Pre-Algebra Review Chapter 1, Sections 1 and 2By Ms. Dewey-Hoffman, 2009 http://msdhpowerpoints.blogspot.com/

Page 2

Section 1: Variables and Expressions

Variables

– Are letters or symbols that act as placeholders for numbers.

– One letter = One number.

Simplify

– To replace a variable with a number.

Expressions: Numerical and Variable

– Expressions don’t have an equal sign. 50 + 10 Expression

– Equations do have an equal sign. 50 + 10 = 60 Equation

Numerical Expressions

– Only have numbers: 50 + 10 No Variables

Variable Expressions

– Have at least 1 Variable: 75 + g + 25 At least 1 Variable

– 3x + y At least 1 Variable

Page 3

Language of Math: Operations

Addition: Total, Sum, Altogether, Increase, and Combine.

Subtraction: Difference, Less Than, More Than, and Decrease.

Multiplication: Product, Times, and Each.

Division: Quotient, Share, and Each.

Operations and their Parts: Addition & Subtraction

Two numbers being added are called ADDENDS.

The answer to an addition problem is called the SUM.

The number being subtracted is the SUBTRAHEND and the number from which we are subtracting is called the MINUEND.

(First NumberMinuend) – (Second NumberSubtrahend) = Difference.

The answer to a subtraction problem is called the DIFFERNCE.

Page 4

Operations and their Parts: Multiplication & Division

Two numbers in a multiplication problem are called the FACTORS.

The answer to a multiplication problem is the PRODUCT.

The number being divided is called the DIVIDEND. The number we are dividing by is called the DIVISOR.

The answer to a division problem is the QUOTIENT.

(Top NumberDividend) / (DivisorBottom Number) = Quotient

Page 5

Writing Variable Expressions: Example Problems

Nine more than number y y + 9

A number z times three z x 3, z • 3, z3

5 times the quantity 4 plus a number c 5 • (4 + c), 5(4 + c)

Try These:

The product of x and y, plus 5 The sum of t and u, divided by 4 R divided by 5, minus 3, equals 2. Y fewer than 27 Daniel has 14 more than Sam. The total of Tommy’s marbles and 13 55 subtracted from 105, divided by 5 equals 10.

Challenge problems are in purple.

Page 6

Section 2: The Order of Operations

Simplify an Expression

– To replace the expression with the simplest name for its value…

– or solve as far as possible!

– What does 36 + 25 ÷ 5 simplify to?

The Order of Operations

– 36 + 25 ÷ 5

Division first! 25 ÷ 5 = 5

Rewrite. 36 + 5

Addition second! 36 + 5 = 41

41 is the simplified expression for 36 + 25 ÷ 5

Page 7

The Order of Operations: PEMDAS

P : Do operations inside PARENTHESES (or other delimiters/grouping symbols, like [BRACKETS] and division bars).

– Work from the inside of the Parentheses/Brackets to the outside.

– Division Bars: Simplify the top and bottom first, then divide!

E : Evaluate terms with EXPONENTS.

– The exponent ONLY effects the NUMBERS/VARIABLES/PARENTHESES in front of the little number (to the left). Example: 510, x2, (5 + 8)3.

D M : Do MULTIPLICATION and DIVISION.

– In order from LEFT to RIGHT.

– 5 • 10 ÷ 2 5 • 10 = 50, 50 ÷ 2 = 25, 5•10÷2=25

A S : ADD and SUBTRACT terms.

– In order from LEFT to RIGHT.

– 8 + 7 – 5 8 + 7 = 15, 15 – 5 = 10, 8+7-5=10

PEDMAS is where order REALLY

matters!

Page 8

Example Problems: Show each Step of PEMDAS

2[(13 – 4) ÷ 3] =

1 + 10 – 2 =

4

4 – 1 • 2 + 6 ÷ 3 =

5 + 6 • 4 ÷ 3 – 1 =

6

3

4

12

Example of Showing Steps: PEMDAS

1) 2[(13 – 4) ÷ 3] = Copy Problem

2) 2[(9) ÷ 3] = Simplify Parentheses

3) 2[3] = Simplify Brackets

4) 2[3] = 6, Multiply

5) 6, Answer, Always Boxed!

Page 9

Assignment #1Pages 6-7: 10-44 even. (Show answers only)

Page 11: 10-30 even. (Copy problem and show each step of PEMDAS)

Extra Credit: Page 11: 36-39 all. (Show problem and answer)

Start your homework!

Fold a lined piece of paper in half. (Holes on the Left Side!)

Top right: Name, Class, Assignment Number, Assignment.

Start on the left side of the fold and show all work.

Remember to box your answers!

Print out of pages 3, 4, 5, and 7 should be pasted in with your notes!