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INTEGERS AND MULTIPLICATION. The University of Texas at Dallas. MULTIPLICATION. Red and yellow tiles can be used to model multiplication. Remember that multiplication can be described as repeated addition. So 2 x 3 = ?. 2 groups of 3 tiles = 6 tiles. The University of Texas at Dallas.

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Integers and multiplication

INTEGERS AND MULTIPLICATION

The University of Texas at Dallas


Multiplication
MULTIPLICATION

  • Red and yellow tiles can be used to model multiplication.

  • Remember that multiplication can be described as repeated addition.

  • So 2 x 3 = ?

2 groups of 3 tiles = 6 tiles

The University of Texas at Dallas


Multiplication1
MULTIPLICATION

  • 2 x -3 means 2 groups of -3

2 x -3 = -6

The University of Texas at Dallas


Multiplication2
MULTIPLICATION

  • Since 2 x 3 = 6 and 3 x 2 = 6, does it make sense that -3 x 2 = -6 ?

  • -3 x 2 = -6 is true.

  • +2 x -3 = -6 and -3 x +2 = -6 belong to a fact family:

  • Write the fact family on comp book page_____

+2 x -3 = -6

-3 x +2 = -6

-6 ÷ +2 = -3

-6 ÷-3 = +2

The University of Texas at Dallas


Multiplication3
MULTIPLICATION

  • Use your tiles to model each multiplication problem.

  • +2 x +4 = ?

ANSWER

2 groups of +4

+2 x +4 = +8

The University of Texas at Dallas


Multiplication4
MULTIPLICATION

  • +3 x -3 = ?

ANSWER

3 groups of -3

+3 x -3 = -9

The University of Texas at Dallas


Multiplication5
MULTIPLICATION

  • -2 x +4 = ?

ANSWER

4 groups of -2

-2 x +4 = -8

  • Use the fact family for

  • -2 x +4 = ?  We can’t show -2 groups of +4

  • +4 x -2 = ? we can show 4 groups of -2

The University of Texas at Dallas


Multiplication6
MULTIPLICATION

  • +1, -1 are opposites

    the products are opposite

  • Since +2 and -2 are opposites of each other,

  • +2 x -3 and -2 x -3 have opposite products.

+1 x +3 = +3

-1 x +3 = -3

The University of Texas at Dallas


Multiplication7
MULTIPLICATION

  • To model -2 x -3 use 2 groups of the opposite of -3

-2 x -3 = +6

The University of Texas at Dallas


Multiplication8
MULTIPLICATION

  • Use tiles to illustrate -3 x -4 =?

ANSWER

3 groups of +4 (the opposite of -4)

-3 x -4 = +12

The University of Texas at Dallas


What do you notice about multiplying integers

What do you notice about multiplying integers???

On comp book page ____ write a few sentences about what you noticed.


Integers and division

INTEGERS AND DIVISION

The University of Texas at Dallas


Division
DIVISION

  • Use tiles to model +12 ÷ +3 = ?

4 yellow tiles in each group.

Divide 12 yellow tiles into 3 equal groups

+12 ÷+3 = +4

The University of Texas at Dallas


Division1
DIVISION

  • Use tiles to model -15 ÷ +5 =?

Divide -15 into 5 equal groups

-15 ÷+5 = -3

The University of Texas at Dallas


Division2
DIVISION

  • Write the fact family

  • -4 x +2 = -8

  • Compare your answer.

  • +2 x -4 = -8

  • -8 ÷ +2 = -4

  • -8 ÷ -4 = +2

The University of Texas at Dallas


Division3
DIVISION

-12 divided into 6 equal groups

7) -12 ÷+6

= -2

8) -8 ÷+2

= -4

-8 divided into 2 equal groups

The University of Texas at Dallas


What do you notice about dividing integers

What do you notice about dividing integers???

On comp book page ____ write a few sentences about what you noticed.


Summary on comp book page

SUMMARYOn comp book page

The product or quotient of two integers with different signs is negative.

The product or quotient of two integers with the same sign is positive.