Properties of Real Numbers

1

100

Multiplying any number by zero give you zero back.

multiplicative property of zero

200

if 3=2+4 then 2+4=3 (if a=b then b=a)

symmetric

300

when three of numbers or multiplied or added, the outcome is the same regardless of the way they are grouped. for example a(bc)=(ab)c or a+(b+c)=(a+b)+c

associative

400

when two or more numbers are added or multiplied the outcome is the same regardless of the order in which you add or multiply them.

communative

500

if a=b and b=c then a=c

transitive

2

100

the sum of any number and zero is the original number

additive identity

200

when a number is multiplied by its reciprocal you get 1

multiplicative inverse

300

when you multiply a number by 1 you get the same number back

multiplicative identity

400

adding a number and its negative together yields 0

additive inverse

500

a=a or 2+3=3+2

reflexive

3

100

a number being multiplied by a sum for example a(b+c)=ab+ac

distributive

200

Which property allows you to group numbers that you are multiplying or adding in different ways?

Associative

300

Both addition and multiplication have this type of property that basically says when you add or multiply this special number by any other number, the other number is not changed. (for addition this special number is 0, and for multiplication, this special number is 1)

identity

400

What type of property is shown by the following examples? a + (-a) = 0 a x 1/a = 1

Inverse

500

Use the distributive property to simplify: (3x - 7)2

6x-14

4

100

Simplify 5x - 3x + 5

2x + 5

200

Simplify 4x + 9 - 6x +7

-2x + 16 or 16 - 2x or 16 + (-2x)

300

a quantity may be substituted for its equal in any expression

substitution

400

if n=2 then 3n=3*2=6

substitution

500

14*1=14

multiplicative identity

5

100

3+0=3

additive identity

200

7*0=0

Multiplicative property of zero

300

4+7=7+4

reflexive

400

if 8=2+6 then 2+6=8

symmetric

500

3-3=0

additive inverse