Problem 43 - Introductory Algebra for College Students

Question

Find each sum without the use of a number line. $$-45+\left(-\frac{3}{7}\right)+25+\left(-\frac{4}{7}\right)$$

Step-by-Step Solution

Answer

The sum of \(-45 + -\frac{3}{7} + 25 + -\frac{4}{7}\) is \(-21\).

Step 1: Addition of Integers

First, focus on the integer part of the equation: \(-45 + 25\). Subtract the smaller absolute value from the larger absolute value, keeping the sign of the larger absolute value. This equals to \(-45 + 25 = -20\).

Step 2: Addition of Fractions

Next, consider the fraction part of the equation: \(-\frac{3}{7} - \frac{4}{7}\). Since both fractions have the same denominator, they can be added directly. This gives \(-\frac{3}{7} - \frac{4}{7} = -\frac{7}{7}\).

Step 3: Final Calculation

Now, combine the results from Step 1 and Step 2. The equation now becomes \(-20 -1\), which equals to \(-21\).