COLLEGE ALGEBRA FINAL MILESTONE WITH CORRECT ANSWERS AND STEP-BY-STEP RATIONALES
2025/2026
1
Which of the following equations is correctly calculated?
•
-2 × -7 = -14
•
81 ÷ -9 = -9
•
-36 ÷ 4 = 9
•
4 × 12 = -48
RATIONALE
This is correct. The quotient of a positive and negative
number is always negative.
This is incorrect. The product of two negative numbers is
always positive. The correct product is 14.
, This is incorrect. The quotient of a positive and a
negative number is always negative. The correct quotient
is -9.
This is incorrect. The product of two positive numbers is
always positive. The correct product is 48.
CONCEPT
Multiplying and Dividing Positive and Negative Numbers
2
Select the solution to the following system of equations:
•
•
correct
•
•
RATIONALE
,Before you can add equations, sometimes you
must multiply entire equations by a scalar value for
the method to work as intended. For this system,
we can multiply the second equation by .
Here, by multiplying by , the result
contains a term, which will cancel when
combined with the second equation. Now, we can
add the two equations together.
When we add the two equations, the term will
cancel, leaving . Now we can solve for by
dividing both sides by .
Once we divide both sides by , we get a
solution of . We can solve for by plugging
in for in either equation.
Let's use the second equation . Once
is plugged in for , evaluate and solve for .
Subtracting a negative is the same as adding a
postive . Next, subtract from both sides.
On the right side, minus equals . Now we
can solve for by dividing both sides by .
Dividing by gives a solution of .
, This is the solution to the system of equations.
CONCEPT
Solving a System of Linear Equations using the Addition Method
3
Perform the following operations and write the result as a single
number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
•
10 correct
•
10.8
•
2
•
1.8
RATIONALE
Following the Order of Operations, we must first
evaluate everything in parentheses and grouping
symbols. When there are brackets or braces, evaluate
the innermost operations first. Here, we must evaluate
5 minus 3 first.
5 minus 3 is 2. There are still operations inside
grouping symbols to evaluate. Multiplication comes
before addition, so we must evaluate 8 times 2 next.
2025/2026
1
Which of the following equations is correctly calculated?
•
-2 × -7 = -14
•
81 ÷ -9 = -9
•
-36 ÷ 4 = 9
•
4 × 12 = -48
RATIONALE
This is correct. The quotient of a positive and negative
number is always negative.
This is incorrect. The product of two negative numbers is
always positive. The correct product is 14.
, This is incorrect. The quotient of a positive and a
negative number is always negative. The correct quotient
is -9.
This is incorrect. The product of two positive numbers is
always positive. The correct product is 48.
CONCEPT
Multiplying and Dividing Positive and Negative Numbers
2
Select the solution to the following system of equations:
•
•
correct
•
•
RATIONALE
,Before you can add equations, sometimes you
must multiply entire equations by a scalar value for
the method to work as intended. For this system,
we can multiply the second equation by .
Here, by multiplying by , the result
contains a term, which will cancel when
combined with the second equation. Now, we can
add the two equations together.
When we add the two equations, the term will
cancel, leaving . Now we can solve for by
dividing both sides by .
Once we divide both sides by , we get a
solution of . We can solve for by plugging
in for in either equation.
Let's use the second equation . Once
is plugged in for , evaluate and solve for .
Subtracting a negative is the same as adding a
postive . Next, subtract from both sides.
On the right side, minus equals . Now we
can solve for by dividing both sides by .
Dividing by gives a solution of .
, This is the solution to the system of equations.
CONCEPT
Solving a System of Linear Equations using the Addition Method
3
Perform the following operations and write the result as a single
number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
•
10 correct
•
10.8
•
2
•
1.8
RATIONALE
Following the Order of Operations, we must first
evaluate everything in parentheses and grouping
symbols. When there are brackets or braces, evaluate
the innermost operations first. Here, we must evaluate
5 minus 3 first.
5 minus 3 is 2. There are still operations inside
grouping symbols to evaluate. Multiplication comes
before addition, so we must evaluate 8 times 2 next.
