<p>Study Guide: Adding Integers</p><p>Adding Integers: Using a number line:</p><p>You can use a number line to help see what happens when you add integers. a. A + sign indicates moving to the right b. A – sign indicates moving to the left. </p><p>Start at 0. Move as indicated by the signs of the integers. Your stopping point will be the sum. </p><p>Example: - 9 + 12 </p><p>Start at 0. Move left 9 steps, then move right 12 steps. Where did you stop? </p><p>-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 So, -9 + 12 = 3 </p><p>Example: 5 – 8 Start at 0. Move right 5 steps, then move left 8 steps. Where did you stop? </p><p>-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 </p><p>So. 5 – 8 = -3</p><p>Example: -8 – 4 Start at 0. Move left 8 steps, then continue left for 4 more steps. Where did you stop? </p><p>-16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 </p><p>So, -8 – 4 = - 12 </p><p>As you can imagine, using a number line can become very tedious, especially when you are working with large integers. You don’t want to draw a number line that goes ½ mile. </p><p>To make it easier to add and subtract integers, we have “rules” which you can follow. Adding Integers: Using Rules:</p><p>1. To add two integers with the same sign, add their absolute values and keep the sign.</p><p>Examples: 7 + 4 = 11 Both of these integers are positive. - 8 + (-6) = -14 Both of these integers are negative. </p><p>*** If the problem is written as -6 – 7, consider the sign in front of the integer as the sign of that integer. In this case, we have a negative 6 and a negative 7. They have the same sign. Then using the rule above, – 6 – 7 = – 13 </p><p>2. To add two integers with different signs, subtract their absolute values and take the sign of the number with the larger absolute value. (The one farther from 0.)</p><p>Examples: 9 + (-4) = 5 Absolute values are 9 and 4, the difference is 5. 9 has the larger absolute value and is positive, so the answer will be positive. </p><p>-12 + 8 = – 4 Absolute values are 12 and 8, the difference is 4. -12 has the larger absolute value and is negative, so the answer will be negative.</p><p>3. To subtract two integers, be sure to have only one sign between the integers. Then use the addition rules. a. If you are subtracting a positive integer, change the middle sign to – . 8 – (+ 5) : change this to 8 – 5 ( a + and – together make a – )</p><p> b. If you are subtracting a negative integer, change the middle sign to +. 8 – ( – 5 ) : change this to 8 + 5 (a – and – together make a +) </p><p>Examples: 1. 5 – 9 = – 4 (different signs, subtract) 2. – 6 + 10 = 4 (different signs)</p><p>3. 7 – ( – 2 ) = 7 + 2 = 9 (same signs, add) 4. – 5 – 6 = - 11 (same signs)</p><p>5. – 8 + 6 = – 2 (different signs) 6. – 9 – (+6) = – 9 – 6 = -15 (same signs)</p><p>7. 4 + 10 = 14 (same signs) 8. 7 – 3 = 4 (different signs)</p><p>9. – 5 – (– 3 ) = – 5 + 3 = – 2 (different signs) 10. – 4 – 13 = – 17 (same signs) </p>