1.1.2 Adding and Subtracting Real Numbers

Key Objectives • Add and subtract numbers on a number line. • Add and subtract real numbers. Key Terms • Real numbers are all numbers on a number line. • Absolute value is the distance of a number from zero on a number line; shown by | |. • On a number line, opposites are two numbers the same distance from 0 but on different sides of 0. Two numbers are opposites if their sum is 0. The process for adding two signed numbers depends on whether the two numbers have the same sign or different signs. • To find the sum of two numbers with different signs (i.e., one number is positive and the other number is negative), find the difference of their absolute values and then apply the sign of the number with the greater absolute value. • To find the sum of two numbers with the same sign (i.e., two positive numbers or two negative numbers), find the sum of their absolute values and then apply the common sign.

Example 1 Adding and Subtracting Numbers on a Number Line

A number line can be used to model addition and subtraction of signed numbers. To model the addition of a positive number, move that number of units to the right along the number line. To model the addition of a negative number, move that number of units to the left along the number line.

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