Ms. Hannafey's Math Class

We use ratios to make comparisons between two things. When we express ratios in words, we use the word "to" -- we say "the ratio of something to something else"





These are all equivalent ratios 3:6 = 12:24 = 6:12 = 15:30



A rate is a ratio that is used to compare different kinds of quantities.

A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Some common unit rates are miles (or kilometers) per hour, cost per item, ea...

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Inverse Property of Addition
Any addend added to its negative will have a sum of zero
Ex: 5 + -5 = 0

Inverse Property of Multiplication
any factor multiplied by its reciprocal will have a product of 1.

Ex: 6 x 1/6 = 1

Zero Property of Multiplication
Any factor times 0 is 0
Ex: 5 x 0 = 0

Identity Property of Addition
Any number added to 0 equals 0
Ex:  7 + 0 = 7

Identity Property of Multiplication
any number multiplied by 1 equals itself.
Ex: 12 x 1 = 12
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The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

4 × (2 + 3) = (4 × 2) + (4 × 3)

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Associative Properties

• Associative Property of Addition

o When adding 3 or more numbers, changing the grouping does not change the sum.

(3 + 4) + 5 =  3 + (4 + 5)

7 + 5 = 12    3 + 9 = 12

• Associative Property of Multiplication

o When multiplying any 3 numbers, changing the grouping does not change the product.

(3 x 4)x 5= 3x(4 x 5)

12 x 5 = 60       3 x 20 = 60

Commutative Properties

• Commutative Property of Addition

o When adding any 2 or more numbers, changing the or...

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In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.



What is standard notation? This is a number written using digits. Numbers as they should appear

What is expanded notation? expanded notation is when each digit is multiplied by its place value.
Ex: 435 = (4 x 100) + (3 x 10) + (5 x 10)  or 400 + 30 + 5

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