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 positive.

the answer will be negative.

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

When multiplyingIntegers, cover the Two signs you are using

Ex.: 5 (-3)

What sign is left uncovered?Negative, - That is the sign of The answer= -15

Choral Response

Division

Good News: It’s not any different!

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 What’s The

Rule?

DifferentSigns

NegativeAnswer

-24

2. -2 * -61

SameSigns

PositiveAnswer

122

3. (-3)(6)(1)

Just

tak

eTw

o at

a t

ime

(-18)(1) -18

4. 6 ÷ (-3)

-2

5. - (20/-5) - (-4)

4

6.

408

6

68

Start inside ( ) first

Examples

Example 1(-35)(245)= -8,575

Example 2-9(12)= -108

Example 37(-6)(-12)= (-42)(-12)= 504

Example 4(6)(-2)(13)= (-12)(13)= -156

Examples

Example 5112 (-4)= -28

Example 6-56 -2= 28

Example 7-216 (-18)= 12

Example 848 (-6)= -8

7. At midnight the temperature is 8°C. If the temperature rises 4°C per hour, what is the temperature at 6 am?

How longIs it fromMidnightto 6 am?

How muchdoes the

temperaturerise each

hour?

6 hours

+4 degrees

(6 hours)(4 degrees per hour)

= 24 degrees

8° + 24° = 32°C

Add this tothe original temp.

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.

What

does This m

ean?

Multiply

(5 steps) (11 feet)

(55 feet)

5 * 11 = 55

Integer Practice 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 = -93 + -5 = -27 + 2 = 9-4 - 3 = -4 + -3 = -72 - 8 = 2 + -8 = -67 - (-3) = 7 + 3 = 10-3 - (-5) = -3 + 5 = 2

3 • -4 = -12-7 • -2 = 148 • 3 = 24-9 • 2 = -1830 ÷ -2 = -15-24 ÷ -6 = 4-4 ÷ 2 = -214 ÷ 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