section 2.1 - 2.3 integers and rational numbers adding … · integers and rational numbers adding...
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CH 2 Properties of Real Numbers
Section 2.1 - 2.3
Integers and Rational Numbers
Adding and Subtracting Real NumbersYou will learn:
**The differences and overlap between whole numbers, integers, and rational numbers.
**How to evaluate the absolute value of a number
**How to add and subtract integers and rational numbers
CH 2 Properties of Real Numbers
Whole numbers: 0, 1, 2, 3, ...
Integers: ..., 3, 2, 1, 0, 1, 2, 3, ...
Positive Integers: greater than 0
Negative integers: less than 0
0 is neither positive or negative
Rational numbers: a where a and b are integers
Examples: b
CH 2 Properties of Real Numbers
How are these numbers related??
CH 2 Properties of Real Numbers
Tell whether each number in the list is a whole number, an integer, or a rational number. Then order the numbers from least to greatest.
1.) 5, 1/2, 1.9, 2
2.) 0.01, 0.1, 0, 0.2, 2
CH 2 Properties of Real Numbers
Opposites: Same distance from 0 on a number line, but on opposite sides
Example:
Absolute Value: Distance between a number and 0 on the number line
If a is positive, then a = a.
If a is 0, then a = 0.
If a is negative, then a = a.
CH 2 Properties of Real Numbers
Absolute Value Examples:
CH 2 Properties of Real Numbers
When adding and subtracting negative numbers think of a number line.
Adding numbers with the same sign:
1.) 5+9 2.) 5+(9)
Adding numbers with different signs:
3.) 10+6 4.) 10+(6)
CH 2 Properties of Real Numbers
1.) 5 6
2.) 5 (6)
3.) 9 (4)
CH 2 Properties of Real Numbers
Adding and Subtracting Rational Numbers aka Fractions!
Example: Steps:
CH 2 Properties of Real Numbers
More Rational Numbers Examples!
Example: Steps:
CH 2 Properties of Real Numbers
Homework for Section 2.12.3
Operations with Real Numbers Worksheets 1, 2, & 6
From today you can:
**Determine whether a number is a whole number, integer, or rational number.
**Evaluate absolute value problems.
**Evaluate sums and differences of integers and rational numbers.
CH 2 Properties of Real Numbers
Sections 2.4 and 2.6
Multiplying and Dividing Real Numbers
Today we will learn:
**How to multiply and divide real numbers (including negatives and fractions)
CH 2 Properties of Real Numbers
The product of two real number with the same sign is positive.
1.) 8(6) 2.) 6(4)
The product of two real numbers with opposite/different signs is negative.
1.) 5(6) 2.) 7(4)
Product of odd number of negatives = negative
Product of even number of negatives = positive
Why????
CH 2 Properties of Real Numbers
Multiplying Rational Numbers:
Example: Steps:
CH 2 Properties of Real Numbers
Multiplying Rational Numbers:
Example: Steps:
CH 2 Properties of Real Numbers
The quotient of two real number with the same sign is positive.
The quotient of two real numbers with opposite/different signs is negative.
The quotient of 0 and any nonzero number is 0.
Ex.)
CH 2 Properties of Real Numbers
Dividing Rational Numbers:
To divide a by b, multiply a by the multiplicative inverse of b.
Ex.) Ex.)
CH 2 Properties of Real Numbers
Dividing Rational Numbers:
Example: Steps:
CH 2 Properties of Real Numbers
Dividing Rational Numbers:
Example: Steps:
CH 2 Properties of Real Numbers
Exit Slip
1.) 3 1
2.) 6 (8)
Justify/Explain your answers!! What were the steps or why did you do what you did? Why was your answer negative/positive?
If you don't know that's ok. Just try to get something down so I can see your thinking process.
+5 3
If you are struggling with a certain type of problem tell me what type or the HW #
CH 2 Properties of Real Numbers
Exit Slip:
What are you struggling with the most?
You can give the type of problem or a number from your homework.
Please give me one or two types of problems.
CH 2 Properties of Real Numbers
Homework for Section 2.4 & 2.6
Operations with Real Numbers
Worksheets 3 &4
After today you can:
**Multiply and divide integers and rational numbers
CH 2 Properties of Real Numbers
Section 2.5 Apply the Distributive Property
** Identify terms, coefficients, constant terms, and like terms.
** Apply distributive property and combine like terms.
CH 2 Properties of Real Numbers
Terms: separated by + or signs
Coefficients: numbers in front of and being multiplied by the variables
Constant term: a number with no variable attached
Like terms: terms that have the same variable parts
2x x + 3y 4
***Note: Constants are also like terms!!
CH 2 Properties of Real Numbers
Ex 1. List like terms and state how many terms are in each expressiona. 2x2, 3, 5y, x, 7y, 8
# Terms: _______________ Like Terms: ________________
Constants: _________________
b. 5xy, 8, 7x, 6y, 2x
# Terms: _______________ Like Terms: ________________
Constants: _________________
CH 2 Properties of Real Numbers
Ex 2. Rewrite each expression using the distributive property.
a. 2(a b)
b. 3 (2 + 4x)
c. (5y 3n)
CH 2 Properties of Real Numbers
Ex 3. Rewrite each expression using the distributive property and combine like terms.
a. 2(3a 7) + 4a + 10 b. 4(2x + 3y) 5x 6y + 1
CH 2 Properties of Real Numbers
a. (6y 3n) + 2(4n + 2y) b. 3(2s + 4 6t) 2(9 3s + 5t)
Ex 4. Rewrite each expression using the distributive property and combine like terms.
CH 2 Properties of Real Numbers
Section 2.5 Homework & Exit Slip
Homework: Both 2.5 WS
Exit Slip:
What are you still struggling with/was easiest on the quiz?
Today: Try the following: 3(x 2y) + 5x 8y
After Today: Can you distribute in an expression??
CH 2 Properties of Real Numbers
Section 2.7 Square Roots
You will learn:
How to simplify square roots and
How to evaluate expression containing square roots
CH 2 Properties of Real Numbers
List of Perfect Squares
You will need to memorize these!!!
CH 2 Properties of Real Numbers
Ex. 1 : Simplify each square root
a. 25
b. - 49
c. 81 +
CH 2 Properties of Real Numbers
Ex 2. : Simplify each square root
a. 5 + 64
b. 2 - 3 100
c. 10 2 16+
CH 2 Properties of Real Numbers
2.7 Homework & Exit Slips
After Today: Can you simplify expressions containing square roots?
Homework: WS 2.7
Exit Slip:
CH 2 Properties of Real Numbers