Download Document

Welcome to MM204!
Unit 3 Seminar
To resize your pods:
Place your mouse here.
Left mouse click and hold.
Drag to the right to enlarge the pod.
To maximize chat,
minimize roster by
clicking here
MM204 Unit 3 Seminar Agenda
• Write repeated multiplication in exponential form
• Evaluate numerical expressions containing exponents
• Simplify numerical expressions containing addition,
subtraction, multiplication, division, and exponents by
correctly using the order of operations
• Simplify numerical expressions using the distributive
property
Variables
• A variable is a letter that represents an
unknown amount.
• Example:
t would represent time
a, b, c, d, x, y, etc. could all be variables.
Exponents
• Used to express repeated multiplication.
• Example:
The long notation would look like this:
2 * 2 * 2 * 2 which equals 16; our special
shorthand would be 2^4 and is read as two to
the power of four.
• In this expression:
2^4 two to the power of four
‘2’ is the base
‘4’ is the actual exponent or power
• Note:
On the discussion board and in the chat
dialogue we must use the caret symbol,
which is ‘shift 6’ to stand for ‘to the power
of’. For our Word project we will use the
superscript formatting.
• We will also deal with exponents that contain
variables for the base.
Example: Write x * x * x * x in exponential
notation.
Since we are multiplying x by itself 4 times, we
would express this expression as
x^4
This would be our final answer since we don’t
know the value of x.
What do we do if the base is negative?
• When evaluating an exponent with a
negative non-variable base the following
statements are true as long as the negative
sign is within parentheses:
-if the exponent is even, the term will be
positive
- if the exponent is odd the term will be
negative.
Example
• Example: Evaluate (-2)^6
= (-2)(-2)(-2)(-2)(-2)(-2)
= 64 Even power; positive results.
You try one:
Everyone: Evaluate (-4)^3
One more note
• Be careful where the negative sign is
(-2)^4 is very different from -2^4.
(-2)^4 = (-2)(-2)(-2)(-2) = 16
But -2^4 = - (2)(2)(2)(2) = -16
Order of Operations
1) Parentheses: Perform all operations on any
terms within parentheses.
2) Exponents: Evaluate all exponents.
3) Multiplication/Division performed in order from
left to right as they appear in the expression.
4) Addition/Subtraction performed in order from
left to right as they appear in the expression.
Examples
• Evaluate 6 – 3^2 * 6 + 4
• Evaluate (1/4) / (2/3) + 11 * (1/6)
Distributive Property
• 2 ( x + 3) = 2*x + 2*3 = 2x + 6
• (9 – x)*11 = 11*9 – 11*x = 99 – 11x
Be sure to “distribute” the number outside the parenthesis to all
of the terms inside the parenthesis.
Think of the numbers in the parenthesis like siblings, could you
give one sibling something without giving the other one the
same exact thing (without one getting upset)?
Example
• Multiply 4(x + 3y)
Since we don’t know the values for either x or y
then we cannot add those terms together so
we must apply the distributive property.
= 4(x) + 4(3y)
= 4x + 12y This is our final answer as again, we
don’t know the values for x or y so we cannot
further simplify nor combine those terms.
More examples
• Example: Multiply - 2(3x^2 – 4x + 3)
• We will still apply the distributive property,
but this time we apply it to all three terms
within the parentheses.
= (-2)(3x^2) + (-2)(-4x) + (-2)(3)
= -6x^2 + 8x – 6
•
•
•
•
Example:
Evaluate -5(a – 2b)
Evaluate (y/3)(3y – 4x – 6)
Evaluate -3(2x + 3y – 5)
• Questions?