## Negative Numbers: When Students Ask

**Why should I bother learning this?**

Students should realize that not all situations can be modeled by positive numbers. Many situations require numbers that indicate the opposite direction of another number, such as distances above and below sea level, moving forward or backward, and depositing and withdrawing money. Students are in the process of making the transition from arithmetic to algebra. A good understanding of negative numbers and integers is needed to be successful in algebra.**Why do we change the sign of the second number and add when we are subtracting integers?**

Use a number line to demonstrate the meanings of*addition*and*subtraction.*On a number line, negative numbers are to the left and positive numbers to the right. To add on a number line, you move in the same direction as the number being added; to subtract, you move in the opposite direction. Demonstrate on the number line that to find 5 −^{-}3, you need to move three units. Which direction? Since^{-}3 signals you to move left 3, but the subtraction sign is a signal to go the opposite direction, you need to move 3 units to the right. Then show that this is the same answer you get by adding 5 + 3.**How do I know if the sum of two integers is positive or negative?**

After having done several examples, students should generalize that the sum of two positive integers will be positive and that the sum of two negative integers will be negative. It will probably be more difficult for them to guess the sum when adding two numbers opposite in sign. By having them examine specific cases, some students might be able to find that the integer which is farther from zero determines the sign of the sum. That is, if the negative integer is farther from zero than the positive integer, the sum is negative. For example,^{-}8 + 5 =^{-}3 because^{-}8 is farther from zero than 5 is. And if the positive integer is farther from zero than the negative integer, the sum is positive. For example, 6 + (^{-}2) = 4, since 6 is farther from zero than^{-}2 is.