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1. 1. Adding Integers Mrs. Young EMC 1
2. 2. Problem <ul><li>George owes his friend Jeanne \$3. If he borrows another \$6, how much will he owe her altogether? </li></ul><ul><ul><li>Now I know that you are thinking this is simple, but just wait! </li></ul></ul>
3. 3. Solution <ul><li>Actually, this problem is quite simple: just add \$3 and \$6 and the result is \$9. </li></ul><ul><li>However, the problem can be solved using addition of integers . </li></ul><ul><ul><li>Owing \$3 can be represented by -3 and owing \$6 can be represented by -6. </li></ul></ul><ul><ul><ul><li>The problem becomes: -3 + -6 = -9 </li></ul></ul></ul>
4. 4. Let’s Use A Number Line! <ul><li>Look at the number line below: </li></ul><ul><ul><li>Start at 0 </li></ul></ul><ul><ul><li>Move to the left 3 spaces (why left???) </li></ul></ul><ul><ul><li>Move 6 more spaces to the left (why???) </li></ul></ul><ul><ul><li>We end at -9 </li></ul></ul><ul><ul><ul><li>So -3 + -6 = -9 </li></ul></ul></ul>
5. 5. Let’s Try Another! <ul><li>How can we solve +5 + -3??? </li></ul><ul><ul><li>Simple! Use a number line! </li></ul></ul><ul><ul><ul><li>Start at 0 </li></ul></ul></ul><ul><ul><ul><li>Move to the right 5 spaces (why right??) </li></ul></ul></ul><ul><ul><ul><li>Now move 3 spaces to the left (why left??) </li></ul></ul></ul><ul><ul><ul><ul><li>You can see that +5 + -3 = +2 </li></ul></ul></ul></ul>
6. 6. Let’s Try One More! <ul><li>Solve -5 + 3 </li></ul><ul><ul><li>Start at 0 </li></ul></ul><ul><ul><li>Move to the left 5 spaces (why??) </li></ul></ul><ul><ul><li>Now move 3 spaces to the right (why?) </li></ul></ul><ul><ul><ul><li>You can see that we end up at -2! </li></ul></ul></ul>
7. 7. Let’s Check Out Some Rules! <ul><li>When adding integers that have the same sign, the answer will have the same sign. </li></ul><ul><ul><li>For example: The sum of two negative integers is a negative integer. </li></ul></ul>- 20 - 13 + - 7 = - 13 - 5 + - 8 = - 11 - 2 + - 9 = Sum Integers Adding Negative Integers
8. 8. Rules Continued… <ul><li>Also, when adding two positive integers, the answer will be a positive integer. </li></ul>+ 45 + 29 + + 16 = + 22 + 17 + + 5 = + 11 + 2 + + 9 = Sum Integers Adding Positive Integers
9. 9. Uh oh! Wait! <ul><li>But, what if I want to add a positive integer and a negative integer… what should I do?? </li></ul><ul><li>It’s simple! </li></ul><ul><li>Follow these steps: </li></ul>The result from Step 2 takes the sign of the integer with the greater absolute value. 3. Subtract the smaller number from the larger number you get in Step 1. 2. Find the absolute value of each integer. 1.
10. 10. Let’s Try It! <ul><li>We can use a number line, or you don’t have to! </li></ul><ul><ul><li>Solve +7 + -3 </li></ul></ul><ul><ul><ul><li>Always start at 0 </li></ul></ul></ul><ul><ul><ul><li>Move to the ____________ 7 spaces </li></ul></ul></ul><ul><ul><ul><li>Then move to the ________ 3 spaces </li></ul></ul></ul>
11. 11. Let’s do it without the number line! <ul><li>Find the absolute value of -7 and the absolute value of +3 (7 and 3) </li></ul><ul><li>Subtract the smaller number from the larger number in the Step 1 (7 – 3) </li></ul><ul><li>The result from Step 2 takes the sign of the integer with the greater absolute value. </li></ul><ul><ul><li>The answer would be -4 because the integer with the greater absolute value is negative! </li></ul></ul>
12. 12. Try this one! <ul><li>Solve -9 and +5. </li></ul><ul><li>Use a number line or not! </li></ul><ul><li>Find the absolute value of -9 and the absolute value of +5 </li></ul><ul><li>Subtract the smaller number from the larger number in the Step 1 </li></ul><ul><li>The result from Step 2 takes the sign of the integer with the greater absolute value. </li></ul><ul><li>And the answer is…… </li></ul>
13. 13. Yep! You’re right! <ul><li>-4 </li></ul>
14. 14. Here’s a Song For You! <ul><li>(to the tune of “Row, row, row your boat”) </li></ul><ul><li>&quot;Same Sign, Add and keep, Different sign, subtract. Take the sign of the higher number Then it'll be exact!&quot; </li></ul>