Find each sum or difference. See Example 1. -6 + (-13)

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Identify the operation: The problem asks to find the sum of -6 and -13, which means we are adding two negative numbers.

Recall that adding two negative numbers results in a more negative number. So, we add their absolute values and keep the negative sign.

Calculate the absolute values: | -6 | = 6 and | -13 | = 13.

Add the absolute values: 6 + 13 = 19.

Attach the negative sign to the result: The sum is -19.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding Integer Addition and Subtraction

Integer addition and subtraction involve combining or removing quantities on the number line. Adding a negative number is equivalent to subtracting its absolute value, and subtracting a negative number is like adding its absolute value. This concept helps simplify expressions like -6 + (-13).

Number Line Visualization

Visualizing integers on a number line aids in understanding addition and subtraction. Moving left represents subtracting or adding negative numbers, while moving right represents adding positive numbers. This helps clarify operations involving negative integers.

Combining Like Terms

Combining like terms means adding or subtracting numbers of the same type, such as integers. When adding two negative integers, you add their absolute values and keep the negative sign. This principle is essential for correctly finding sums or differences.

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Related Practice

Textbook Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)

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Textbook Question

Work each matching problem.

Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x².

I II

a. y = (x - 7)² A. a translation to the left 7 units

b. y = x² - 7 B. a translation to the right 7 units

c. y = 7x² C. a translation up 7 units

d. y = (x + 7)² D. a translation down 7 units

e. y = x² + 7 E. a vertical stretching by a factor of 7

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