Problem 36 - Beginning and Intermediate Algebra

Question

Add $$\left(\frac{3}{4} c+\frac{1}{8}\right)+\left(\frac{3}{2} c-\frac{5}{6}\right)$$

Step-by-Step Solution

Answer

The short answer is: $$\frac{9}{4}c - \frac{17}{24}$$

Step 1: Identify the Terms

In the given expression, there are two terms with the common variable 'c' and two constants. Identify these terms: Terms with 'c': \(\frac{3}{4}c\) and \(\frac{3}{2}c\) Constants: \(\frac{1}{8}\) and \(-\frac{5}{6}\)

Step 2: Adding Coefficients of 'c'

Now, add the coefficients of the common variable 'c': \(\frac{3}{4}c + \frac{3}{2}c\) To add fractions, we need a common denominator. In this case, the common denominator is 4. So, we can rewrite the expression as: \(\frac{3}{4}c + \frac{6}{4}c\) Now, add the fractions: \(\frac{3 + 6}{4}c = \frac{9}{4}c\)

Step 3: Adding Constants

Next, let's add the constants: \(\frac{1}{8} - \frac{5}{6}\) Find the common denominator for the constants, which is 24. Rewrite the fractions with the common denominator: \(\frac{3}{24} - \frac{20}{24}\) Now subtract the fractions: \(\frac{3 - 20}{24} = -\frac{17}{24}\)

Step 4: Combine Simplified Terms

Finally, combine the simplified terms: \(\frac{9}{4}c - \frac{17}{24}\) The simplified expression after adding is: $$\frac{9}{4}c - \frac{17}{24}$$