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1.1 Number Operations

Types of Numbers

Natural Numbers (N): {1,2,3,…} Whole Numbers (W): {0,1,2,…} Integers: (Z): {…-2, -1, 0, 1, 2, …} Rational Numbers (Q): {a/b a and b are integers and b ≠ 0} Irrational Numbers (I) : {Any non repeating -non terminating number} Real Number (R): {The set of all rational and irrational

numbers}

SimplifySimplify

a. 2 + 48 ÷ 6b. 5(8 - 6) + 2(4 -1)c. 3 - 4(2 - 7)d. 5 + [2 + (4 - 1) + 3(6 ÷ 2)]e. [24 - (2 8)] + 4(12 - 7)

1.1 Number Operations

Write as decimalsWrite as decimals

1.1 Number Operations

€

a.3

5

€

b.7

4€

c. 12

3

€

d.1

6

Write as percentsWrite as percents

1.1 Number Operations

€

a.3

4

€

b.1

5€

c. 1.25

€

d. .06

Write as fractionsWrite as fractions

1.1 Number Operations

€

a. .7

€

b. 24%

€

c. 2.4

€

d. .09

Find the areaFind the area

1.1 Number Operations

8 in

5 in

4 ft

2 ft

1.2 Variables in Algebra

Definition of Algebraic Expression

A collection of letters (called variables) and real numbers(called constants) combined using the operations of addition, subtraction, multiplication and division is calledan algebraic expression.

• Term An expression separated by a plus or minus sign• Variable A letter that represents a number• Coefficient A number in front of a variable

Algebraic ExpressionsAlgebraic Expressions

5 + 5 + xx 6 6 yy 3 3 yy – 4 + – 4 + xx

44xx means 4 means 4 xx

andand

xyxy means means xx yy

1.2 Variables in Algebra

Evaluate if Evaluate if aa = 2, = 2, b b = 3, and = 3, and cc = 4 = 4

• 3a - 2b• 4ac - 3a• 4(a + 2c)

1.2 Variables in Algebra

1.3 Exponents and PowersExponents

If a is a real number and n is a natural number, then the nth power of a, or a raised to the nth power, written as an, is the product of n factors, each of which is a. exponent base an = a • a • a … • a

72 is read as seven to the second power or 7 squared.

43 is read as 4 to the third power or 3 cubed.

1.3 Exponents and Powers

Solve if x = 4 and y = 3

•3x2 + 2y3

•4(x + 3y)3

•(2x)3

•2x3

1.3 Exponents and Powers

1.3 Exponents and Powers

A formula is an equation that describes a known relationship among measured quantities.

Formula Meaning

A = lw Area of a rectangle

A = πr2 Area of a circle

V = lwh Volume of a rectangular solid

d =rt Motion equation

Order of OperationOrder of Operation

1.1. Do all operations within grouping symbols such as parentheses or brackets.

2. Evaluate any expressions with exponents.3. Multiply or divide in order from left to

right.4. Add or subtract in order from left to right.

1.4 Order of Operation

1. 24 - 12 + 3 • 52. 16 + 21 ÷ 3 - 63. 4 • (3 + 7) - 2 • 44. 3 + (2 + 3)2 - 7

1.4 Order of Operation

Evaluate the expression if Evaluate the expression if xx = 2, = 2, yy = 4, and = 4, and zz = 5 = 5

• x + 2z - 5• x3 + 3x - 2• 4 • (3x - y)2 + 5 • 4

1.4 Order of Operation

€

4. 6 +2x

y− z

An An equation is formed when an equal sign is formed when an equal sign is placed between two expressions.is placed between two expressions.

Equations that contain variables are Equations that contain variables are open open sentences.sentences.

Equations that do not contain variables are Equations that do not contain variables are closed sentences.closed sentences.

1.5 Equations and Inequalities

Check whether the numbers 3, 4, and 5 are Check whether the numbers 3, 4, and 5 are solutions of the following equations.solutions of the following equations.

1.1. 33x x - 5 = 7- 5 = 72.2. 44xx22 - 31 = 5 - 31 = 53.3. 33xx + 7 = 2 + 7 = 2xx + 12 + 12

1.5 Equations and Inequalities

1.5 Equations and InequalitiesA solution of an inequality is a value of the variable that makes the inequality a true statement.

The solution set of an inequality is the set of all solutions.

1.5 Equations and Inequalities

Order on Real-Number Line

a < b a is less than b a < b a is less than or equal to b a > b a is greater than b a > b a is greater than or equal to b a ≠b a is not equal to b

1.5 Equations and Inequalities

Determine if x = 3 is a solution of each

inequality

n 3x - 1 < 5n 2x - 3 > 5x + 2n 4x + 9 > 3(x + 4)

Addition Subtraction Multiplication Division Equals

sum difference product quotient is

plus minus times divided by gives

added to subtracted multiply into yields

more than

less than twice per same

increased decreased by of ratio

total less double

1.6 Models

Write each statement in mathematical terms

1. Twice the sum of 3 and a number is 4.

2. Three more than the square of a number is 6.

3. 15 is 5 less than three times a number.

4. The square of a number increased by 6 is -4.

1.6 Models

1.7 Problem Solving

General Strategies for Problem Solving

1. Read and understand the problem. Choose a variable

2. Translate the problem into an equation. 3. Solve the equation. 4. Interpret the results.(Check your answer)