Extended Algebra Extended Algebra Lesson 3Lesson 3

Math 7Math 7

Distributive PropertyDistributive Property

• The distributive property is illustrated below:

2(x + y) = 2x + 2y

• Think about what it means to have 2 next to a set of parenthesis.

Distributive PropertyDistributive Property

• What does it mean to have the 2 there?• MULTIPLY 2 BY THE MEMBERS OF THE

PARENTHESIS

• Picture it as “2 groups of (x + y)”

Just think of regular multiplication:

3(4) means 3 times 4 (which is 12)….but it

just means you have 3 groups of 4

4 + 4 + 4 = 12

Groups of….Groups of….

• 2 groups of (x + y) means:

x + y + x + y which is 2x + 2y

• Instead of this, you can just “distribute” the 2 all the way through the members of the parenthesis (by multiplying).

2(x + y) means 2x + 2y

DistributeDistribute

• 5(m + n) = __________

• 9(a + b) = __________

• 7(x + 4) = __________

• 8(2w – 5) = _________

• 4(3x + 9) = _________

• 6(-2x – 7) = _________

FRACTIONS AND MIXED FRACTIONS AND MIXED NUMBERSNUMBERS

• As always, these will show up…no need to panic

• It is just multiplying, so you multiply top by top and bottom by bottom, then simplify

• Ex.

DISTRIBUTING WITH DISTRIBUTING WITH NEGATIVESNEGATIVES

• When distributing a negative, you have to pay close attention to signs!

• -5(2x + 7)

• -3(-4x + 9)

• -2(8x – 5)

• -(6x – 9)

• -(-8x + 3)

• You can see these with fractions too!

WORD PROBLEMSWORD PROBLEMS

• A rectangular kitchen has a width of 10 feet and a length of 12 feet. Jim is going to expand the length of the kitchen, but is unsure how many feet he is going to expand it.

• Write an expression that would represent the area of the newly expanded kitchen.

• A picture should help.

JIM’S KITCHENJIM’S KITCHEN

• A rectangular kitchen has a width of 10 feet and a length of 12 feet. Jim is going to expand the length of the kitchen, but is unsure how many feet he is going to expand it.

• Write an expression that would represent the area newly expanded kitchen.

• Draw a picture of his current rectangular kitchen:

• Add on to the length.• How do you find the area of the “new” kitchen?• What does each term of the expression represent?

MARY’S GARDENMARY’S GARDEN

• Mary has a garden that is 8 feet wide and 11 feet long. She wants to add more pepper plants to her garden, which would make the garden longer. She is unsure of how much longer she wants to make it.

• Write an expression that will represent the area of her newly expanded garden.

• What does each term of the expression represent?

Distribute, Regroup, CombineDistribute, Regroup, Combine

• 3(x – 9) + 4x + 13

• 7x + 5(x + 7) – 15

• 8x – 12 – 9(2x – 5)

Distribute, Regroup, CombineDistribute, Regroup, Combine

• 3(-2x + 7) – 11 + 7x

• 5p – 9x + 4(-4x – 3) + 2(3p + 11)

• 7x + 3 – 2(3x – 9) – 12x + 35