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Chapter 1: Problem 43

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

Short Answer

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

Step by step solution

01

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 \(-45 + 25 = -20\).
02

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 \(-\frac{3}{7} - \frac{4}{7} = -\frac{7}{7}\).
03

Final Calculation

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

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(7-(-2)=5\)

Order the expressions \(|x-y|,|x|-|y|,\) and \(|x+y|\) from least to greatest for \(x=-6\) and \(y=-8\).

Perform the indicated subtraction. $$-45-(-45)$$

Simplify each algebraic expression. $$2 x-10 x$$

Simplify each series of additions and subtractions. $$-19-8-(-6)+(-21)$$
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