How are adding integers and subtracting integers related? Work with a partner. Use integer counters to find 4 2. Remove 2 positive counters.

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1 . How are adding integers and subtracting integers related? ACTIVITY: Work with a partner. Use integer counters to find 4. Start with 4 positive counters. Remove positive counters. What is the total number of counters? So, 4 =. 4 4 ACTIVITY: Adding Integers Work with a partner. Use integer counters to find 4 + ( ). Combine 4 positive counters and negative counters. Remove any zero pairs. What is the total number of counters? 4 4 () COMMON CORE Integers In this lesson, you will subtract integers. solve real-life problems. Learning Standards 7.NS.c 7.NS.d 7.NS. So, 4 + ( ) =. ACTIVITY: Work with a partner. Use a number line to find. Then move unit left to end at 4. Subtract. Start at 0. Move units to the left So, =. 4 Chapter Integers

2 Math Practice Make Sense of Quantities What integers will you use in your addition expression? 4 ACTIVITY: Adding Integers Work with a partner. Write the addition expression shown. Then find the sum. Then move unit left to end at 4. Add. Start at 0. Move units to the left Inductive Reasoning Work with a partner. Use integer counters or a number line to complete the table. Exercise Operation: Add or Subtract Answer Subtract ( ) ( ) ( 8) ( ). 6 ( ) () 5. 5 ( ) IN YOUR OWN WORDS How are adding integers and subtracting integers related? 8. STRUCTURE Write a general rule for subtracting integers. 9. Use a number line to find the value of the expression What property can you use to make your calculation easier? Explain. Use what you learned about subtracting integers to complete Exercises 8 5 on page 8. Section. 5

3 . Lesson Lesson Tutorials Words To subtract an integer, add its opposite. Numbers 4 = + ( 4) = Subtract Add opposites (4) same answer EXAMPLE a. Find. = + ( ) Add the opposite of. = 9 Add. The difference is 9. b. Find 8 ( ). 8 ( ) = 8 + Add the opposite of. = 5 Add. The difference is 5. c. Find 5 ( 4). 5 ( 4) = Add the opposite of 4. = 9 Add. The difference is 9. Exercises 8 Subtract ( 8) 6. ( ) 6 Chapter Integers

4 EXAMPLE Evaluate 7 ( ) 4. 7 ( ) 4 = Add the opposite of. = 5 4 Add 7 and. = 5 + ( 4) Add the opposite of 4. = 9 Add. So, 7 ( ) 4 = 9. Exercises 7 Evaluate the expression ( 5) 0. 8 ( 6) 0. 5 ( 0) EXAMPLE Real-Life Application Which continent has the greater range of elevations? North America Africa Highest Elevation 698 m 5895 m Lowest Elevation 86 m 55 m To find the range of elevations for each continent, subtract the lowest elevation from the highest elevation. North America range 698 (86) m Africa range 5895 (55) m Because 684 is greater than 6050, North America has the greater range of elevations.. The highest elevation in Mexico is 5700 meters, on Pico de Orizaba. The lowest elevation in Mexico is 0 meters, in Laguna Salada. Find the range of elevations in Mexico. Section. 7

5 . Exercises Help with Homework. WRITING How do you subtract one integer from another?. OPEN-ENDED Write two integers that are opposites.. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. Find the difference of and. What is less than? How much less is than? Subtract from. MATCHING Match the subtraction expression with the corresponding addition expression ( 5) ( 5) A B. 9 + ( 5) C. 9 + ( 5) D (-6)= +(-)= 4+(-9)= 9+(-)= Subtract ( 5) 0. 6 ( 7) ( ) ( ) 8. 9 ( ) 9. 7 ( 8) 0. 6 ( 6). 0. ( 6) ERROR ANALYSIS Describe and correct the error in finding the difference 7 ( ). 7 ( ) = 7 + ( ) = 5 5. SWIMMING POOL The floor of the shallow end of a swimming pool is at feet. The floor of the deep end is 9 feet deeper. Which expression can be used to find the depth of the deep end? SHARKS A shark is at 80 feet. It swims up and jumps out of the water to a height of 5 feet. Write a subtraction expression for the vertical distance the shark travels. Evaluate the expression ( ) 9. ( 5) ( 8) ( ) 8 Chapter Integers

6 MENTAL MATH Use mental math to solve the equation.. m 5 = 9 4. w ( ) = c = 9 ALGEBRA Evaluate the expression when k =, m = 6, and n = n 7. m ( 8) k n 9. m k 40. PLATFORM DIVING The figure shows a diver diving from a platform. The diver reaches a depth of 4 meters. What is the change in elevation of the diver? 4. OPEN-ENDED Write two different pairs of negative integers, x and y, that make the statement x y = true. m 4. TEMPERATURE The table shows the record monthly high and low temperatures for a city in Alaska. Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec High ( F) Low ( F) a. Find the range of temperatures for each month. b. What are the all-time high and all-time low temperatures? c. What is the range of the temperatures in part (b)? REASONING Tell whether the difference between the two integers is always, sometimes, or never positive. Explain your reasoning. 4. two positive integers 44. two negative integers 45. a positive integer and a negative integer 46. a negative integer and a positive integer For what values of a and b is the statement true? 47. a b = b a 48. a + b = a + b 49. a b = a b Add. (Section.) ( 5) + ( 5) + ( 5) ( 9) + ( 9) + ( 9) + ( 9) Multiply. (Skills Review Handbook) MULTIPLE CHOICE Which value of n makes the value of the expression 4n + a composite number? (Skills Review Handbook) A B C D 4 Section. 9

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