Transcript Properties and Mental Math

2-1 Properties and Mental Math
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-1 Properties and Mental Math
Warm Up
Find each sum or product.
1. 17 + 15
32
2. 29 + 39 68
3. 8(24)
192
4. 7(12)
5. 3(91)
84
273
6. 6(15)
90
2-1 Properties and Mental Math
Problem of the Day
Determine the secret number from the
following clues:
• The number is a multiple of 5.
• It is divisible by 3.
• It is less than 200.
• Its tens digit equals the sum of its
other two digits.
165
2-1 Properties and Mental Math
Sunshine State Standards
MA.6.A.3.5 Apply the Commutative,
Associative, and Distributive Properties to
show that two expressions are equivalent.
2-1 Properties and Mental Math
Vocabulary
Commutative Property
Associative Property
Distributive Property
2-1 Properties and Mental Math
Mental math means “doing math in
your head.”
Many mental math strategies use
number properties that you already
know to make equivalent expressions
that may be easier to simplify.
2-1 Properties and Mental Math
COMMUTATIVE PROPERTY (Ordering)
Words
Numbers
You can add or multiply
numbers in any order.
18 + 9 = 9 + 18
15  2 = 2  15
2-1 Properties and Mental Math
ASSOCIATIVE PROPERTY (Grouping)
Words
When you are only
adding or only
multiplying, you
can group any of
the numbers
together.
Numbers
(17 + 2) + 9 = 17 + (2 + 9)
(12  2)  4 = 12  (2  4)
2-1 Properties and Mental Math
Caution!
The Commutative and Associative
Properties do not apply to subtraction
or division.
2-1 Properties and Mental Math
Additional Example 1A: Using Properties to
Add and Multiply Whole Numbers
Simplify 17 + 5 + 3 + 15.
17 + 5 + 3 + 15
Look for sums that are
multiples of 10.
17 + 3 + 5 + 15
Use the Commutative Property.
Use the Associative
(17 + 3) + (5 + 15) Property to make groups
of compatible numbers.
20 + 20
40
Use mental math to add.
2-1 Properties and Mental Math
Additional Example 1B: Using Properties to
Add and Multiply Whole Numbers
Simplify 4  13  5.
4  13  5
Look for products that are
multiples of 10.
13  4  5
Use the Commutative Property.
13  (4  5)
Use the Associative Property to
group compatible numbers.
13  20
Use mental math to multiply.
260
2-1 Properties and Mental Math
Helpful Hint
The expressions in each row of example 1B are
equivalent because they have the same value.
2-1 Properties and Mental Math
Check It Out: Example 1A
Simplify 23 + 8 + 12 + 7.
23 + 8 + 12 + 7
= 23 + 7 + 8 + 12
= 30 + 20
= 50
2-1 Properties and Mental Math
Check It Out: Example 1B
Simplify 49 + 17 + 51.
49 + 17 + 51
= 49 + 51 + 17
= 100 + 17
= 117
2-1 Properties and Mental Math
Check It Out: Example 1C
Simplify 6 × 33 × 5.
6 × 33 × 5
= 6 × 5 × 33
= 30 × 33
= 990
2-1 Properties and Mental Math
Check It Out: Example 1D
Simplify 2 × 69 × 5.
2 × 69 × 5
= 2 × 5 × 69
= 10 × 69
= 690
2-1 Properties and Mental Math
DISTRIBUTIVE PROPERTY
Words
Numbers
To multiply a number
6  (10 + 4) = (6  10) + (6  4)
by a sum, multiply
= 60
+
24
by
each number in the
=
84
sum and then add.
2-1 Properties and Mental Math
When you multiply two numbers, you can
“break apart” one of the numbers into a sum
and then use the Distributive Property.
2-1 Properties and Mental Math
Additional Example 2A: Using the Distributive
Property to Multiply
Use the Distributive Property to find the product.
6  35
6  35 = 6  (30 + 5)
“Break apart” 35 into 30 + 5.
= (6  30) + (6  5)
Use the Distributive Property.
=
Use mental math to multiply.
=
180
+
210
30
Use mental math to add.
2-1 Properties and Mental Math
Additional Example 2B: Using the Distributive
Property to Multiply
Use the Distributive Property to find the product.
9  87
9  87 = 9  (80 + 7)
“Break apart” 87 into 80 + 7.
= (9  80) + (9  7)
Use the Distributive Property.
=
Use mental math to multiply.
=
720
+
783
63
Use mental math to add.
2-1 Properties and Mental Math
Check It Out: Example 2A
Use the Distributive Property to find each
product.
6  71
6  71 = 6  (70 + 1)
= 6  70 + 6  1
= 420 + 6
= 426
2-1 Properties and Mental Math
Check It Out: Example 2B
Use the Distributive Property to find each
product.
28  5
28  5 = (20 + 8)  5
= 20  5 + 8  5
= 100 + 40
= 140
2-1 Properties and Mental Math
Check It Out: Example 2C
Use the Distributive Property to find each
product.
8  44
8  44 = 8  (40 + 4)
= 8  40 + 8  4
= 320 + 32
= 352