NUMBER & ALGEBRA REVIEW

NUMBER & ALGEBRA REVIEW

(With your built-in calculator!)

By Mr. Barnard

Number Types

Whole Numbers (0, 1, 2, 3,…)

Integers (…, -2, -1, 0, 1, 2, …)

Decimals (…,-1.9, 0.8, …) Rational (…,-1 4/7, 1/5, …)

We will:

Simplify numerical operations

Correctly use order of operations

Simplifying algebraic expressions

(ALL WITHOUT A CALCULATOR)

Expressions

Statements without an equals sign.

Simplifying an expression means to combine “like” terms.

Answers to expressions include:

Addition Sum Subtraction Difference Multiplication Product Division Quotient

Algebraic Expressions

4x - 9

Variable

ConstantCoefficient

Whole Number Operations

30 + 80 = ?Think 3 +

8!110Think 12 -

4!80

120 - 40 = ?

65 + 97 = ?Think 60 + 90!162

142 – 57 = ?Think 13 - 5!

85Think 12 -

7!Think 5 + 7!

More Whole Number Operations

82x3

246 324360

36x19

684

Even More Whole Number Operations

142837 -14 0

-28 03

2 0 4 0

2 8

7

3

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>>>

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>>>

7

4

G. 360H. 30

I. 324

J. 44

K. 270L. 103

4

1

Integer Operations

-19 + 245

-11 - 18THINK -11 + -18

-29

90 x -7-630

-3500 -7050

Integer Practice M.-18 + -39

N.-40 - -65

O.12 x - 6

P. -240 -60

M.-57

N.25

O.-72

P. 4

ANSWERS>>>

Decimal Operations

3.8 + 11.29 = ?15.09

-0.7 - -2.39 = ?THINK -0.7 +

2.391.69

225250

-2.5x 0.19

-0.475

3.60.8 4.

-32 4

0

0

5

-40 0

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>>>

Rational Operations

3

23

4

32

12

83

12

92

12

56

12

175

4

18

2

12

2

12

4

18 THINK

4

22

4

18

4

22

4

57

4

35

7+4

4

35

More Rational Operations

3

13

8

3

8

3

2

14

3

10

8

3

3

10

8

3

1

14

5

4

11

4

5

3

8

2

9

3

1

4

1

=12

Rational Practice

4

33

6

51

ANSWERS>>>

4

34

8

15

3

12

8

11

4

32

8

5

12

75

8

3

8

52

22

5

U.

V.

W.

X.

U.

V.

W.

X.

Simplifying Expressions

7 + 3 8 ÷ 4 – 97 + 6 – 9

4

2 – 3(4 + 1)2 – 3 52 – 15-13

More Simplifying Expressions

3x + 5x – 88x - 8

9x +10y - x8x + 10y

3 – 5(2x – 4)3 – 10x + 20

-10x + 23

(x – 3)(2x + 4)2x2 -6x + 4x - 122x2 -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

x x2 3x

+5 5x 15

Combine like terms!!!

x2 + 8x + 15

Algebra Tiles

x

x x2 x

1

x

11 1

(x + 3)(x + 2) x

x

11

1 1 1

?

(x + 3)(x + 2) x

x

11

1 1 1

x2 x x x

x

x1 1 11 1 1

x2

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 = x2 + 32 ?

Simplifying Rational Expressions

10x + 86

5x + 43

5

3

4 15x2 + 7x

5x

2x2 + 6xx2 + 5x +

615x + 75

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

3)2xx + 2

Simplifying Practice Y. -2 + 5 3 – 8 4

Z. 5x - 2(3x – 4)

AA.(3x – 1)(5x +

2)

AB. 6x2 – 14x

10x

Y. 11

Z. -x + 8

AA. 15x2 + x - 2

AB. 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!

WE’LL DISCUSS THE PRACTICE AT THE END OF THIS LESSON…BE READY FOR

THE CONCEPT QUIZ!!!