Multiplying & Dividing Integers

Multiplying and Dividing Integers 6.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Student Objectives I can multiply and divide integers. I can use multiplication and division of integers in real life situations.

State the rule for multiplying and dividing integers…. If the signs are the same, If the signs are different, the answer will be negative. the answer will be positive.

Here’s a way I can Remember! To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use: Mr. Multiplivision

= -15 What sign is left uncovered? When multiplying Integers, cover the Two signs you are using Choral Response What sign is left uncovered? Ex.: 5 (-3) Negative, - That is the sign of The answer = -15

Division It’s not any different! Good News: Ex.: -48  (-4) = + 12

Multiply Integer Rules Negative • Negative = Positive Positive • Positive = Positive Positive • Negative = Negative Negative • Positive = Negative

Divide Integers Rules Positive  Positive = Positive Negative  Negative = Positive Positive  Negative = Negative Negative  Positive = Negative

We can also say…. If the signs are the SAME the answer is positive If the signs are DIFFERENT the answer is negative

What if I have more that 2 Integers? If there are an even number of negative signs, the answer is positive. If there are an odd number of negative signs, the answer is negative.

1. -8 * 3 4. 6 ÷ (-3) -24 -2 2. -2 * -61 5. - (20/-5) 122 - (-4) 4 Different Signs Negative Answer What’s The Rule? 1. -8 * 3 4. 6 ÷ (-3) -24 -2 Start inside ( ) first 2. -2 * -61 5. - (20/-5) 122 - (-4) Same Signs Positive Answer 4 3. (-3)(6)(1) (-18)(1) 6. -18 Two at a time Just take 68

Examples Example 1 (-35)(245) = -8,575 Example 2 -9(12) = -108

Examples Example 5 112  (-4) = -28 Example 6 -56  -2 = 28

7. At midnight the temperature is 8°C 7. At midnight the temperature is 8°C. If the temperature rises 4°C per hour, what is the temperature at 6 am? How long Is it from Midnight to 6 am? How much does the temperature rise each hour? 6 hours +4 degrees (6 hours)(4 degrees per hour) Add this to the original temp. = 24 degrees 8° + 24° = 32°C

(5 steps) (11 feet) (55 feet) 5 * 11 = 55 8. A deep-sea diver must move up or down in the water in short steps in order to avoid getting a physical condition called the bends. Suppose a diver moves up to the surface in five steps of 11 feet. Represent her total movements as a product of integers, and find the product. Multiply What does This mean? (5 steps) (11 feet) (55 feet) 5 * 11 = 55

Integer Practice -5 + - 4 = 3 + -5 = 7 + 2 = -4 - 3 = 2 - 8 = Complete the following questions to practice adding, subtracting, multiplying and dividing integers. -5 + - 4 = 3 + -5 = 7 + 2 = -4 - 3 = 2 - 8 = 7 - (-3) = -3 - (-5) = 3 • -4 = -7 • -2 = 8 • 3 = -9 • 2 = 30 ÷ -2 = -24 ÷ -6 = -4 ÷ 2 = 14 ÷ 7 =

Check your Answers -5 + - 4 = -9 3 + -5 = -2 7 + 2 = 9 -4 - 3 = -4 + -3 = -7 2 - 8 = 2 + -8 = -6 7 - (-3) = 7 + 3 = 10 -3 - (-5) = -3 + 5 = 2 3 • -4 = -12 -7 • -2 = 14 8 • 3 = 24 -9 • 2 = -18 30 ÷ -2 = -15 -24 ÷ -6 = 4 -4 ÷ 2 = -2 14 ÷ 7 = 2

Multiplying and Dividing Integers Classwork: Try these educational games to help you practice multiplication and division with integers Integer Warp (Multiplying Integers) & Grade or No Grade? Homework: HW: Reteaching 10.4 & 10.5 HO