Problem 19 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-\frac{7}{10}+\left(-\frac{3}{10}\right)$$

Step-by-Step Solution

Answer

The sum of the described fractions equals to -1.

Step 1: Identify the fractions to be summed

The fractions to be summed are \(-\frac{7}{10}\) and \(-\frac{3}{10}\). All fractions share the same denominator (10), simplifying the task.

Step 2: Sum the numerators

When adding fractions with the same denominator, simply add the numerators. Both fractions are negative, hence the sum will also be negative. Compute \(-7 - 3\)

Step 3: Write the result as a fraction

\(-7 - 3\) equals to -10 . Thus, the sum of these fractions is \(-\frac{10}{10}\).

Step 4: Simplify the fraction

The fraction \(-\frac{10}{10}\) can be simplified to -1 as both the numerator and the denominator are the same.