chapter 4.1 and 4.2

Agenda Monday, Nov. 9

Homework 2 p. 182 # 22 - 30p. 188 # 3 - 6, 8 - 11, 16 - 23,

36 - 39

Do NowWrite down all the divisibility rules you know.

Example: a number is divisible by 2 if it ends in 0, 2, 4, 6, or 8

Divisibility rules Exponents

Daily Scribe - Danielle

a number is divisible by 9 if the sum of its digits is divisible by 9

The Magic Tunnel!

grab a number and slide through

the tunnel to determine the divisibility rule

a number is divisible by 3 if the sum of its digits is divisible by 3

a number is divisible by 5 if it ends in 0 or 5

a number is divisible by 10if it ends in 0

a number is divisible by 4 if it's last two digits are divisible by 4

a number is divisible by 2 if it ends in 0, 2, 4, 6, 8

Factors

··one integer divides into another number with a remainder of zero··example: factors of 6 are 1, 2, 3, 6

List the positive factors of:

1. 10 1, 2, 5, 10

2. 21 1, 3, 7, 21

3. 24 1, 2, 3, 4, 6, 8 ,12 ,24

4. 31 1, 31

Exponents

··exponents can be used to show repeated multiplication; 25 = 2 * 2 * 2 * 2 * 2··a power has two parts··a base and an exponent··the expression 32 is read "three to the second power

Examples

1. 5 * 5 * 5 = 53

2. (-3)(-3) = (-3)2 read as negative three to the second power

When expression involve variables:

4. 4 * b * a * b = 4ab2

5. -3 * x * x * y * y = -3x2y2

read as the opposite of three times x squared times y squared

Write the expression using exponents.

1. 4 * 4 * 4 43

2. 3 * x * y * y3xy2

-x4 means the opposite of x to the fourth power

(-x)4 means negative x to the fourth power

Evaluate each for x = 2

-24 = -2 * 2 * 2 * 2 = -16

(-2)4 = (-2)(-2)(-2)(-2) = 16

You try: Evaluate -x4 and (-x)4, for x = 3

-x4 = -34 = -3 * 3 * 3 * 3 = -81

(-x)4 = (-3)4 = (-3)(-3)(-3)(-3) = 81

Using Order of Operations

Simplify 2(3 + 4)2

2(7)2 Parenthesis2*49 Exponents 98

Evaluate -3x3 + 4y for x = -2 and y = 4

-3(-2)3 + 4 * 4

-3 * -8 + 4 * 4 24 + 16

40

Your turn.

1. Simplify 2 * 52 + 4 * (-3)3

2 * 25 + 4 * -27

50 + - 108 -58

2. Evaluate 3a2 + 6, for a = -5

3(-5)2 + 6 3 * 25 +

6 75 + 6

81

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