Transcript R1 Real Numbers

Review #1
Real
Numbers
When we want to treat a
collection of similar but distinct
objects as a whole, we use the
idea of a set.
S = {4, 5, 6}
The numbers 4, 5, and 6 are
called elements.
The order in which you list
elements in a set is not relevant.
If a set has no elements, it is
called the empty set or null set.
We do not list an element more
than once, because the
elements of a set are distinct.
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Classification of
NaturalNumbers
Numbers – N
Whole Numbers – W
Integers – I
Rational Numbers – Q
Irrational Numbers – IR
Natural Numbers
1, 2, 3, 4, 5, 6, 7, …
Whole Numbers
0, 1, 2, 3, 4, 5, 6, …
Integers
…, – 2, – 1, 0, 1, 2, …
Rational Numbers
Any number that can be written
in the form of a fraction.
Irrational Numbers
Any number that neither
terminates nor repeats.
Approximations
Truncation
Drop all the digits that follow the
specified final digit in the decimal.
Rounding
Identify 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.
Approximate 24.7486 to 3
decimal places by both
truncating and rounding.
Truncating: 24.748
Rounding: 24.749
Mathematical
Operations
Addition – Sum
Subtraction –
Difference
Multiplication –
Product
Division –
Quotient
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 x  72
Order of Operations
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.
Adding and Subtracting
Rational Numbers
1. Find the LCD
2. Multiply the numerator by a factor
of the LCD
3. Add the numerators together
4. Keep the denominator the same
5. Simplify the expression
Adding and Subtracting
Rational Numbers
Multiplying and Dividing
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