6th Grade Math Textbook, Fundamentals

Remember:

Commutative Property of Addition

abba

Associative Property of Addition

a(bc) (ab) c

Distributive Property of Multiplication over Addition

a(bc) abac

Distributive Property of Multiplication over Subtraction

a(bc) abac

 &KDSWHU

14-3

2 x 24 x 5

2 x 4 x 5  26 x 7

Write each addend as a polynomial.

Let xthe price of a single long-lasting candle.

2 x 2

4 x 5 This polynomial represents the second

discount: Buy 4 long-lasting candles

for $5 less than the regular price.

This polynomial represents the first

discount: Buy 2 long-lasting candles

for $2 less than the regular price.

Model each addend with algebra tiles.

So the polynomial 6x7 represents the cost of the 6 candles.

Write the polynomial for the resulting

model.

Rearrange tiles to combine like terms.

The properties of operations on whole

numbers, integers, and rational numbers

are also true for operations on algebraic

expressions. In accordance with the

Commutative and Associative Properties

of Addition, the tiles can be arranged

so that like tiles can be grouped together.

Steps 3 and 4 above, in which the like

terms 2xand 4xare being combined,

involve the Distributive Property

of Multiplication over Addition.

2 x 4 xx(2 4)

x• 6 or 6x

Add Polynomials

Objective To model addition of polynomials with algebra tiles • To add polynomials algebraically

Claire’s Candles is having a sale: You can buy 2

long-lasting candles for $2 less than the regular price

and 4 long-lasting candles for $5 less than the

regular price. Suppose you buy 6 candles, and you

receive both discounts. What polynomial could you

use to represent the total cost of the candles?

To find the polynomial, first write the polynomial

that represents the cost when each discount is taken.