Problem 36 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-\frac{3}{8}+\left(-\frac{2}{3}\right)$$

Step-by-Step Solution

Answer

The sum of \(-\frac{3}{8}\) and \(-\frac{2}{3}\) is \(-1\frac{1}{24}\).

Step 1: Identifying the Fractions

Firstly, identify the fractions to be added. They are \(-\frac{3}{8}\) and \(-\frac{2}{3}\). Notice that both fractions are negative values.

Step 2: Finding a Common Denominator

In order to add the fractions, we need a common denominator. Multiples of 8 are 8, 16, 24, ..., and multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, .... So, we may choose the common denominator as 24.

Step 3: Writing Fractions using the Common Denominator

Using the common denominator, we can rewrite the fractions as equivalent fractions with the common denominator. The fraction \(-\frac{3}{8}\) may be written as \(-\frac{9}{24}\) and the fraction \(-\frac{2}{3}\) may be written as \(-\frac{16}{24}\).

Step 4: Adding Fractions using the Common Denominator

Now we add the two fractions using the common denominator: \(-\frac{9}{24}+\left(-\frac{16}{24}\right)=-\frac{25}{24}\).

Step 5: Simplifying the Resultant Sum

The resultant sum \(-\frac{25}{24}\) can be simplified and written as a mixed number. The final answer simplifies to \(-1\frac{1}{24}\).