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Chapter 1: Problem 35

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

Short Answer

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

Step by step solution

01

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 \(-\frac{28}{35}\).
02

Add the fractions

Now, simply add the fractions: \(-\frac{15}{35} + - \frac{28}{35} = -\frac{43}{35}\)
03

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.

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Most popular questions from this chapter

Simplify each series of additions and subtractions. $$-726-422-921-(-816)$$

Simplify each algebraic expression. $$13-(-7 x)+4 x-(-11)$$

Perform the indicated subtraction. $$-\frac{4}{5}-\frac{1}{5}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The difference between 6 times a number and \(-5\) times the number.

Perform the indicated subtraction. $$\frac{1}{2}-\frac{1}{4}$$
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