Problem 35 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-\frac{3}{7}+\left(-\frac{4}{5}\right)$$

Step-by-Step Solution

Answer

The sum of -3/7 and -4/5 is -1 8/35.

Step 1: Convert Fractions to Common Denominator

First, find a common denominator for the two fractions. In this case, the smallest number that both 7 and 5 divide evenly into is 35. Multiply the numerator and denominator of each fraction by the value that was used to obtain the common denominator. So, we multiply \(-\frac{3}{7}\) by 5/5 giving us \(-\frac{15}{35}\). We multiply \(-\frac{4}{5}\) by 7/7 giving us \(-\frac{28}{35}\).

Step 2: Add the fractions

Now, simply add the fractions: \(-\frac{15}{35} + - \frac{28}{35} = -\frac{43}{35}\)

Step 3: Simplify the Fraction

The fraction \(-\frac{43}{35}\) can't be simplified further. However, it is an improper fraction (that is, the absolute value of the numerator is larger than the absolute value of the denominator). We can convert it to a mixed number. Dividing 43 by 35 gives 1 remainder 8. We represent this division as the mixed number -1 8/35.