1. What number should come next?1, 4, 7, 10, ____

2. What is the 10th term of the sequence?2, 4, 6 ….

3. Translate each phrase into an algebraic expression.a. a number divided by 7

b. the sum of w and 14

4. Evaluate the expression if a = 5, b= 8, c= 05a + bc

Number PropertiesNumber Properties

Today we will be studying various number properties. It is important that you understand how to use them. Think about each property that we discuss and why the rule is true.

Example:2 + 3 = 3 + 2

Rule:For any number a and b, a + b = b + a

Nunc rule- “SWITCH”

Only works for add and multiply

Example:5 x 6 = 6 x 5

Rule:For any number a and b, ab = ba

Example:(3 + 4) + 5 = 3 + (4 + 5)

Rule:For any number a, b,and c, (a + b) + c = a + (b + c)Nunc rule- move the parenthesis

Example:(5 x 6) x 4 = 5 x (6 x 4)

Rule:For any number a, b,and c, (ab)c = a(bc)

Example:5 (3 + 4) = 5(3) + 5(4)

Rule:For any number a, b,and c, a(b+c) = ab + aca(b-c) = ab-ac

Nunc rule- party property

4 (5+6) = 4(5)

Did we touch the operation??

+ 4(6)

8(5+3) = 8(5) + 8(3)

Example:2 + (-2) = 0

Rule:The sum of an integer and its additive inverse is zero.

Example:2 x ½ = 1

Rule:A number times its multiplicative inverse is equal to 1.

Example:10 + 0 = 10

Rule:The sum of an integer and zero is always the integer.

Example:33 x 1 = 33

Rule:The product of an integer and one is always the integer.

QUIZQUIZWhat property is this 25+ 33= 33 +252.What property is move the parenthesis?3.Perform the distributive property 7 (x + y)4. If the temperature is 5 degrees at night and it drops to –

9, how many degrees did it drop?5. A running back carries 4 times and they are… lose 3 yards, gain 5 yards, gain 4 yards, lose 5 yards and

gain 12 yards. What is his total?

commutative

associative

7x + 7y

14

13