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Chapter 2: Problem 32

For the following problems, use the order of operations to find each value. $$\left(\frac{5}{12}-\frac{1}{4}\right)+\left(\frac{1}{6}+\frac{2}{3}\right)$$

Short Answer

Expert verified
Answer: The value of the given expression is 1.

Step by step solution

01

Identify the operations within each parentheses

Inside the first parentheses, we need to subtract the two fractions, and inside the second parentheses, we need to add the two fractions.
02

Find common denominators for the fractions within each parentheses

For the first set of fractions, the common denominator is 12. In the second set, the common denominator is 6.
03

Perform the operations within the parentheses

For the first set, we can rewrite the fractions as: $$\frac{5}{12}-\frac{3}{12}$$ And then perform the subtraction: $$\frac{5-3}{12} = \frac{2}{12}$$ For the second set, the fractions can be rewritten as: $$\frac{1}{6}+\frac{4}{6}$$ And then perform the addition: $$\frac{1+4}{6} = \frac{5}{6}$$
04

Add the results from step 3

Now we have $$\frac{2}{12}+\frac{5}{6}$$ To add these fractions, we need to find a common denominator, which in this case is 12. We can rewrite the second fraction as follows: $$\frac{10}{12}$$ Now, we can add the fractions: $$\frac{2+10}{12} = \frac{12}{12}$$
05

Simplify the result

Since the numerator and denominator of the fraction are the same, the fraction simplifies to 1: $$\frac{12}{12} = 1$$ Therefore, the final answer is 1.

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