Math - Laws Of Addition And Multiplication

Front 1

Commutative Law of Addition:

Back 1

Let a and b be real number,
a + b = b + a

Front 2

Commutative Law of Multiplication:

Back 2

Let a and b be real numbers,
a•b = b•a

Front 3

Is the commutative law valid for subtraction or division?

Back 3

No, eg., 5+2 = 7; 2+5 = 7 but, 5 - 2 = 3 ≠ 2 - 5. Same thing goes for division.

Front 4

Associative Law of Addition:

Back 4

Let a, b, and c be any real numbers,
(a+b) + c = a + (b + c)

Front 5

Associative Law of Multiplication:

Back 5

Let a, b, and c be any real numbers,
(a•b) • c = a • (b • c)

Front 6

Is the Associative Law valid for subtraction or division?

Back 6

No

Front 7

What are the different types of the Distributive Law?
When does the distributive law not apply?

Back 7

The Distributive Law of Multiplication over addition and the Distributive Law of Multiplication over subtraction. Does not apply to division over addition or subtraction, ie. a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Front 8

Distributive Law of Multiplication over addition:

Back 8

Let a, b, and c be any real numbers,
a(b + c) = (a • b) + (a • c)

Front 9

Distributive Law of Multiplication over subtraction:

Back 9

Let a, b, and c be any real numbers,
a(b - c) = (a • b) - (a • c)

Front 10

Identity property of addition and multiplication:
What is the Identity Element for addition?
What is the Identity Element for multiplication?

Back 10

0 is the Identity Element for for addition, eg. 5 + 0 = 5
1 is the Identity Element for multiplication, eg. 15(1) = 15

Front 11

Identity property of addition:

Back 11

Let a be any real numbers,
a + 0 = a
0 + a = a

Front 12

Identity property of multiplication:

Back 12

Let a be any real number,
a • 1 = a
1 • a = a

Front 13

Inverse property of addition:

Back 13

Let a be a real number,
a + (-a) = 0
-a + (+a) = 0

Front 14

Inverse property of multiplication:

Back 14

Let a be a real number and a is not equal to 0, (if a = 0, then 1 ÷ a is undefined.)
a • 1/a = 1
1/a • a = 1