Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 28
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36December 2009
What is the value of the expression?
27
34
A
64
B
66
C
132
D
Since the question is asking what the value of the expression is, I know that I need to simplify it.
This looks complicated, but I do recognize all of the operations in the expression.
In order to simplify this expression correctly, I need to use the proper order of operations:
parentheses, exponents, multiplication, division, addition, subtraction.
2+2(3 + 7)
–
73–9
2
3
First, I will carry out what is in the parentheses
and what is in the radical.
3
Then, I will carry out the exponent that is on the 10,
2+2 • 10
–
64
2
3
and the cubed root of 64. I remember that cubed
3
means a number times itself and times itself again.
Sine 4 • 4 • 4 • 4 is 64, the cube root of 64 is 4.
2 + 2 • 100 – 4
Next in order is multiplication and division. Normally
I would look left to right for multiplication and division
3
and perform whichever comes first. I can’t forget
the 2 that was outside of the parentheses.
2 + 200 – 4
3
I do also have a denominator, but I will save that
for last to see if it can be further simplified. Now I will go
202 – 4
to the next operation of addition and subtraction. They follow
the same rule as multiplication and division – whichever
3
comes first from left to right. So, first I will add, then subtract.
198 =
66
Now I am left with a much simpler fraction. I will see if
3
3 198
I can divide 198 by 3.
–18
198 divides evenly by 3, which is 66. The value of the
18
expression is then 66, or answer choice C.
–18
0
Arizona Department of Education
28
Grade 8
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