Speed Bump #2 – Integers A concept that students find challenging is integers, positive and negative numbers. Positive integers represent numbers greater than 0. They are used when adding more of something. Negative integers are numbers whose value is less than 0. They represent taking away some number of units. You can think of adding and subtracting integers as moving along the number line. When dealing with positive integers you move to the right in addition. In subtraction, you move to the left. When the integers are negative the direction of the movement is reversed. Adding negative integers causes you to move to the left. Subtracting negative integers causes you to move to the right. When you are adding integers, if the sign is the same (both negative or both positive) the sign of your answer will also be the same. 3 + 4 = 7 -­‐3 + -­‐4 = -­‐7 Adding a negative integer to a positive integer is just like subtraction. Think, when the signs are different, find the difference, and give it the sign of the larger number. -­‐3 + 4 = 1 the difference (the value I get by subtracting) between 3 and 4 is 1. 4 is larger and is positive, so my answer is positive. When subtracting integers you want to change the operation to addition. Think same change change. Leave the first number the same. Change the subtraction to addition and change the sign of the second number. -­‐3 – 4 = -­‐3 + -­‐4 5 – (-­‐2) = 5 + 2 Now you can proceed as with any addition problem. Just like with fractions, most students find multiplication and division easier. For both multiplication and division if the signs of the numbers in your problem are the same, your answer is positive. If the signs of the numbers are different, your answer is negative. 3 × −2 = −6 − 3 × −2 = 6 − 6 ÷ 2 = −3 − 6 ÷ −2 = 3 Some students really struggle with adding and subtracting integers, particularly when faced with a problem containing more than 2 terms. Think of the positive integers as being on one team and the negative integers as being on the other team. Add up their score. Who won and by how much? 3 + -­‐2 + -­‐5 + 7 + 4 The red (positive ) team scored scored 3 + 7 + 4 runs for a total of 14. The blue (negative )team scored 2 + 5 runs for a total of 7. Who won? The positive team. By how much? 7 runs so your answer is 7 Practice problems and answers are provided.