Equivalent Expressions

Geometry applications

100

Generate 2 equivalent expressions that could be used to find the perimeter of any rectangle. 

l + l + w + w

2(l) + 2(w)

2 (l+w)

200

Chaplin says that the expression 4y-2 + 2y could be used to determine the perimeter of the rectangle. Do you agree? If yes, generate an equivalent expression that could also be used. If no, explain the mistake that was made and how he could change his expression so that it is correct.

Chaplin is incorrect. His expression only measures two of the four sides. He could change his expression the following ways.

1) Multiply his entire expression by 2.       2 (4y - 2 + 2y)

2) Add the length and width twice.  (4y - 2) + (4y - 2) + (2y) + (2y)

3) Multiply the length by 2 and the width by 2.   2(4y-2) + 2(2y)

300

Generate 3 expressions that could be used to find the perimeter of the rectangle below. Then, simplify each expression to prove they are equivalent. 

(x + 8) + (x + 8) + (1/3x +2) + (1/3x + 2)

2 2/3x + 20

2 ((x+8)+(1/3x + 2))

2 2/3x + 20

2(x + 8) + 2(1/3x + 2)

2 2/3x + 20

Percent Applications

100

1) .45

2) .67

3) .6

4) .03

200

A student received a coupon for 17% off the total purchase price at a clothing store. Let b represent the original price of the purchase. Use the expression b - 0.17b for the new price of the purchase. Write an equivalent expression by combining like terms.

.83b

300

A new box of pasta claims that it has 25% more than the usual box. Generate 2 equivalent expressions that represent the amount of pasta, p, in the new box.

p + .25p

1.25p

Simplifying

100

-3x + 5 - 1/3x -10

- 3 1/3x -5

200

1/2 (4x - 6) - (x - 3)

x

300

Factor the expression using the greatest common factor.

18m - 12r + 36

6 (3m - 2r + 6)