11 6 Multiplying Dividing Integers Warm Up Problem

11 -6 Multiplying & Dividing Integers Warm Up Problem of the Day Lesson Presentation Course 1

11 -6 Multiplying Integers Warm Up Find each product. 1. 3. 5. 7. Course 1 8 • 4 3 • 9 80 • 6 40 • 90 32 27 480 3, 600 2. 4. 6. 8. 7 • 12 84 6 • 5 30 50 • 6 300 20 • 700 14, 000

Notes on Multiplying and Dividing Integers • Steps – Multiply and Divide as usual. – When there is an even amount of negative signs, the final answer is positive. – When there is an odd amount of negative signs, the final answer is negative.

Examples

11 -6 Multiplying Integers Numbers 3 • 2 – 3 • 2 Words 3 groups of 2 the opposite of 3 groups of 2 Addition 2+2+2 –(2 + 2) Product 6 – 6 Course 1

11 -6 Multiplying Integers Numbers Words Addition Product Course 1 3 • (– 2) – 3 • (– 2) 3 groups of – 2 the opposite of 3 groups of – 2 (– 2) + (– 2) –[(– 2) + (– 2)] – 6 6

11 -7 Dividing Integers Because division is the inverse of multiplication, the rules for dividing integers are the same as the rules for multiplying integers. Dividing Integers If the signs are the same, the product is positive. 24 ÷ 3 = 8 – 6 ÷ (– 3) = 2 If the signs are different, the quotient is negative. – 20 ÷ 5 = – 4 72 ÷ (– 8) = – 9 Zero divided by any integer equals 0. 0 0 __ __ =0 =0 – 11 14 You cannot divide any integer by 0. Course 1

11 -6 Multiplying Integers Additional Example 1: Multiplying Integers Find each product. A. 5 • 2 = 10 Think: 5 groups of 2. B. 4 • (– 5) = – 20 Think: 4 groups of – 5. Remember! To find the opposite of a number, change the sign. The opposite of 6 is – 6. The opposite of – 4 is 4. Course 1

11 -6 Multiplying Integers Additional Example 1: Multiplying Integers Find each product. C. – 3 • 2 = – 6 D. – 2 • (– 4) = 8 Think: the opposite of 2 groups of – 4. Course 1 Think: the opposite of 3 groups of 2.

11 -6 Multiplying Integers Check It Out: Example 1 Find each product. A. 3 • 4 = 12 Think: 3 groups of 4. B. 2 • (– 7) = – 14 Course 1 Think: 2 groups of – 7.

11 -6 Multiplying Integers Check It Out: Example 1 Find each product. C. – 5 • 3 = – 15 Think: the opposite of 5 groups of 3. D. – 4 • (– 6) = 24 Think: the opposite of 4 groups of – 6. Course 1

11 -6 Multiplying Integers MULTIPLYING INTEGERS If the signs are the same, the product is positive. 4 • 3 = 12 – 6 • (– 3) = 18 If the signs are different, the product is negative. – 2 • 5 = – 10 7 • (– 8) = – 56 The product of any number and 0 is 0. 0 Course 1 • 9=0 (– 12) • 0=0

11 -7 Dividing Integers Additional Example 1: Dividing Integers Find each quotient. A. – 30 ÷ 6 Think: What number times 6 equals – 30? – 5 • 6 = – 30, so – 30 ÷ 6 = – 5. B. – 42 ÷ (– 7) Think: What number times – 7 equals – 42? 6 Course 1 • (– 7) = – 42, so – 42 ÷ (– 7) = 6.

11 -6 Multiplying Integers Additional Example 2: Evaluating Integer Expressions Evaluate – 7 x for each value of x. A. x = – 3 – 7 x Write the expression. – 7 • (– 3) Substitute – 3 for x. The signs are the same, so the answer 21 is positive. B. x = 5 – 7 x Write the expression. – 7 • 5 Substitute 5 for x. – 35 The signs are different, Remember! so the answer is negative. – 7 x means – 7 • x. Course 1

11 -6 Multiplying Integers Check It Out: Example 2 Evaluate – 4 y for each value of y. A. y = – 2 – 4 y Write the expression. – 4 • (– 2) Substitute – 2 for y. 8 B. y = 7 – 4 y – 4 • 7 – 28 Course 1 The signs are the same, so the answer is positive. Write the expression. Substitute 7 for y. The signs are different, so the answer is negative.

11 -6 Multiplying Insert Lesson Integers Title Here Lesson Quiz Find each product. 1. 6 • 3. – 9 (4) 24 • (– 2) 18 2. 3 • 4. – 6 (– 2) – 6 • 5 – 30 5. Evaluate 3 y for y = – 7. – 21 6. During a football game, Raymond’s team lost 6 yards on each of 3 plays and gained 8 yards on each of two plays. What integer represents the total change in the team’s position? – 2 Course 1