1.3 Properties of Numbers

1.3 Properties of Numbers

8-30-22

Reflexive Property

​

​

5=5

​

4+7 = 4+7​

​Examples

Any number is equal to itself.

​Definition

If 2+6 = 8 then 8 = 2+6

​

If 2​(5) = 10 then 10 = 2(5)

Examples

If one quantity equals a second quantity, then the second quantity equals the first.

​Definition

Symmetric Property

If 6+9 = 3+12

and 3+12=15

​

then 6+9=15​

​Example

If one quantity equals a second quantity and the second equals the third quantity... then the first quantity also equals the third.

​Definition

Transitive Property

​Examples

A quantity may be substituted for its equal in any expression.

​Definition

Substitution Property

if x=11

​

then​ 4+x can be wrote as 4+11

Multiple Choice

Which property does 2+7=2+7 represent?

• Reflexive

• Symmetric

• Transitive

• Substitution

Multiple Choice

Which property does "If 1+2=3 then 3=2+1" represent?

• Reflexive

• Symmetric

• Transitive

• Substitution

3+0=3

​

0+5=5​

​Examples

For any number x, the sum of x and 0 is x.

​Definition

Additive Identity

3+(-3)=0

​

4-4=0

​

-2+2=0​

​Examples

A number and its opposite are additive inverses of each other. (equals zero)

​Definition

Additive Inverse

5(1)=5

​

1(10)=10​

​Examples

For any number x, the product of x and 1, is x.

​Definition

Multiplicative Identity

6(0)=0

​

0(7)=0

​

300(0)=0​

​Examples

For any number x, the product of x and zero is x.

​Definition

Multiplicative Property of Zero

​Examples

​Definition

Multiplicative Inverse

Multiple Choice

Which property does "5(1)=5" represent?

• Additive Identity

• Multiplicative Identity

• Multiplicative Inverse

• Additive Inverse

Multiple Choice

Which property does "3+0=3" represent?

• Additive Identity

• Multiplicative Identity

• Multiplicative Inverse

• Additive Inverse

6+7=7+6

​

5(4)=4(5)

​

4+1+2=2+4+1​

​Examples

The order in which you ADD or MULTIPLY numbers does not change the solution.

​Definition

Commutative Property

​Examples

The way you group three or more numbers when ADDING or MULTIPLYING does not change the solution.

​Definition

Associative Property

Multiple Choice

Which represents the commutative property?

• 4+2 = 4+2

• 3-1 = 1-3

• 2+4 = 4+2

• (1+3)+2 = 1+(3+2)

Multiple Choice

Which represents the associative property?

• 2+5 = 5+2

• (1-2)-4 = 1-(2-4)

• 5+(1+3) = (5+1)+3

• 5(2) = 2(5)

Evaluate Using Properties

Some text here about the topic of discussion

Multiple Choice

Evaluate $$5\cdot7\cdot4\cdot2$$  

• 280

• 360

• 120

• 340