Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers

•Classification of Numbers

•Properties of Real Numbers

•Order of Operations

R1 Real Numbers

The numbers 3, 4, 5, and 6 are called elements.

S = { 3, 4, 5, 6 }

When we want to treat a collection of similar but

distinct objects as a whole, we use the idea of a set.

We do not list an element more than once, because the elements of a set are

distinct.

If a set has no elements, it is called the empty set or null

set.

The order in which you list elements in a set is not

relevant.

Natural Numbers – N1, 2, 3, 4, 5, 6, 7, …Whole Numbers – W0, 1, 2, 3, 4, 5, 6, …Integers – I…, – 2, – 1, 0, 1, 2, …

Classification of Real Numbers

Rational NumbersAny number that can be written in the form of a fraction.

Irrational NumbersAny number that neither terminates nor repeats.

64, 0.72, 2.914, 36

4 , 2, 8 3

TruncationDrop all the digits that follow the specified final digit in the decimal.RoundingIdentify the specified final digit in the decimal. If the next digit is 5 or more, add 1 to the final digit. Otherwise leave the number as it appears.

Approximations

Truncating: 24.748Rounding: 24.749

Approximate 24.7486 to 3 decimal places by both truncating and rounding.

Convert Natural Numbers, Whole

Numbers, and Integers into fractional form 31. 64 2. 4

3. 14 4. 6

1

325. 16 6. 27

Convert each mixed number into fractional

form

Multiply the whole number by the denominator and add the numerator all over the

denominator

3 7

1. 8 2. 64 8

Convert terminating decimals into fractional

form

The number of places you move the decimal point is

equal to the number of zeros in the denominator.

21. 0.42 2. 6.8 3. 4.8 10x

Convert repeating decimals into fractional

form

Repeating decimals are over 9Nonrepeating decimals are over 0Work from right to left in the denominatorSubtract the nonrepeating digits from the entire decimal for the numerator

1. 0.4 2. 0.74 3. 2.5

4. 0.246 5. 0.246 6. 0.246

1. Perform all operations within grouping symbols from innermost outward.

2. Perform all operations with exponents from left to right.

3. Perform all multiplication and division from left to right.

4. Perform all addition and subtraction from left to right.

Order of Operations

1. Find the LCD2. Multiply numerator by factor

of LCD3. Add the numerators together4. Keep the denominator the

same5. Simplify the expression

Adding and Subtracting Rational

Numbers

Adding and Subtracting Rational

Numbers

5 4 3 4 7

3. 2 4. 6 26 3 4 9 6

5 7 8 5

1. 2. 4 78 12 3 2

1. Inverse Property for division2. Reduce fractions with common

factors3. Multiply the numerators

together4. Multiply the denominators

together5. Simplify the expression

Multiplying and Dividing Rational

Numbers

Multiplying and Dividing Rational

Numbers

15 9 14 21

3. 4. 24 28 27 36

16 7 24 9

1. 2. 21 12 20 16

R2 Algebra Review

•Graphing Inequalities

•Absolute Value

•Evaluating Expressions

A real number that corresponds to a particular point on the

number line is called a coordinate.The origin corresponds to the

real number zero.The correspondence between points on a line and the real

numbers is called a coordinate system.

Real Number Line

Graph the following inequalities on the number line.

Graphing Inequalities

or uses and or uses

1. Graph all the numbers x for which x 2

2. Graph all the numbers x for which x 4

Distance from zero on the number line.

The absolute value of a real number a is denoted by the

symbol |a|.

Absolute Value

4 4 and 9 9

The distance between two points P and Q is denoted by

d(P,Q) = |b – a|.Let P, Q, and R be points on the number

line with coordinates –7, 4, and –3 .

1. Find the distance between P and Q.2. Find the distance between Q and R..

Write an equivalent expression without using absolute value

bars.

5. 6 6. 3x 9 , if x 3

3. 5 2 4. 3 5

1. 2 6 2. 19 7

1.Substitute each value for the variable using a grouping symbol

2.Follow all order of operations

3.Simplify your answer

Evaluating Expressions

Evaluate each expression, if x = 4, y = –2, and z = 3

3x 2xz 2 3 5 43. 4.

3y 8 y 2z 3 y x 3

31. 3xy 4z 9 2. 2z 3x 4y

3 x 4 y 3x 2y5. 6.

y z 5 5z x 1