Name: ____________________________________
Lesson 2.5 – Number Properties
1. Say whether each equation is true or false
a. 8 + 0 = 8
e. 24 + 0 = 24
b. 8 + 0 = 80
f. 24 + 0 = 240
c. 8 + 0 = 0
g. a + 0 = a
d. 8 = 8 + 0
2. When you add 0 to a number what is the result?
3. Say whether each equation is true or false.
a. 5  1  5
e. 25  1  25
b. 5  1  50
f. 25  1  1
c. 5  1  15
g. a 1  a
d. 5  1  1
4. When you multiply a number by 1 what is the result?
5. Say whether each equation is true or false (show if it’s true or false for a-d!)
a. 5 + 1 = 1 + 5
d. 9 – 3 = 3 – 9
b. 9 + 3 = 3 + 9
e. a + b = b + a
c. 5 – 1 = 1 – 5
f. a – b = b – a
6. When you add two numbers together, what happens to the sum if you change the order of the numbers?
7. When you subtract one number from another number, what happens to the difference if you change the
order of the numbers?
8. Say whether each equation is true or false (show if it’s true or false for a-d!).
a. 5  1  1  5
d. 9  3  3  9
b. 9  3  3  9
e. ab  ba
c. 5  1  1  5
f. a  b  b  a
9. When you multiply two numbers together, what happens to the product (answer) if you change the order
of the numbers?
Name: ____________________________________
10. When you divide one number by another, what happens to the quotient (answer) if you change the order
of the numbers?
11. Say whether each equation is true or false (show your work for a-d!)
a. (4 + 3) + 2 = 4 + (3 + 2)
d. (5  3)  7  5  (3  7)
b. (5 + 3) + 7 = 5 + (3 + 7)
e. (a  b)  c  a  (b  c)
c. (4  3)  2  4  (3  2)
f. (a  b)  c  a  (b  c)
12. When you add more than two numbers together, what happen to the sum if you group the numbers
differently using parentheses?
13. When you multiply more than two numbers together, what happens to the product if you group the
numbers differently using parentheses?
14. In this table are the first six number properties of Algebra. These properties are always true for all
numbers.
I would like you to re-copy the table exactly how you see it into your notebooks. For each property,
add your own example using numbers instead of variables. Put a title at the top of the page that says
“The Number Properties.” (Copy it nicely and use fun colors if you’d like!)
Leave room at the end to add more later!!
Properties of Addition
Properties of Multiplication
The Identity Property of Addition
a0  a
Ex: _____________
The Commutative Property of Addition
ab  ba
Ex: ______________
The Associative Property of Addition
(a  b)  c  a  (b  c)
Ex: ____________________
The Identity Property of Multiplication
a 1  a
Ex: ___________
The Commutative Property of Multiplication
ab  ba
Ex: ___________
The Associative Property of Multiplication
(a  b)  c  a  (b  c)
Ex: _______________________
Name: ____________________________________
15. 0 is often called the additive identity. Why do you think this is true?
16. 1 is often called the multiplicative identity. Why do you think this true?
17. Dwayne said that the equation 10  20  20  10 is true because 10  20 has the same value as 20 10 .
Rosa said that the equation is false because 10  20 does not have the same value as 20 10 .
Who is correct? Say why.
18. Say whether each equation is true or false. For each false equation, explain why it is false.
15
15
 15  (3  2)
 2  15  3  2
a.
c.
3 2
3
b.
15
 15  3  2
3 2
d.
15
 2  15  (3  2)
3
19. Decide whether each equation is true or false.
For each true equation, write the number property shown by the equation
a. 0 + 6 = 6
f. 8  1  8
b. 6 + 0 = 60
g. (2  3)  4  2  (3  4)
c. 3  7  7  3
h. 5 + 9 = 9 + 5
3 7

7 3
i. 5 – 9 = 9 – 5
d.
e. (3 + 9) + 8 = 3 + (9 + 8)
Name: ____________________________________
20. An inverse is ________________________________________________________________________
21. The inverse of an action undoes that action. List as many words as you can think of that mean the same
thing as “inverse” (they don’t have to be math words!!)
22.
a. What is the inverse of division?
b. What is the inverse of addition?
c. What is the inverse of multiplication?
d. What is the inverse of subtraction?
23. Write the inverse of each of these actions or operations:
a. Multiplying by 7
b. Subtracting
d. Dividing by
2
3
e. Subtracting
1
2
1
2
c. Dividing by 2
Using the Inverse to Divide:
24. –a is called additive inverse of a
1
is called the multiplicative inverse or reciprocal of a
a
a. What is the additive inverse of 2?
b. What is the multiplicative inverse of 2?
c. What is the additive inverse of
1
?
2
d. What is the multiplicative inverse of
1
?
2
Evaluate
3
5
x
for x   and y  
4
2
y