# Properties of Real Numbers

```Name: ____________________________________________ Date: _______________ Block: ______
Learning Target 7.16: The student will apply
the following
properties of operations with real numbers:
the distributive property;
and the multiplicative property of zero.
Properties of
Real Numbers
Associative vs. Commutative
Associative Properties
Numbers being added may be regrouped
without affecting the final sum.
Associative Property of Multiplication
Numbers being multiplied may be regrouped
without affecting the final product.
Commutative Properties
Changing the order of the numbers being
added will not change the final sum.
Commutative Property of Multiplication
Changing the order of factors being multiplied
will not change the final product.
What makes associative and commutative different?
__________________________________________________________
Commutative &amp; Associative Properties
Match-draw a line to the correct definition.
1. Commutative Property
2.
Associative Property
a. When adding or multiplying multiple numbers, the
order stays the same, but the grouping changes.
b. When adding or multiplying multiple numbers the
same.
Identify if the equation is an example of the commutative or associative property. Use the following:
3. 6+5=5+6_____________________
4. 2(6∙7)=(2∙6)∙7_________________
Commutative of multiplication
Associative of multiplication
Complete the process for the
Commutative Property
Ex: 5+6 = 6+5
5. 8∙3=3∙8______________________
12.12+14=______________________
6. 14+(22+6)=(14+22)+6__________
13. ab=_________________________
7. 7+16=16+7___________________
14.5∙8=_________________________
8. ab=ba_______________________
15.b+a=________________________
9. a+(b+c)=(a+b)+c______________
Complete the process for the Associative
Property
16.2(5∙8)=______________________
10.m+n=n+m____________________
11.a (bc)=(ab)∙c__________________
17.(5+9)+7=_____________________
18.a+(b+c)=_____________________
19.(ab)∙c=_______________________
20.7(8∙9)=______________________
Distributive Property
Definition:
This property is used to multiply a number by the sum or difference of two numbers in
parentheses. The first number is “distributed” across the parentheses by multiplying it
with both of the numbers inside the parentheses.
Examples:
How can you use the Distributive Property to multiply large numbers?
3 • 34
1.)
3.)
5 (4 + 6)
6 • 47
______________
8 • 103
2.)
8 (12 – 5) _______________ 4.)
–6 (12 + 3) _______________
y (2 – x)
__________________
7.)
9 (13) – 9 (3) = _______________
8.) 4 (11) + 4 (14) = __________
22.)
4(12 + 15)
23.)
3(a + 2b)
24.)
x (6 + 8)
25.)
6(9 – r)
26.)
15(p – 2q)
27.)
9(f – 3e)
28.) Create your own distributive problem.
```