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

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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, …)

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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)

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

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

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Algebraic Expressions 4x - 9 Variable Constant Coefficient

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Whole Number Operations 30 + 80 = ? Think 3 + 8! 110 Think 12 - 4! 80 120 - 40 = ? 65 + 97 = ? Think 60 + 90! 162 142 – 57 = ? Think 13 - 5! 85 Think 12 - 7! Think 5 + 7!

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More Whole Number Operations 82x3 246324 360 36 36x19 684

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Even More Whole Number Operations -14 -14 0 -28 -28 03 03 2 0 4 0 2 8

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Whole Number Practice Whole Number Practice A. 70 + 40 B. 180 – 130 C. 110 + 40 D. 150 – 90 E. 84 + 97 F. 125 - 86 A. 110 B. 50 C. 150 D. 60 E. 181 F. 39 ANSWERS>>>

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Whole Number Practice Whole Number Practice G. 90 x 4 H. 180 6 I. 36 x 9 J. 312 7 K. 30 x 9 L. 413 4 ANSWERS>>> G. 360 H. 30 I. 324 J. 44 K. 270 L. 103

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Integer Operations -19 + 24 5 -11 - 18 THINK -11 + -18 -29 90 x -7 -630 -3500 -70 50

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Integer Practice Integer Practice M. -18 + -39 N. -40 - -65 O. 12 x - 6 P. -240 -60 M. -57 N. 25 O. -72 P. 4 ANSWERS>>>

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Decimal Operations 3.8 + 11.29 = ? 15.09 -0.7 - -2.39 = ? THINK -0.7 + 2.39 1.69 225 250 -2.5 -2.5 x 0.19 -0.475 4. 4. -32 -32 4 0 0 5 -40 -40 0

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Decimal Practice Decimal Practice Q. -2.91 + -32.4 R. 6.7 - 0.32 S. 4.4 x 0.3 T. -22.5 0.05 Q. -35.31 R. 6.38 S. 1.32 T. -450 ANSWERS>>>

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Rational Operations THINK 7 +4

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More Rational Operations 1 14 5 3 1 4 1 =12

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

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Simplifying Expressions 7 + 3 8 ÷ 4 – 9 7 + 6 – 9 4 2 – 3(4 + 1) 2 – 3 5 2 – 15 -13

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More Simplifying Expressions 3x + 5x – 8 8x - 8 9x +10y - x 8x + 10y 3 – 5(2x – 4) 3 – 10x + 20 -10x + 23 (x – 3)(2x + 4) 2x 2 -6x + 4x - 12 2x 2 -2x - 12

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

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

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Algebra Tiles x xx2x2 x 1 x 1 11

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(x + 3)(x + 2) x x 1 1 111 ?

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x x 1 1 111 x2x2 xxx x x 111 111 x2x2 5x 6 + +

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

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

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Simplifying Rational Expressions 10x + 8 6 5x + 4 3 5 3 4 15x 2 + 7x 5x 2x 2 + 6x x 2 + 5x + 6 15x + 7 5 2x(x + 3) (x + 2)(x + 3) 2x x + 2

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Simplifying Practice Simplifying Practice Y. -2 + 5 3 – 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>>>

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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!

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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!!!

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