VARIABLES, EXPRESSIONS AND THE DISTRIBUTIVE PROPERTYAugust 26, 2013

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1. 3(4 + 12)

2. -2(5 + 8)

3. -7(9 – (-2))

4. 8(-3 + 6)

5. 10(5 + (-1))

Solutions:

1. 3(16) = 482. -2(13) = -10 + -16 = -263. -7(11) = -774. 8(3) = 245. 10(4) = 40

VOCAB WORDS FOR CHAPTER 1 Search definitions and write each one on a post-it.

Counterexample

Deductive Reasoning

Distributive Property

VARIABLES AND EXPRESSIONS A VARIABLE is a symbol, usually a letter, that represents one or more numbers.

Examples: x, a,

A ALGEBRAIC EXPRESSION is a mathematical phrase that can include numbers, variables and operation symbols.

Examples: x + 6

n – (4n)

DISTRIBUTIVE PROPERTY

DISTRIBUTIVE PROPERTY: WHAT YOU ALREADY MAY KNOW For every real number a, b, and c,

a ( b + c ) = ab + ac ( b + c ) a = ba + ca

a ( b – c ) = ab – ac ( b – c ) a = ba – ca

DISTRIBUTIVE PROPERTY WITH GENERIC RECTANGLES Area Model of the Distributive Propertya ( b + c )

b + c

a Area = ab

Area = ac

The area of the whole rectangle is the sum of the areas of the two smaller rectangles!

ab + ac

Does it really matter where we put a and b+c ?

Yes, it does matter! But why do you think that is?

b+c goes on the longer side of the rectangle

because it is a sum of two lengths!

DISTRIBUTIVE PROPERTY: NUMERICAL EXPRESSIONSUse the Distributive Property and generic rectangles to multiply:

7 (98)

7

90 + 8

630 56

The areas of the smaller rectangles inside:7(90) = 6307(8) = 56

The total area of the whole rectangle:Area = 630 + 56 = 686

7(98) = 7(90 + 8)

7(90) + 7(8) =

630 + 56 =

686

Rewrite 98 as a sum:

90 + 8

Then, find the areas of the two smaller rectangles.

DISTRIBUTIVE PROPERTY: VARIABLE EXPRESSIONSUse the Distributive Property and generic rectangles to multiply:

2(5x + 3)

It works the same way with

variables!! BUT no need to rewrite as a sum because it already IS written

as a sum!

2

5x + 3

The areas of the smaller rectangles inside:2(5x) = 10x2(3) = 6

The total area of the whole rectangle:Area = 10x + 6

10x 6

Why is it 10x + 6 and not

16x?

2(5x + 3) =

2(5x) + 2(3) =

10x + 6