5.1. Expressions

5.1. Expressions

Chapter 5: Equation and Inequalities

Student Learning Objectives

In the end of this handout, we expect you to:

1. able to assess whether two mathematical expressions have the same value

2. able to create simple mathematical models

3. able to simplify mathematical expressions

Pre-KBM

Let's check your readiness to learn!!

Fill in the Blanks

When we combine numbers or variables using mathematical operations, we form a mathematical ...

Multiple Choice

Which one of the following form is an expression?

• 3 + a - 5

• a + 5 = 10

Drag and Drop

A ​

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is a product of a number and a ​

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raised to some power.

We say that the number in a term is the ​

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of the power of the variable. For example, in the expression 6x + 3y , the terms are 6x and 3y , the coefficient of x is 6, and the coefficient y of is 3.

A number by itself is a term as well, so in the expression 3x + 7 , both 3x and 7 are terms.

A term that is just a number by itself is called a ​

Placeholder

Drag these tiles and drop them in the correct blank above

term

variable

coefficient

constant

expression

letter

Expressions

Multiple Select

$$5x^2-3x+2y-6$$
Checklist the following box that are true ...

• The expression has 4 terms

• 6 is the constant

• The coefficient of variable x is -3

• The expression has 3 terms

• -6 is the constant

Equivalencies

Multiple Choice

Write the expression using EXPONENTS

$$r\times r\times r\times r$$  

• $$r^4$$  

• $$4r$$  

• $$r+4$$  

• $$r^2$$  

Multiple Choice

Write the expression using EXPONENTS.

$$2\times d\times d\times d$$  

• $$d^2$$  

• $$d^3$$  

• $$2d^3$$  

• $$2+d^3$$  

Problems 1

​Solutions 1

Multiple Choice

The expression $$\frac{-3x+6}{3}$$ is equivalent to ...
Remember: $$\frac{4+8}{2}=\frac{4}{2}+\frac{8}{2}$$

• $$-x+2$$

• $$-3x+2$$

• $$x+2$$

Multiple Choice

Are the expressions $$(2/x)/4$$ and $$2/(x/4)$$ equivalent?

• YES

• NO

Problems 2

​Solutions 2

Math Response

Jeremy has 5 packs and 6 pcs of gum and Shannon has 6 packs and 8 pcs of gum. Suppose each pack of gum has $$x$$ pieces of gum. Write an expression for the number of pieces of gum Jeremy has.

Type answer here

Correct Answer: 5x+6

Deg^°

Rad

Math Response

Jeremy has 5 packs and 6 pcs of gum and Shannon has 6 packs and 8 pcs of gum. Suppose each pack of gum has $$x$$ pieces of gum. Write an expression for the number of pieces of gum Shannon has.

Type answer here

Correct Answer: 6x+8

Deg^°

Rad

Multiple Choice

Mitch has 35 more bouncy balls than Rudy. Rudy has b bouncy balls. Choose the expression that shows how many bouncy balls Mitch has.

• 35 - b

• b

• 35

• b + 35

Multiple Choice

A cell phone company charges $40 per month plus a $35 activation fee. What is the expression for the total cost for m months?

• 40 - 35m

• 40m - 35

• 40m + 35

• 40 + 35

Simplify

How to simplify the expressions?

Fill in the Blanks

Simplify the following expression:

$2r+3r-7r$

Fill in the Blanks

Simplify the following expression:

$3y-2y+7y-9y$

Fill in the Blanks

Simplify the following expression:

$6-t+3t-4+2t$

(NOTE: e.g 2x+3 or 3-2x, DON'T use space to separate between terms)

Fill in the Blanks

Simplify the following expression:

$7(x-2)+5(2x+3)$

(NOTE: e.g 2x+3 or 3-2x, DON'T use space to separate between terms)

Fill in the Blanks

Simplify the following expression:

$4(3a-4)-6(2a-1)$

(NOTE: e.g 2x+3 or 3-2x, DON'T use space to separate between terms)

Simplify

How to simplify the expressions? (2)

Math Response

Simplify the following expression:

$$-5z+\frac{3}{2}-2+3z$$

Type answer here

Correct Answer: -2z-\frac{1}{2}

Deg^°

Rad

Math Response

Simplify the following expression:

$$-\frac{x}{2}+x+\frac{x}{3}$$

Type answer here

Correct Answer: \frac{5}{6}x

Deg^°

Rad

Math Response

Simplify the following expression:

$$5-\frac{5}{2}t+7-\frac{7}{3}t$$

Type answer here

Correct Answer: -\frac{29}{6}t+12

Deg^°

Rad

Fill in the Blanks

Simplify the following expression:

$\frac{1}{2}(6-4y)+\frac{3}{2}(6y+4)$

(NOTE: e.g 2x+3 or 3-2x, DON'T use space to separate between terms)

Fill in the Blanks

Simplify the following expression:

$-3(1+3t)-(t+3)(1+4)$

(NOTE: e.g 2x+3 or 3-2x, DON'T use space to separate between terms)