Section 1.2 Expressions
Unfortunately math isn’t read the same as English…from left to right.
There is an order that you have to do things.
You may have heard of the acronym, “PEMDAS.”
Please
Excuse
My
Dear
Aunt
Sally
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
But you group Multiplication & Division together.
You also group Addition & Subtraction together.
1) Parenthesis
2) Exponents
3) Multiplication/Division
4) Addition/Subtraction
Example 1) 5 ∙ 4 + 3
Example 2) 5 ∙ (4 + 3)
You Try: 6 ÷ 2 + 5
You Try: 60÷ (2 ∙ 6 + 8)
Example 3) 42 + 5 − 8 ÷ 2 ∙ (3 + 1)
Example 4) 7 + 32 [6 − (3 + 1)]
You Try: 5 − 42 [5 − (2 + 2)]
6+4
Example 5) 8−3
Example 6)
You Try:
2+52 (18÷6)
4−10
32 +42 −(2÷1)+1
3200 +4
You Try: Put grouping symbols in the following expression so that it equals 2.
159 − 81 ÷ 32 + 12
You Try: Put grouping symbols in the following expression so that it equals 10.
720 ÷ 2 + 7 ∙ 23
Section 1.3 Notes Variables
Example: Identify the terms of the following expression: 6x + 8y – 5
Example: Identify the terms of the following expression: 14ab + x
Try this: Identify the terms and the coefficient of the following expression: y
Try this: Identify the terms and the coefficient of the following expression: 6x + 8y – 5
Try this: Identify the terms and the coefficient of the following expression:
2𝑥
5
Example: Evaluate the expression: 5x + 7 when x = -2
Example: Evaluate the expression: 3x -2y when x = 4 and y = -7
Try this: Evaluate the expression:
2𝑎+3𝑐
4𝑏
when a = 5, b = -1 and c =6
Try this: Evaluate the expression: 2𝑥 𝑦 + 1 when x = 5 and y = 3.
Section 1.5: Notes Translating Words into Variable Expressions
Operation
Addition
Subtraction
Multiplication
Division
Words and Phrases
plus, more than, increased by, sum
minus, less than, decreased by, difference
times, product
divided by, quotient
4x + 8 “four times x plus eight”
4(x+8) “four times the quantity x plus eight”
Example: one less than a number and twice its product
Example: fifteen more than three times a number
Example: the quotient of four and a number
Example: twice the sum of three and a number
You Try: six more than five times a number
You Try: the quotient of a number and seven
You Try: one-half of the sum of a number and nine
You Try: eight less than a number and four times its product
A reminder: the area of a rectangle is found by multiplying the length by the width
Example: If the length of a rectangle is five more than three times the width, write an expression for the
area. (You do not need to simplify)
You Try: Usher Cat is two years younger than four times the age of Odie. Write a variable expression to
represent the age of Usher Cat.
Unit 1 Lesson 7 Translating Words into Equations
Example: Three less than five times a number is equal to seven.
Try It: One more than the product of eight times a number is thirty-three.
Try It: Fifty-five less than three times a number is two.
Unit 1 Lesson 9 Replacement Sets
The key word is “replacement.” Mathematically the word “substitution” is more commonly used.
Example: Identify the solution set of each equation or inequality.
5x + 1 = 21; {3, 4, 5}
Example: Identify the solution set of each equation or inequality.
𝑥 + 31
= 𝑥 + 1; {4, 5, 6}
𝑥+1
Try It: Identify the solution set of each equation or inequality.
2x + 8 = x + 16; {2, 8, 20}
Example: Identify the solution set of each equation or inequality.
|5x| = |2x – 12|; {-3, -4, -5}
Try It: Identify the solution set of each equation or inequality.
|4m – 2| = |3m – 5|; {-2, -3, -4, -5}
Try It: Milo must put 100 feet of fencing around her rectangular garden. The length of the garden is one
foot longer than twice the width. Find the solution set for 2w + 2(2w + 1) = 100 given the replacement
set {6, 7, 8, 9} to determine the width of the garden.
Unit 1 Lesson 10 Problem Solving
Identify the knowns and unknowns
Strategize
Set up the equation(s)
Solve
Check your answer and for the reasonableness in the context.
Example: Twenty people need to be shuttled from the airport to their hotel. A van can hold eight
people. How many vans are needed?
Example: Three times as many cars as trucks went over a bridge. Nineteen trucks went over the bridge.
How many vehicles in all went over the bridge?
Try It: A playground is shaped like a square. Each side is 50 yards long. How many trips did Usher Cat
run around the entire border of the playground if Usher Cat ran 2600 yards?
Try It: Mr. Dean has 3 quarters and 4 more dimes than quarters. How much money does Mr. Dean
have?
Try It: The area of a rectangle is 70 square meters. The length is three meters longer than the width.
Write an equation that models this and find the width and length.
Try It: Solve the given problem. Donald is 2 years older than three times her sister Allie’s age. If Allie is 5
years old, how old is Donald?
Unit 1 Lesson 6 Equations
This section is a “guess and check” progress.
Open-sentence: do not know whether the statement is true.
Example: 3x + 4 = 12; x = 2
Example: 4y = 2y + 5; y = 5
Try It: 3x + 3 = 2x + 6; x = 5
Try It: A phone company offers two different monthly plans. The first plan is $20 per month plus $0.30
per minute. The second plan costs $15 per month plus $0.40 per minute. Determine if the cost is the
same after 50 minutes.
54