Problem 32 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$\frac{7}{10}+\left(-\frac{2}{5}\right)$$

Step-by-Step Solution

Answer

The result of \(\frac{7}{10}+\left(-\frac{2}{5}\right)\) is \(\frac{3}{10}\).

Step 1: Finding a Common Denominator

In this case, the denominators are 10 and 5. The least common multiple (LCM) of 10 and 5 is 10. Thus, 10 will be the common denominator.

Step 2: Converting Fractions to have a Common Denominator

\(\frac{7}{10}\) is already expressed with the common denominator. However, \(-\frac{2}{5}\) needs to be converted to have the denominator 10. This can be done by multiplying both the numerator and denominator by 2 to get \(-\frac{4}{10}\).

Step 3: Performing the Addition

Now that both fractions have the same denominator, they can be added as follows: \(\frac{7}{10} - \frac{4}{10} = \frac{3}{10}\)