Problem 31 - 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

\(\frac{3}{10}\)

Step 1: Identify the denominators

The denominators of the two fractions are 10 and 5. We need to find a common denominator to add the fractions. The lowest common denominator for 10 and 5 is 10.

Step 2: Convert the fractions to have the common denominator

The fraction \( \frac{7}{10} \) already has the denominator 10. So we leave it as it is. The fraction \( -\frac{2}{5} \) needs to be converted to have the denominator 10. To do this, multiply \( -\frac{2}{5} \) by \( \frac{2}{2} \) to get \( -\frac{4}{10} \). Then, our fractions are \( \frac{7}{10} \) and \( -\frac{4}{10} \).

Step 3: Add the fractions

Now that both fractions have the same denominator, we can add them by adding the numerators and keep the same denominator. \( \frac{7}{10} - \frac{4}{10} = \frac{7-4}{10} \)

Step 4: Simplify the fraction

Simplifying the fraction \( \frac{3}{10} \) we get the final answer: \( \frac{3}{10} \).