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How to Subtract Integers Using Models www.fortheloveofteachingmath.com Subtracting Integers In order to subtract integers, you need to remember what zero pairs are. Zero pairs is a + and a - set. For instance -1 and +1 is a zero pair. Let's start with the subtraction problem -3 - 2. Start with modeling -3. The problem says to take away two positives. You'll notice that you do not have two positives. How could you put positives in your model without changing the value of the problem? You could add zero pairs. Remember that the value of a zero pair is zero, so you do not change the value of the problem by adding zero pairs to it. How many zero pairs do you need to add in order to have two positives away? Two. Once you've added the zero pairs, you can take away the two positives. What are you left with? Five negatives. So, -3 - 2 = -5 www.fortheloveofteachingmath.com Subtracting Integers With your magnet models, work the following problem: -5 - 3 Start with five negatives. It says to take away three positives. Do you have any positives? No. You are going to have to add zero pairs until you have enough positives to take three away. How many zero pairs are you going to have to add? Three. Your model should look something like this. Then take way the three positives. What do you have left? Eight negatives, so -5 - 3 = -8 Now try this problem 1 - 4 Start with one positive. It says to take away four positives, but you only have one. What are you going to have to do? Add enough zero pairs so that you can take away four. How many zero pairs do you need to add? Three What do you have left? Three negatives. So...... 1 - 4 = -3 www.fortheloveofteachingmath.com Subtracting Integers Here's another problem for you...... -2 - (-4) You are going to start with two negatives. It then says to take away four negatives. You only have two negatives, so you are going to have to add enough zero pairs to be able to take away four. How many zero pairs do you need to add? Two. What are you left with? Two positives. So...... -2 - (-4) = 2 Find the value of the following expressions by either using the magnets or by drawing the figures. 1. -4 - 5 2. 6 - (-4) 3. 2-6 4. -7 - (-2) After you have modeling subtracting integers, I go back to the Integer Song. The Integer Song only works when you are adding integers. There is no song for subtracting integers, so I always change my subtraction signs to addition signs so that I can use the song. When you change one thing in a math problem, you always have to change something else. In this case, when we change the subtraction sign to addition, I am going to change the sign of the number following the subtraction sign. www.fortheloveofteachingmath.com Subtracting Integers For example: Find the value of -4 - (-9) -4 - (-9) First you have to change the negative to a positive -4 + (-9) Now thange the sign of the number AFTER the subtraction sign. -4 + (+9) Now you can sing the song. Do you have same or different signs? Different. So you subtract 9 - 4 = 5. Take the sign of the higher number +. So -4 - (-9) = 5 You now have a couple of ways to find the value of integer subtraction problems. Find the value of the following problems 1. -10 - 7 2. -8 - (-10) 3. 7-9 4. 2 - (-11) Congratulations! You now know how to add and subtract integers!!! www.fortheloveofteachingmath.com