Module 5 - Numerical & Algebraic Expressions

Powers & Exponents

100

Write using an exponent: 

1/4 x 1/4 x 1/4 x 1/4 x 1/4

(1/4)⁵

200

Write using an exponent:

p x p x p x p

p⁴

300

Evaluate:   7³

343

400

Write in expanded form:  (3/4)³

3/4 x 3/4 x 3/4

500

True or False:

4x4x4x4x4x4  =  6x4 + 4x4

False

Writing Expressions

100

Write as a numerical expression:

fourteen doubled 

14 x 2

200

Write as a numerical expression:

seven decreased by three

7 - 3

300

Evaluate the following:

2^{3 +} 3 x 4² - 10 + 6

52

400

Evaluate the following:

5(3³ + 10) + (13 + 2 x 5²)

158

500

Are the following expressions equivalent?

5(2 + 3) + 4²                       10 + 3 + 5 + 16

No

Algebraic Expressions

100

How many terms are there in this expression?

3s + 2s² - 5 + 6s³ + 10 - 3 + s

7 terms

200

Write as an algebraic expression:

a number q tripled and increased by 7

3q + 7

300

Are the following expressions equivalent?

8x + 3 + 2x + 4 - 7x                   3x + 8

No

400

What is the vocabulary word for each item in an algebraic expression?

2x + 5

2 = 

x = 

5 = 

2 = coefficient

x = variable

5 = constant

500

Evaluate when x = 1/3   y = 4   z = 5

6(x + y) + 10z - z²

51

Factors & Multiples

100

Factor the following expression using the GCF:

56 + 72

8(7 + 9)

200

Talia has 12 roses and 15 daisies. She wants to arrange the flowers into equal size bouquets. Each bouquet should have the same number of roses and daisies in it. What is the greatest number bouquets made? 

3 bouquets 

300

There are two subway lines that are both at the station right now. Subway A arrives every 11 minutes and  Subway B arrives every 7 minutes. In how many minutes will both subways be at the station again?  

77 minutes

400

Use the GCF to factor 48x + 60

12(4x + 5)

500

Gretchen has 24 apples and 32 pears. She wants to arrange the fruit into equal size groups. Each group should have the same number of apples and the same number of pears in it. What is the greatest number of groups she can create? And how many of each fruit will be in each group?

8 groups, 3 apples and 4 pears in each group

Simplifying Expressions

100

Simplify the following expression by combining like terms:

3s + 2s² - 5 + 6s³ + 10 - 3 + s

6s³ + 2s² + 4s + 2

200

Use the distributive property to simplify the following expression:

4(x + 3 + y)

4x + 12 + 4y

300

Simplify:

3x + 10 + 6x³ + 7(3x + 8)

6x³ + 24x + 66

400

Simplify:

8(1/2x + 4) + 3x + 5(2x + 3²)

17x + 17

500

Are the following expressions equivalent?

1.5x + 3x² + 2.5 + 0.5x²    

x + 1.5x² + 2 + 0.5x + 2x² + 0.5

Yes