1 / 5

# Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c - PowerPoint PPT Presentation

Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c and pictorially (rectangular array area model):. b. c. a. a × b. a × c. An example: 6 x 13 using your mental math skills . . . symbolically:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c' - claral

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Recall the distributive property of multiplication over addition . . .

symbolically:

a × (b + c) = a × b + a × c

and pictorially (rectangular array area model):

b

c

a

a × b

a × c

An example: addition . . . 6 x 13

using your mental math skills . . .

symbolically:

6 × (10 + 3) = 6 × 10 + 6 × 3

and pictorially (rectangular array area model):

10

3

6

6 × 10

6 × 3

200 addition . . .

30

40

+ 6

276

20

3

What about 12 x 23?

Mental math skills?

(10+2)(20+3) = 10×20 + 10×3 + 2×20 + 2×3

10

10 × 20

10 × 3

2

2 × 20

2×3

c addition . . .

d

And now for multiplying binomials

(a+b)×(c+d) = a×(c+d) + b×(c+d)

= a×c + a×d + b×c + b×d

a

a × c

a × d

b

b × c

b×d

We note that the product of the two binomials has four terms – each of these is a partial product. We multiply each term of the first binomial by each term of the second binomial to get the four partial products.

F + O + I + L

( a + b )( c + d ) = ac + ad + bc + bd

Product of the FIRST terms of the binomials

Product of the OUTSIDE terms of the binomials

Product of the INSIDE terms of the binomials

Product of the LAST terms of the binomials

Because this product is composed of the

First, Outside, Inside, and Last terms,

this pattern is often referred to as FOIL method of multiplying two binomials. Note that each of these four partial products represents the area of one of the four rectangles making up the large rectangle.