Multiply and Divide Integers
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- Robert Cornelius Collins
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1 Domain 1 Lesson 8 Multiply and Divide Integers Common Core Standards: 7.NS.2.a, 7.NS.2.b, 7.NS.2.c, 7.NS.3 Getting the Idea Use these rules to multiply two integers. Rules for Multiplying Two Integers Multiply the two integers as positive numbers. Then find the sign of the product using these rules. If the signs of the two numbers are the same, the product is positive. If the signs of the two numbers are different, the product is negative. Example 1 Multiply. (225)? (23) 5 Step 1 Step 2 Apply the rules for multiplying two integers. Multiply the two integers as positive numbers. 25? Find the sign of the product. The signs of the two numbers are the same, so the product is positive. (2)? (2) 5 (1) The product is 175. Solution (225)? (23) 5 75 Example 2 Marshall has $12 automatically deducted from his checking account each month as a charitable donation. What is the total amount deducted from his account after 1 year? Step 1 Write an expression for the problem. Then solve. Write an expression to represent the problem. The amount deducted each month can be represented by 2$12. There are 12 months in 1 year. So, find 2$12?
2 Step 2 Step 3 Multiply the two integers as positive numbers. 12? Find the sign of the product. The signs of the two numbers are different, so the product is negative. (2)? (1) 5 (2) The product is Solution The total amount deducted from Marshall s account is $144. The distributive property applies the rules for multiplying and adding signed numbers. The work below shows that 2(a 1 b) 5 2a 2 b. 2(a 1 b) 5 21(a 1 b) 5 21? (a 1 b) Apply the distributive property. 5 21? (a) 1 21? (b) Multiply each addend by a 1 (2b) Apply the rules for adding integers. 5 2a 2 b Example 3 Write 2(a 2 b) as a sum. Use the distributive property. Step 1 Rewrite the expression to show the multiplication. 2(a 2 b) 5 21? (a 2 b) Step 2 Apply the distributive property. 21? (a 2 b) 5 21? (a) 2 (21)? (b) Step 3 Multiply each addend by ? (a) 2 (21)? (b) 5 2a 2 (2b) Step 4 Apply the rules for subtracting two integers. The additive inverse of 2b is b. 2a 2 (2b) 5 2a 1 b Solution 2(a 2 b) 5 2a 1 b 77
3 Use these rules to divide two integers. Rules for Dividing Two Integers Divide the two integers as positive numbers. Then find the sign of the quotient using these rules. If the signs of the two numbers are the same, the quotient is positive. If the signs of the two numbers are different, the quotient is negative. All integers can be divided as long as the divisor is not zero. Example 4 Divide. (232) 4 (28) 5 Step 1 Step 2 Apply the rules for dividing two integers. Divide the two integers as positive numbers Find the sign of the quotient. The signs of the two numbers are the same, so the quotient is positive. (2) 4 (2) 5 (1) The quotient is 1 4. Solution (232) 4 (28) Domain 1: The Number System
4 Lesson 8: Multiply and Divide Integers Example 5 The temperature fell 188F in 3 hours. The temperature fell at the same rate every hour. How much did the temperature change each hour? Step 1 Step 2 Step 3 Solution Write an expression for the problem. Then solve. Write an expression to represent the problem. The temperature changed 2188F. (218) or represents the temperature change per hour. 3 Divide the two integers as positive numbers Find the sign of the product. The signs of the two numbers are different, so the product is negative. (2) 4 (1) 5 (2) The quotient is 268. The temperature changed 268F each hour. Instead of using a multiplication sign, sometimes multiplication is shown by putting the factors in parentheses. For example, (23)(2) Coached Example What is the value of (25)(4)(21)(22)? Will the product of the first two integers be positive or negative? 25? 4 5 When you multiply this product by the third integer, 21, will the product be positive or negative? Multiply the product of the first two integers by the third integer, 21.? (21) 5 When you multiply this product by the fourth integer, 22, will the product be positive or negative?? (22) 5 The value of (25)(4)(21)(22) is. 79
5 Lesson Practice Choose the correct answer. 1. Multiply. 29? (25) 5 A B C. 105 D Divide A. 215 B. 25 C. 5 D Divide. 6. What is the value of (23)(5)(24)? (27) 5 A. 254 B. 245 C. 45 D Multiply. 272? (26) 5 A B C. 432 D The temperature fell 368F in 9 hours. If the temperature fell at the same rate every hour, which represents the change in temperature each hour? A F B. 2278F C. 248F D. 458F A. 260 B. 212 C. 12 D A shoreline is changing 23 centimeters each year due to erosion. What is the change in the shoreline over 6 years? A. 218 cm B. 29 cm C. 23 cm D. 22 cm 8. The price of a stock rose $2 yesterday. If the stock continues to change at the same rate each day, what will be the total change over 10 days? A. 2$20 B. 2$5 C. $5 D. $20 80 Domain 1: The Number System
6 Lesson 8: Multiply and Divide Integers 9. Evan withdrew a total of $160 from an ATM machine over a 4-day period. He withdrew the same amount of money each day. A. Write an expression to represent the total amount that Evan s account changed each day. B. What integer represents the total amount that Evan s account changed each day? Show your work. 10. Draw a line from each expression to its equivalent value. A B (210) 227 C D (26) 70 81
7 11. Savannah s dog lost 2 pounds each week for 4 weeks. Circle the weight change after 4 weeks. 8 The dog s weight change after 4 weeks was pounds. 12. Is each equation correct? Select True or False. A (26) 5 90 True False B True False C. (22)(6)(27) 5 84 True False D (29) 5 27 True False 13. Evaluate each expression. Write each expression in the correct box ( 3) 24 ( 2) 48 ( 4) Domain 1: The Number System
8 Lesson 8: Multiply and Divide Integers 14. Use numbers from the box to make each equation true (22) (28) A plant grew 4 inches each month for a year. The rate of growth was constant. Circle the amount that the plant had grown after 7 months. 28 The growth of the plant after 7 months was inches. 16. Which expression is equivalent to 26? Circle all that apply. A B C D E (26) 83
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