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Name_______________________________________ Date__________________ Period _____
MATH 7 CHAPTER 1 PRACTICE TEST
For problem # 1, use both the distributive property and order of operations methods to solve the
problem. Explain why the two methods simplify to equal answers.
O3
1.
Distributive Property
3 (12 - 2 )
3 (12 - 2)
In problems #2 and 3,
a) Decide which method (O3 or Distributive Property) would be easiest,
b) Explain why it’s easier, then
c) SOLVE using ONLY the method that you selected.
Remember: Using the Distributive Property BACKWARDS can be one of your choices.
2. 18 ( 40 + 60 )
a) My choice of method: _______________________________
b) Explanation of choice: ___________________________________________________
________________________________________________________________________
c) Solution using my method (show work below):
__________________
3. 543 (11)
a) My choice of method: _______________________________
b) Explanation of choice: ___________________________________________________
________________________________________________________________________
c) Solution using my method (show work below):
__________________
For problems #4 - 6, solve by using the Distributive Property. Simplify if possible.
4.
5.
6.
12 ( y + 2)
5 ( 2 + x + 3)
Could you have solved #4 & #5 using order of operations? Why or why not?
7. You just solved a numeric expression by using the Distributive Property. The answer was 30.
Now you solve the SAME problem using Order of Operations. What is the answer now? Why?
8. How many counterexamples are there to the Commutative & Associative Properties of
Addition, the Commutative & Associative Properties of Multiplication, and Distributive
Properties?
9. How many counterexamples do you need to show that division is not Commutative? Why?
Justify:
10.
96 + 15 + 4 + 85 = 96 + 4 + 15 + 85
________________________________
(96 + 4) + (15 + 85)
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100 + 100
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200
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Simplify:
11)
054
12.
541
13.
154
14.
540
Use the following word bank to help you answer problems #15 – 17. Some answers are NOT in
the word bank!
constant
variable
algebraic or variable expression
numerical expression
coefficient
15.
7 + y is a combination of a constant, a variable, and at least
one operation so it is an __________________________________ and should be
properly rewritten as _________________.
16.
In 7 + 2y, the 7 is the ___________ or a number that never changes, the 2 is the
___________________________, the y is a ______________ or a value that
changes based on what you substitute.
17.
7 + 2 is called a _____________________________________,
since there are no variables.
18.
Algebraically, the expression 2a 3 should be rewritten as ____________.
19.
Rewrite the product (y)(5) properly _________
Simplify the following expressions. NO WORK = NO CREDIT!
20.
12 ÷ 2  6 + (4 + 2)
21.
9 + 3 (33) ÷ 9 . 3
22.
[40 - (25 + 5)] (5 + 1) - 3 + 8
23.
{ 5 + [ (7 - 1) ÷ 3]  2 }
24.
12
- 3

2
+ 30
0
25. Although generally order of operations should be used to simplify, there are times when you
can choose to simplify in a different way. For the following scenarios, please JUSTIFY which
mathematical property allows you to change the way you simplify.
a.
5 ( 10 + 6) Order of operations states to do the parentheses first, but you decide to do
the following: 5(10) + 5(6). JUSTIFY: _________________________________
b.
(11 + 7) + (23 + 9) Order of operations states do the parentheses first but you decide
to change the problem to this: (11 + 9) + (7 + 23).
JUSTIFY: __________________________________________________________
c. (253)(5)(2)
For the problem above, use your properties to change the problem TO MAKE THE MATH
EASIER: _________________________________________________________
JUSTIFY:_________________________________________________________
26.
Give the FORMAL math word for the answer you get for each operation:
a.
addition
_______________________
b.
multiplication
_______________________
c.
subtraction
_______________________
d.
division
_______________________
27.
Can you evaluate the expression 5 + b? If not, state why.
28.
Evaluate the following expressions where
x = 5, y = 4, and z = 3.
a.
xyz
b.
b-b
In problem #30, use the commutative and associative properties to simplify the problem. State
which property(ies) you used.
29.
(17 + 84) + (83 + 54) + 16 + 46
30.
Give your own real life example of the commutative property.
31.
Give an example from real life that could not possibly be commutative.
32. Give a counterexample (a math one – not real life!) to prove that subtraction is not
commutative.
33.
Give a counterexample to prove that division is not commutative.
EXTRA CREDIT
1.
Give a counterexample to prove that subtraction is not associative.
2.
Give a counterexample to prove that division is not associative.
3. Word attack the following (Give the root word that tells you why they make sense):
Evaluate
Numerical
Variable
Equation
Commutative
Associative
Distributive
4.
(115) (23) = 23 (115)
_________________________________
23 (100 + 15)
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23 (100) + 23 (15)
_________________________________
2,300 + 23 (15)
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2,300 + 15 (23)
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2,300 + 15 (20 + 3)
_________________________________
2,300 + 15 (20) + 15 (3)
_________________________________
2,300 + 300 + 45
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(2,300 + 300) + 45
_________________________________
2,600 + 45
__________________________________
2,645
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