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9.6 Add and Subtract Negative Mixed Numbers Common Core Standards 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. WARM-UP Evaluate the expressions. 1 1) 2 + 4 1 2) 2 − 4 ⎛ 1⎞ 3) 2 + ⎜ − ⎟ ⎝ 4⎠ 1⎞ ⎛ 4) −2 + ⎜ − ⎟ ⎝ 4⎠ 4) Place the fractions and mixed numbers correctly on the number line. 1 3 1 1 3 1 −2 , −1 , − , ,1 ,2 4 4 4 4 4 4 -3 -2 -1 0 1 2 3 Add and Subtract Negative Mixed Numbers How do we add and subtract negative mixed numbers? 1 1 −5 + 1 = −3 2 2 1 ⎛ 1⎞ −5 − ⎜ −1 ⎟ = −3 2 ⎝ 2⎠ -5 -4 -3 -2 -1 0 1 2 3 4 5 NOTES For negative mixed numbers we need to realize that both parts are negative. In a positive mixed number both parts are positive. 2 4 2 4 −1 + 3 = (−1 + 3) + (− + ) 7 7 7 7 Examples Evaluate the expressions. 2 5 −1 + 6 7 7 1 ⎛ 4⎞ 2 + ⎜ −8 ⎟ 5 ⎝ 5⎠ EXAMPLES Evaluate the expressions. 2 ⎛ 1⎞ −1 + ⎜ −7 ⎟ 5 ⎝ 5⎠ 7 7 −4 + 28 28 NOTES If the whole number and fraction part have different signs we need to regroup. Examples Evaluate the expressions. 3 ⎛ 5⎞ 3 + ⎜ −2 ⎟ 7 ⎝ 7⎠ 3 1 −1 + 4 5 5 NOTES Subtraction is still the same as adding the opposite. Examples Evaluate the expressions. 1 3 3 −4 7 7 1 5 8 −6 9 9 1 4 −7 − 5 5 EXAMPLES Mary has to fit a 20 ¾ inches wide cabinet in a cove that is 30 ¼ inches wide. What is the minimum distance the cabinet can be from the edge? ? EXAMPLES Which mixed number problems are represented below? -5 -4 -3 -2 -1 0 1 2 3 4 5 1 a) − 5 + 4 2 1⎞ ⎛ b) − 5 + ⎜ −4 ⎟ ⎝ 2⎠ 1⎞ ⎛ c) − 5 − ⎜ −4 ⎟ ⎝ 2⎠ EXAMPLES Which mixed number problems are represented below? -5 -4 -3 -2 -1 0 1 2 3 4 5 1 a)2 − 3 2 1 b)2 + ( −3 ) 2 1 c)2 − ( −3 ) 2 PRACTICE Evaluate the expressions. 1 ⎛ 5⎞ −6 + ⎜ −2 ⎟ 8 ⎝ 8⎠ 1 3 3 −2 7 7 PRACTICE Which mixed number problems are represented below? -3 1 a)1 − 2 4 -2 -1 0 1 1 b)1 + ( −2 ) 4 2 3 1 c)1 − ( −2 ) 4 FINAL QUESTION Which mixed number problems are represented below? -3 1 1 a) − 2 + 1 4 4 -2 -1 0 1 1 ⎛ 1⎞ b) − 2 − ⎜ −1 ⎟ 4 ⎝ 4⎠ 2 3 1 ⎛ 1⎞ c) − 2 + ⎜ −1 ⎟ 4 ⎝ 4⎠