Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 10: Practice Test on Tutorials 1  9
Problems 1a  1c: Replace ? with < , > ,
or = . 
1a. 5 ? 5
Answer:
Since 5 is to the left of 5 on the number line, then
5 < 5. 
1b. 10 ? 5
Answer:
Since 10 is to the right of 5 on the number line,
then 10 > 5. 
1c. 5 ? 5
Answer:
First of all, 5 = 5.
Next we have 5 = 5.
Since both absolute values equal the same number 5,
then 5
= 5 . 
Problems 2a  2b: Are the following statements
true or false? 
2a.  4 > 4
Answer:
Since  4 is to the left of 4 on the number line, then 
4 <
4.
So, the above statement is false. 
2b.  4 <  4
Answer:
Since  4 is the same number as  4 and the statement
includes where
the two numbers are equal to each other, then this statement is true. 
Problems 3a  3c: Write each sentence as a
mathematical statement. 
3a. 5 is not equal to 5.
Answer:
Reading it left to right we get:
5 is not equal to 5

3b. 2 is less than or equal to 0.
Answer:
Reading it left to right we get:
2 is less than or equal to 0
2 < 0

3c. 7 is greater than 0.
Answer:
Reading it left to right we get:
7 is greater than 0
7 > 0

Problems 4a  4f : List the elements of the
following set
that are also elements of the given set.
{½, 0, 5, , }

4a. Natural numbers
Answer:
The numbers in the given set that are also natural
numbers are
{5, }

4b. Whole numbers
Answer:
The numbers in the given set that are also whole numbers
are
{0, 5, }

4c. Integers
Answer:
The numbers in the given set that are also integers are
{0, 5, }

4d. Rational numbers
Answer:
The numbers in the given set that are also rational
numbers are
{1/2, 0, 5, }

4e. Irrational numbers
Answer:
The number in the given set that is also an irrational
number is
{ }

4f. Real numbers
Answer:
The numbers in the given set that are also real numbers
are
{½, 0, 5, , }

Problems 5a: Write the number as a product of
primes. 
5a. 90
Answer:

Problems 6a: Write the fraction in lowest
terms. 
Problems 7a  7d: Perform the following
operations.
Write answers in the lowest terms. 
Problems 8a  8b: Evaluate. 
Problems 9a  9b: Write each phrase as an
algebraic expression.
Let x represent the unknown number. 
9a. The quotient of 7 and a number.
Answer:
The quotient of 7 and a number

9b. 10 less than 2 times a number.
Answer:
10 less than 2 times a number

Problems 10a  10b: Write each sentence as an
equation.
Let x represent the unknown number. 
10a. The sum of 2 and 10 times a number is the
same as 30.
Answer:
The sum of 2 and 10 times a number is the same as 30

10b. The product of 5 and a number is 2/3.
Answer:
The product of 5 and a number is 2/3

11a. 9 + (10)
Answer:
9 + (10) = 19 
11c. 6.5 + (1.2) + (3.1)
Answer:
6.5 + (1.2) + (3.1) =
5.3 + (3.1) =
2.2 
Problems 12a  12b: Simplify. 
12a. (17)
Answer:
(17) = 17 
Problems 13a  13b: Subtract. 
13a. 15  (3)
Answer:
15  (3) =
15 + 3 =
12 
13b. 1.5  2.5
Answer:
1.5  2.5 =
1.5 + (2.5) =
 4 
Problems 14a  14c: Multiply. 
14a. (5)(12)
Answer:
(5)(12) = 60 
14b. (3)(5)(2)
Answer:
(3)(5)(2) =
(15)(2) =
30 
14c. (15)(0)
Answer:
(15)(0) = 0 
Problems 15a  15c: Divide. 
15b.
Answer:
is undefined. 
Problems 16a  16b: Simplify. 
Problems 17a  17b: Evaluate the
expression. 
17a.
when x = 3 and y = 3.
Answer:

17b.
when x = 2 and y = 2
Answer:

Problems 18a  18b: Decide whether the given number
is a solution
of the given equation. 
18a. Is 1 a solution to 3x  1 =
4?
Answer:
Is 1 a solution?
Since we got a FALSE statement (2 does not equal 4),
then 1 is not
a solution. 
18b. Is 3 a solution to 7  x =
2x + 16?
Answer:
Is 3 a solution?
Since we got a TRUE statement (10 does equal 10), then 3
is a solution. 
Problem 19a: Use a commutative property to
write an
equivalent expression. 
19a. 3a + 2b
Answer:
Using the commutative property of addition (where
changing the order
of a sum does not change the value of it), we get
3a + 2b =
2b + 3a

Problem 20a: Use an associative property to
write an
equivalent expression. 
20a. 8(xy)
Answer:
Using the associative property of multiplication (where
changing the
grouping of a product does not change the value of it), we get
8(xy) = (8x)y

Problems 21a  21b: Use the distributive
property to find
the product. 
21a. 5(a  7)
Answer:

21b. 8(2x + 3y +4z)
Answer:

Problems 22a  22b: Write the opposite (additive
inverse) and the
reciprocal (multiplicative inverse) of each number. 
22a. 10
Answer:
The opposite of 10 is 10, since 10 + 10 = 0.
The reciprocal of 10 is 1/10, since 10(1/10)
= 1. 
22b.
Answer:
The opposite of 4/7 is  4/7, since 4/7 + ( 4/7)
= 0.
The reciprocal of 4/7 is 7/4, since (4/7)(7/4) =
1. 
Problem 23a  23c: The
bar graph
below shows the profit a cd store made over the months of September
through
December of last year. Use the graph to answer questions
23a
 23c.

23a. About how much was the profit in
December?
Answer:
The bar that associates with December is the fourth bar
from the left.
The top of that bar is in between 20 and 25 on the vertical axis.
A good approximation is 22.
The profit in December is about $22000.
23b. Which month had the lowest profit?
Answer:
It looks like October had the lowest profit.
23c. What is the sum of the profits of October and
November?
Answer:
The bar that associates with October is the second bar
from the left.
The top of that bar matches with 5 on the vertical axis.
The bar that associates with November is the third bar
from the left.
The top of that bar matches with 10 on the vertical axis.
The sum of the profits of October and November would
be 5,000 + 10,000
= $15,000. 
Problems 24a  24b: The line graph below shows last
week's high
temperatures in Fahrenheit. Use the graph to answer
questions
24a  24b.

24a. How much was Monday's high
temperature?
Answer:
The point that matches with Monday on the horizontal
axis also matches
85 on the vertical axis.
Monday's high temperature was 85 degrees Fahrenheit.
24b. Which day had the highest high
temperature?
Answer:
It looks like Wednesday had the highest high
temperature. 
Last revised on July 25, 2011 by Kim Seward.
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