Real Numbers

Review #1

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

S = {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

, 2, 13

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.

Addition – Sum Subtraction –

Difference

Multiplication – Product

Division – Quotient

Mathematical Operations

The difference 4 less than x is 12.

The quotient of 16 and x is 8.

The product of x and 6 is 72.6 72x

Order of Operations1. 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.

1. Find the LCD2. Multiply the numerator by a

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

same5. Simplify the expression

Adding and Subtracting Rational

Numbers

Adding and Subtracting Rational

Numbers

1.Multiplicative Inverse for division

2.Multiply the numerators together

3.Multiply the denominators together

4.Simplify the expression

Multiplying and Dividing Rational

Numbers

Multiplying and Dividing Rational

Numbers