Check out this

slideshow made just for YOU…

First, I’d like to say a special thank you to for working

this weekend! I’m proud of your dedication!

Kimberly

For those in Module 1 Lesson 2, we’re going to review the properties of addition and multiplication that you must understand for your mastery assignment.

Examples taken from Yevgeniya Podolyakina

Commutative Property + and x

This property says that you can swap numbers around

and still get the same answer when you add or when you

multiply.

Examples:When adding :

3 + 6 = 6 + 3 = 9When multiplying: 2 × 4 = 4 × 2 = 8

It doesn't matter how you group the numbers when you add or multiply.

(In other words it doesn't matter which you calculate first.)

Example of addition: (6 + 3) + 4 = 6 + (3 + 4)  = 13Because 9 + 4 = 6 + 7 = 13

It makes no difference if you group 6 + 3 or 6 + 4 or 3 + 4 first and then add the third number, when adding, the sum will always end up the same

Associative Property +

Example of multiplication: (2 × 4) × 3 = 2 × (4 × 3)  = 24

8 × 3 = 2 × 12 = 24

It makes no difference if you group 2 × 4 or 2 × 3 or 4 × 3 first and then multiply the third number, when multiplying, the product will always end up the same

Associative Property x

Additive Identity +This property says that when adding Zero to any number, that number is unchanged

a + 0 = 0 + a = a

2 + 0 = 2 0 + 2 = 2

Teddy catches 2 fish from the pond in the morning. Then he goes back in the afternoon but doesn’t catch anymore fish. He has caught 2 fish total for the day.

2 fish + 0 fish = 2

Multiplicative Identity xThis property says that when multiplying any number by 1, that number is unchanged

a × 1 = 1 × a = a 

2 × 1 = 2 1 × 2 = 2

If Teddy catches 2 fish every time he visits the pond and on Monday he only visited the pond once, then he only caught 2 fish on Monday.

2 fish × 1 visit = 2 fish

Multiplication Property of Zero xWhen multiplying any number by zero, the product is always zero

a × 0 = 0 0 × a = 0

4 × 0 = 0 0 × 13 = 0 -8 × 0 = 0 ½ × 0 = 0

Another way to think about the last three properties is in sets or groups

If Stacy has 8 sets of earring and Jody has 0 sets of earring, together they have 8 sets of earrings – Additive Identity [ 8 + 0 = 8]

If after a day of sales a fruit cart only has 1 bunch of 4 bananas left, all together the cart has 4 bananas left - Multiplicative Identity [ 1 × 4 = 4]

If you have ZERO sets or groups of anything, then all together you have NOTHING (zero) – Multiplication Property of Zero [ 0 × 1 = 0]

Inverse Addition Property +

The sum of a number and its opposite is zero.a + (-a) = 0

4 + (-4) 27 + (-27) .476 + (-.476) 4 - 4 27 – 27 .476 - .476 = 0 = 0 = 0 

Inverse Multiplication Property x

The product of any number and its reciprocal equal 1. 1/5 × 5 = 1

b × 1/b = 1 ½ × 2 = 1 2/3 × 3/2 = 1

Since reciprocals are multiplicative inverses, you need to know how to find a reciprocal:

For whole numbers, put 1/number 5 1/5For fractions, flip the fraction over 4/7 7/4

For review of number sets, go to: http://www.mathsisfun.com/sets/number-types.html

When solving literal equations, remember to use opposite operations to move variables.If something is multiplied, divide by it on both sides to move it. If it’s added, subtract it.

Given M=a+th2, you’re asked to solve for t… M-a = a+th2-a M-a = th2 h2 h2

M-a = t h2

• Make sure you’re reading my feedback in the Gradebook before retrying an assignment.

• Remember if you need help, chat with me during my BBIM hours from 4-5pm.

• Call or text me.

• Click on the Peer Tutoring Tab to chat with a peer who can help… OR• Click on the Math III room in Blackboard

for tutors.