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1. 1. What is 5 + 7? We can show how to do this by using algebra tiles. 1 1 1 1 1 1 1 1 1 1 + = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 + 7 = 12 What is –5 + -7? -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 + = -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -5 + -7 = -12
2. 2. We can show this same idea using a number line. 9-10 -5 0 5 10What is 5 + 4? Move five (5) units to the right from zero. Now move four more units to the right. The final point is at 9 on the number line. Therefore, 5 + 4 = 9.
3. 3. -9-10 -5 0 5 10What is -5 + (-4)? Move five (5) units to the left from zero. Now move four more units to the left. The final point is at -9 on the number line. Therefore, -5 + (-4) = -9.
4. 4. To add integers with the same sign, add the absolutevalues of the integers. Give the answer the same sign asthe integers. Examples Solution 1. 15  12 27 2.  14  ( 33)  47 3.  4 x  ( 12x )  16x
5. 5. What is (-7) + 7? -10 -5 0 5 10 To show this, we can begin at zero and move seven units to the left. Now, move seven units to the right. Notice, we are back at zero (0). For every positive integer on the number line, there is a corresponding negative integer. These integer pairs are opposites or additive inverses.Additive Inverse Property – For every number a, a + (-a) = 0
6. 6. When using algebra tiles, the additive inverses make whatis called a zero pair.For example, the following is a zero pair. 1 -1 1 + (-1) = 0. This also represents a zero pair. x -x x + (-x) = 0
7. 7. Add the following integers: (-4) + 7. -10 -5 0 5 10 Start at zero and move four units to the left. Now move seven units to the right. The final position is at 3. Therefore, (-4) + 7 = 3.
8. 8. Add the following integers: (-4) + 7. -10 -5 0 5 10 Notice that seven minus four also equals three. In our example, the number with the larger absolute value was positive and our solution was positive. Let’s try another one.
9. 9. Add (-9) + 3 -10 -5 0 5 10Start at zero and move nine places to the left.Now move three places to the right.The final position is at negative six, (-6).Therefore, (-9) + 3 = -6.
10. 10. Add (-9) + 3-10 -5 0 5 10 In this example, the number with the larger absolute value is negative. The number with the smaller absolute value is positive. We know that 9-3 = 6. However, (-9) + 3 = -6. 6 and –6 are opposites. Comparing these two examples shows us that the answer will have the same sign as the number with the larger absolute value.
11. 11. To add integers with different signs determine the absolutevalue of the two numbers. Subtract the smaller absolute valuefrom the larger absolute value. The solution will have the samesign as the number with the larger absolute value. Example Subtract Solution 12  15 15  12 3 17  ( 25 ) 25  17 8
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