properties of addition

Properties of Addition

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.

Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4

Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)

Additive Identity Property: The sum of any number and zero is the original 

number. For example 5 + 0 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

decimals to fractions

Decimals to FractionsDecimals to Fractions

(Multiply top and bottom by 10 until you get a whole number, then simplify)

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75

1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100
0.75	=	75
1		100
× 100

(Do you see how it turns the top number 
into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

	÷5		÷ 5
75	=	15	=	3
100		20		4
	÷5		÷ 5

Answer = ³/₄

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Example: Express 0.625 as a fraction

Step 1: write down:

0.625

1

Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

625

1,000

Step 3: Simplify the fraction (it took me two steps here):

	÷ 25		÷ 5
625	=	25	=	5
1,000		40		8
	÷ 25		÷ 5

Answer = ⁵/₈

Example: Express 0.333 as a fraction

Step 1: Write down:

0.333

1

Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

333

1,000

Step 3: Simplify Fraction:

Can't get any simpler!

Answer = ³³³/_1,000

But a Special Note:

If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In this case we would write down:

0.333...

1

Then MULTIPLY both top and bottom by 3:

× 3
0.333...	=	0.999...
1		3
× 3

And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:

(Multiply top and bottom by 10 until you get a whole number, then simplify)

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75

1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100
0.75	=	75
1		100
× 100

(Do you see how it turns the top number 
into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

	÷5		÷ 5
75	=	15	=	3
100		20		4
	÷5		÷ 5

Answer = ³/₄

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Example: Express 0.625 as a fraction

Step 1: write down:

0.625

1

Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

625

1,000

Step 3: Simplify the fraction (it took me two steps here):

	÷ 25		÷ 5
625	=	25	=	5
1,000		40		8
	÷ 25		÷ 5

Answer = ⁵/₈

Example: Express 0.333 as a fraction

Step 1: Write down:

0.333

1

Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

333

1,000

Step 3: Simplify Fraction:

Can't get any simpler!

Answer = ³³³/_1,000

But a Special Note:

If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In this case we would write down:

0.333...

1

Then MULTIPLY both top and bottom by 3:

× 3
0.333...	=	0.999...
1		3
× 3

And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:

Answer = 1/3