Section 4.1 And 4.2 Plus Warm Ups

Chapter 4: Welcome to the Exponential Jungle By Ms. Dewey-Hoffman October 13 th , 2008 There are a ton of notes today, so get settled and get going.

Warm Ups for Chapter 4
Find the Quotient: 147  3 =
Find the Quotient: 273/3 =
Find the Quotient: 450/10 =
Find the Product: 4 • 4 • 4 =
Find the Product: (-2)(-2)(-2) =
Find the Product: (10)(10)(10)(10) =

Warm Ups for Chapter 4
Write TWO numbers, that when multiplied together, give this product:
12
50
36
24

Section 4.1: Divisibility and Factors
One integer is DIVISIBLE by another if the remainder is 0 when you divide.
Divisibility Rules for 2, 5, and 10 .
An integer is divisible by…
2, if it ends in 0, 2, 4, 6, and 8 .
5, if it ends in 0 or 5 .
10, if it ends in 0 .

Examples: Divisibility Rules
Is the first number divisible by the second?
567 and 2?
1,015 and 5?
111,120 and 10?
53 and 2?
1,118 and 2?

Divisibility Rule for 3 and 9.
See if you can pick out the pattern…
Yes Yes Yes Yes 1 + 0 + 1 + 7 = 9 1,017 No No No No 2 + 1 + 5 = 8 215 Yes Yes Yes Yes 4 + 6 + 8 = 18 468 No Yes No Yes 2 + 8 + 2 = 12 282 Is the Number Divisible by: 3? 9? Is the Sum Divisible by: 3? 9? Sum of Digits Number

Divisibility Rule for 3 and 9.
From the pattern we saw before…
An integer is divisible by…
3, if the sum of its digits is divisible by 3 .
9, if the sum of its digits is divisible by 9 .

Example Problems:
Is the first number divisible by the second? Explain.
64 by 9?
472 by 3?
174 by 3?
43,542 by 9?

Finding Factors
One integer is a FACTOR of another integer if it divides that integer with remainder zero.
number number number

Finding Factors
So find all the different combinations of factors
12?
16?
18?
24?
1(12), 2(6), 3(4): so, 1, 2, 3, 4, 6, and 12 1(16), 2(8), 4(4): so, 1, 2, 4, and 16 1(18), 2(9), 3(6): so, 1, 2, 3, 6, 9, and 18 1(24), 2(12), 3(8), 4(6): so, 1, 2, 3, 4, 6, 8, 12, and 24

Word Problem:
There are 20 choral students singing at a school concert. Each row of singers much have the same number of students. If there are at least 5 students in each row, what are all the possible arrangements?

List the positive factors of each number.
10
21
31
1, 2, 5, 10 1, 3, 7, 21 1, 31

Section 4.2: Exponents
You can use EXPONENTS to show repeated multiplication.
(Just like multiplication can show repeated addition).
A POWER has two parts:
A BASE: the factor.
And an EXPONENT: the number of times the base (or factor) is multiplied by itself.

Exponents: Exponential Notation
So show me the EXPANDED version of 2 to the 6 th power. Or 2 6 .
2 • 2 • 2 • 2 • 2 • 2 = 64 = 2 6

Exponents…Show me!
Exponential Notation.
And Value. (The answer).
Twelve to the first power.
Six to the second power, or six squared.
The opposite of the quantity seven to the fourth power.
Negative eight to the fifth power.

Exponential Notation and Answers
Twelve to the first power.
12 1 , 12
Six to the second power, or six squared.
6 2 , 6 • 6 = 36
The opposite of the quantity seven to the fourth power.
-7 4 , - (7 • 7 • 7 • 7) 4 = - (2,401) = -2,401
Negative eight to the fifth power.
(-8) 5 , (-8)(-8)(-8)(-8)(-8) = -32,768

Writing Exponential Notation
Remember to include the Negative Sign.
(-5)(-5)(-5) = (-5) 3
Rewrite the expression using the commutative and associative properties.
-2 • a • b • a • a =
-2 • a • a • a • b = -2a 3 b

Exponents and Negative Integers
So when you multiply 2 negative numbers…what do you get?
A positive number
When you multiply 3 negative numbers…what do you get?
A negative number

Exponents and Negative Numbers
When you multiply an EVEN number of negative integers, the answer will be positive.
When you multiply an ODD number of negative integers, the answer will be negative.

Example Problems
Write these in exponential notation…
6 • 6 • 6 • 6 =
(-3)(-3)(-3) =
4 • y • x • y = 4y 2 x

Word Problem:
A microscope can magnify a specimen 10 3 times. How many times is that?

Example Problems:
Simplify: 6 2
Evaluate: - a 4 , for a = 2
Evaluate: (-a) 4 , for a = 2

Orders of Operations
Work inside the grouping symbols
Simplify any terms with exponents.
Multiply and divide in order from left to right.
Add and subtract in order from left to right.

Example Problem:
4(3+2) 2 =
Grouping Symbols: 3+2 = 5
Exponents: 5 2 = 5 • 5 = 25
Multiplying/Dividing: 4 • 25 = 100.
Addition/Subtraction?: Nope
So, 100 is the answer.

Example Problem:
-2x 3 + 4y, for x = -2 and y = 3.
Substitute Variables: -2(-2) 3 + 4(3)
Grouping Symbols: None
Exponents: (-2) 3 = (-2)(-2)(-2) = -8
-2(-8)+ 4(3)
Multiplication/Division: 16 + 12 = 28
Addition/Subtraction: None
So, 28 is the answer.

Assignment #22:
Pages 174-175: 15-29 Odd.
Pages 178-179: 13-43 Odd.

Section 4.1 And 4.2 Plus Warm Ups

by Middle School on Oct 13, 2008

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Section 4.1 And 4.2 Plus Warm Ups — Presentation Transcript