NUMBER & ALGEBRA REVIEW (With your built-in calculator!) By Mr. Barnard

Number Types Whole Numbers (0, 1, 2, 3,…) Whole Numbers (0, 1, 2, 3,…) Integers (…, -2, -1, 0, 1, 2, …) Integers (…, -2, -1, 0, 1, 2, …) Decimals (…,-1.9, 0.8, …) Decimals (…,-1.9, 0.8, …) Rational (…,-1 4/7, 1/5, …) Rational (…,-1 4/7, 1/5, …)

We will: Simplify numerical operations Simplify numerical operations Correctly use order of operations Correctly use order of operations Simplifying algebraic expressions Simplifying algebraic expressions (ALL WITHOUT A CALCULATOR) (ALL WITHOUT A CALCULATOR)

Expressions Statements without an equals sign. Simplifying an expression means to combine like terms.

Answers to expressions include: AdditionSum AdditionSum SubtractionDifference SubtractionDifference MultiplicationProduct MultiplicationProduct DivisionQuotient DivisionQuotient

Algebraic Expressions 4x - 9 Variable Constant Coefficient

Whole Number Operations = ? Think 3 + 8! 110 Think ! = ? = ? Think ! – 57 = ? Think ! 85 Think ! Think 5 + 7!

More Whole Number Operations 82x x19 684

Even More Whole Number Operations

Whole Number Practice Whole Number Practice A B. 180 – 130 C D. 150 – 90 E F A. 110 B. 50 C. 150 D. 60 E. 181 F. 39 ANSWERS>>>

Whole Number Practice Whole Number Practice G. 90 x 4 H I. 36 x 9 J K. 30 x 9 L ANSWERS>>> G. 360 H. 30 I. 324 J. 44 K. 270 L. 103

Integer Operations THINK x

Integer Practice Integer Practice M N O. 12 x - 6 P M. -57 N. 25 O. -72 P. 4 ANSWERS>>>

Decimal Operations = ? = ? THINK x

Decimal Practice Decimal Practice Q R S. 4.4 x 0.3 T Q R S T ANSWERS>>>

Rational Operations THINK 7 +4

More Rational Operations =12

Rational Practice Rational Practice ANSWERS>>> U. V. W. X. U. V. W. X.

Simplifying Expressions ÷ 4 – – – 3(4 + 1) 2 – –

More Simplifying Expressions 3x + 5x – 8 8x - 8 9x +10y - x 8x + 10y 3 – 5(2x – 4) 3 – 10x x + 23 (x – 3)(2x + 4) 2x 2 -6x + 4x x 2 -2x - 12

Tools to Help You Simplify Algebraic Expressions! What is the formula for the area of a rectangle? L W AREA = LW

(x + 3)(x + 5) x+3 xx2x2 3x +55x15 Combine like terms!!! x 2 + 8x + 15

Algebra Tiles x xx2x2 x 1 x 1 11

(x + 3)(x + 2) x x ?

x x x2x2 xxx x x x2x2 5x 6 + +

Use tiles and/or area method! (x + 4)(x + 1) (2x + 1)(x + 2) (x + 5)(x + 2)

Use tiles to answer this question: Is (x + 3) 2 = x ?

Simplifying Rational Expressions 10x x x 2 + 7x 5x 2x 2 + 6x x 2 + 5x x x(x + 3) (x + 2)(x + 3) 2x x + 2

Simplifying Practice Simplifying Practice Y – 8 4 Z. 5x - 2(3x – 4) AA. (3x – 1)(5x + 2) BB. 6x 2 – 14x 10x 10x Y. 11 Z. -x + 8 AA. 15x 2 + x - 2 BB. 3x – 7 5 ANSWERS>>>

It is expected that YOU can independently complete all of the previous numeric and algebraic examples without a calculator. If you are able to, GREAT!, as you will be able to really focus on Geometry this year!!! Seek immediate help if you are unable to perform these necessary ideas!

YOUR FIRST PRACTICE! BE ABLE TO COMPLETE PROBLEMS WITHOUT A CALCULATOR CHECK YOUR WORK WITH EACH OTHER, WITH A CALCULATOR, OR WITH THE ONLINE TOOLS! WELL DISCUSS THE PRACTICE AT THE END OF THIS LESSON…BE READY FOR THE CONCEPT QUIZ!!!