Mathematical Properties

Reflexive Property

ex) 1=1, y=300

• You must add the same value to both sides of the equals sign to maintain the equality of the values.

• A value is equal to itself.

• Equal values may be placed on either side of the equals sign.

Tags

CCSS.6.EE.A.4

Symmetric Property

ex) x=2 or 2=x

• Equal values may be placed on either side of the equals sign.

• A value is equal to itself.

• If one value equals a second value and the second value equals a third value, then the third value equals the first.

Tags

CCSS.HSA.REI.A.1

Transitive Property

x=y

y=z

x=z

• If one value equals a second value and the second value equals a third value, then the third value equals the first.

• You must multiply the same value to both sides of the equals sign to maintain the equality of the values.

• When solely adding values, you may change the order without changing the result. The same is true for multiplication.

Tags

CCSS.HSA.REI.A.1

Commutative Property

ex)

1 x 4 x 5 = 20

5 x 4 x 1 =20

• Equal values may be placed on either side of the equals sign.

• When solely adding values, you may change the order without changing the result. The same is true for multiplication.

• When dividing values, it is the same thing as multiplying the value in the numerator by the reciprocal of the value in the denominator.

Tags

CCSS.3.OA.B.5

Associate Property

ex) 2 × (3 × 6) = (2 × 3) × 6

• You must add the same value to both sides of the equals sign to maintain the equality of the values.

• A value is equal to itself.

• When solely adding or multiplying values, you may change the groupings of values without changing the result. The groups are separated by parentheses.

Tags

CCSS.6.EE.A.3

Addition Property

ex) x + 3 = y + 3

• You must add the same value to both sides of the equals sign to maintain the equality of the values.

• If the product of two values is zero, one of the values is zero.

• You may multiply a value to a sum by first multiplying the value to the sum’s addends and then adding those products together.

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Multiplication Property

ex) 4(10) = 4(10)

• If one value equals a second value and the second value equals a third value, then the third value equals the first.

• You must multiply the same value to both sides of the equals sign to maintain the equality of the values.

• The quotient of any value and zero is considered undefined.

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Distributive Property

ex) 2(3 + 1) = 2(3) + 2(1) = 6 + 2 = 8

• If the product of two values is zero, one of the values is zero.

• When solely adding values, you may change the order without changing the result. The same is true for multiplication.

• You may multiply a value to a sum by first multiplying the value to the sum’s addends and then adding those products together.

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Definition of Division

ex) (15/5) = 15 x (1/5)

• The quotient of any value and zero is considered undefined.

• When solely adding values, you may change the order without changing the result. The same is true for multiplication.

• When dividing values, it is the same thing as multiplying the value in the numerator by the reciprocal of the value in the denominator.

Tags

CCSS.HSA.APR.D.7

Multiplication Property of Zero

ex) 121× 11 × 7 × 0 = 0

• The quotient of zero and any value (except zero) is zero.

• The product of any value and zero will be zero.

• Equal values may be placed on either side of the equals sign.

Tags

CCSS.7.NS.A.2