Commutative Property
Write an addition expression that shows the commutative property of addition.
Changing the order of the addends does not change the sum.
Example:
4 + 12 + 10 = 10 + 12 + 4
4 + 12 + 10 = 26
10 + 12 + 4 = 26
Write an addition expression that shows the associative property of addition.
Changing the grouping of the addends does not change the sum.
Example:
4 + (12 + 10) = (4 + 12) + 10
4 + 22 = 26
16 + 10 = 26
Write an addition expression that shows the addition property of zero.
Adding zero to a number doesn't change its value.
Examples:
8 + 0 = 8
4,567 + 0 = 4,567
Write an expression that shows the distributive property.
Multiplying an addition or subtraction expression is the same as multiplying the parts, then adding or subtracting them.
Examples:
5 x 23 = 5 x (20 + 3) = (5 x 20) + (5 x 3)
5 x 19 = 5 x (20 - 1) = (5 x 20) - (5 x 1)
What is the order of operations?
1. ___________________
2. ___________________
3. ___________________
1. Perform operations in Parentheses ()
2. Multiply and divide from left to right x ÷
3. Add and subtract from left to right + -
49 + 8 + 21 = ?
49 + 8 + 21 = 49 + 21 + 8
↓
70 + 8 = 78
(19 + 14) + 6 = ?
(19 + 14) + 6 = 19 + (14 + 6)
↓
19 + 20 = 39
Write a multiplication expression that shows the multiplication property of zero.
Multiplying a number by zero will always equal zero.
Examples:
5 x 0 = 0
1,987,654 x 0 = 0
6 x 14 = 6 x ( __ + __ )
( __ x __ ) + ( __ + __ )
___ + ___ = ____
6 x 14 = 6 x (10 + 4)
(6 x 10) + (6 + 4)
60 + 24 = 84
Solve this expression using the order of operations:
(10 + 12) ÷ 2 - 4
(10 + 12) ÷ 2 - 4
↓
22 ÷ 2 - 4
↓
11 - 4 = 7
Write an expression that shows the commutative property of multiplication.
Changing the order of the factors does not change the product.
Example:
2 x 3 x 8 = 8 x 3 x 2
2 x 3 x 8 = 48
8 x 3 x 2 = 48
Write a multiplication expression that shows the associative property of multiplication.
Changing the grouping of the factors does not change the product.
Example:
2 x (3 x 8) = (2 x 3) x 8
2 x 24 = 48
6 x 8 = 48
Write a multiplication expression that shows the multiplication property of one.
Multiplying a number by one doesn't change its value.
Examples:
5 x 1 =5
9,999,999,999,999 x 1 = 9,999,999,999,999
12 x 28 = 12 x ( ___ - __ )
( __ x ___ ) - ( __ x __ )
___ - ___ = ___
12 x 28 = 12 x (30 - 2)
(12 x 30 ) - (12 x 2)
360 - 24 = 336
Solve this expression using the order of operations:
10 + 12 ÷ 2 - 4
10 + 12 ÷ 2 - 4
↓
10 + 6 - 4 = 12
6 x 9 x 5 = ?
6 x 9 x 5 = 6 x 5 x 9
↓
30 x 9 = 270
5 x (2 x 7) = ?
5 x (2 x 7) = (5 x 2) x 7
↓
10 x 7 = 70
6 + 0 x 100 + 10 = ?
6 + 0 x 100 + 10
↓
6 + 0 + 10
↓
6 + 10 = 16
8 x 109 = 8 x ( ___ + __ )
( __ x ___ ) + ( __ x __ )
___ + ___ = ___
8 x 109 = 8 x ( 100 + 9 )
( 8 x 100 ) + ( 8 x 9 )
800 + 72 = 872
Solve this expression using the order of operations:
10 - 12 ÷ (2 + 4)
10 - 12 ÷ (2 + 4)
↓
10 - 12 ÷ 6
↓
10 - 2 = 8