Download Properties of Numbers

Properties of Real Numbers
Objective: Identify and use properties of real
numbers.
The Commutative Property
• You can add and multiply real numbers
in any order.
•
Examples:
2+7=7+2
3●9=9●3
• Algebraically:
a+b=b+a
ab = ba
The Commutative Property
• Commute: to move to and from
Think of commuting to and from school.
Just like you moving from one place to the
other, numbers can too!
State whether each situation below is commutative
or not commutative.
1) Waking up in the morning and going to school.
not commutative
2) Brushing your teeth and combing your hair.
commutative
3) Putting on your socks and putting on your
shoes.
not commutative
4) Eating cereal and drinking orange juice.
commutative
The Associative Property
• You can regroup real numbers when
you add and multiply.
•
Examples:
(6 + 8) + 2 = 6 + (8 + 2)
(7 ● 4) ● 5 = 7 ● (4 ● 5)
• Algebraically:
(a + b) + c = a + (b + c)
(ab)c = a(bc)
The Associative Property
• Associate: to keep company, as a friend
Think of associating with your friends: you
hang out with them and stick together.
Numbers in parentheses are grouped, or
friends!
Commutative vs. Associative
Identify each property shown below.
1) 7 + 4 = 4 + 7
Comm. Prop. Of Add.
2) 6  (2  8)  (6  2)  8 Assoc. Prop. Of Mult.
3) 5  9  9  5 Comm. Prop. Of Mult.
4) (4 + 2) + 3 = (2 + 4) + 3 Comm. Prop. Of Add.
Identity Property of Addition
• The sum of 0 and any
number is the number
• Example with
numbers: 4 + 0 = 4
• Algebraic example:
a+0=a
Identity Property of Multiplication
 The product of 1 and any
number is the number
 Example with numbers:
8x1=8
 Algebraic example:
ax1=a
The Distributive Property
• Multiply the outside value with the
quantity in the parentheses.
• Examples:
3(4 + 8) = 3(4) + 3(8)
3(12)= 12 + 24
36 = 36
• Algebraically:
a(b + c) = ab + ac
a(b – c ) = ab – ac
The Distributive Property
• Distribute: to spread out, to share
Think of mail. The postal worker must
distribute all letters to the houses. One
person, many houses: One number to all
numbers in the parentheses!
The Distributive Property
•
Use the Distribute Property to rewrite and/or solve.
1) 9(52)
2) 12(98)
3) 7(34)
Simplify using the distributive property.
1) 5(x  3)
4) 4(3  y)
5 x  5  3
43 4 y
12  4y
5x  15
2) 6(y  7)
6  y  6 7
6y  42
5) 10(x  7)
3) 3(m  8)
3 m  3  8
6) 4(k  2)
4 k  4 2
3m  24
10  x  10  7
10x  70
4k  8
Simplify using the distributive property.
1) 4(x  7)
4) 7(8  x)
4  x  4 7
78 7 x
4x  28
2) y(y  3)
y y  y3
y  3y
2
3) x(2x  9)
x  2x  x  9
2x  9x
2
56  7x
5) x(a  b  c)
xa  xb xc
ax  bx  cx
6) 4(3  m  k)
43 4 m  4 k
12  4m  4k
Which Property is Represented?
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1 + (6 + 7) = (1 + 6) + 7
1 x 10 = 10
3x5=5x3
6+0=6
4 x (4 x 2) = (4 x 4) x 2
x+y=y+x