Problem 32 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

Answer: The value of the given expression is 1.

Step 1: 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.

Step 2: 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.

Step 3: 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: $$\frac{1+4}{6} = \frac{5}{6}$$

Step 4: 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: $$\frac{2+10}{12} = \frac{12}{12}$$

Step 5: 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.