find the least common denominator (LCD) for 2 and 3. Normally, the LCD is the least common multiple (LCM) of the two numbers. Here, the LCM of 2 and 3 is 6. So, the common denominator is 6.
03

Convert the fractions

Convert \(\frac{1}{2}\) and \(\frac{2}{3}\) into two equivalent fractions with the denominator 6. \(\frac{1}{2}\) will become \(\frac{3}{6}\) and \(\frac{2}{3}\) will become \(\frac{4}{6}\).
04

Add the Fractions

Add \(\frac{3}{6}\) and \(\frac{4}{6}\) to get \(\frac{7}{6}\).
05

Simplify

The answer, \(\frac{7}{6}\) is already in its simplest form, because the numerator and the denominator do not share any other common factors than 1.

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Most popular questions from this chapter

What is a compound inequality and how is it solved?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I evaluated \(\frac{3 x-3}{4 x(x-1)}\) for \(x=1\) and obtained 0.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(a x^{2}+c=0, a \neq 0,\) cannot be solved by the quadratic formula.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car. what is the time interval that the mechanic will be working on the job?

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).
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