WGU D771 Quantitative Literacy
(MATH 101) Final Exam
Comprehensive Study Guide | New
2026 Update | 100% Correct.
Quantitative Literacy
An equation is a math statement where each side of the equal sign =
evaluate to the same value (the word "equation" comes from making
"equal"). Each side of an equation is an expression: Numbers and possibly
operators like +, -, ×, or /, like 2 + 3, or like 5, that evaluate to a value.
To evaluate an expression means to determine the expression's value, as in
2 + 3 evaluates to the value 5.
Commonly, a real-life problem can be written as an equation, with an
"unknown" value that should be determined. Ex: If a sandwich costs $8 and a
drink costs $3, how much is a meal? In other words, 8 + 3 = ?.
Often, the unknown value is not alone on a side, but rather in the middle of
an expression. Ex: If a sandwich costs $8 and the meal's bill was $11, how
much was the drink? The equation is 8 + ? = 11. A person can "guess"
values for the unknown until the sides are equal. 8 + 1 would be 9, too low. 8
+ 2 would be 10, too low. 8 + 3 is 11, so the drink cost 3 dollars.
A more methodical approach is to apply the same operation to both sides of
an equation, which maintains the equality, and can be done to make the
unknown value alone on one side, thus "solving" for that unknown value.
Example:
Some problems have an unknown value alone on one side. If a sandwich is
$8 and a drink is $3, what is the meal's cost? 8 + 3 = ?
A person simply evaluates the other side to determine the unknown value: 8
+ 3 is 11. So the unknown value is 11. And indeed, 8 + 3 = 11.
But sometimes the unknown value is inside an expression. Mia is asked how
much a drink costs. She remembers her meal was $11 and her sandwich was
$8. So 8 + ? = 11.
What is the unknown value? Applying the same operation on both sides of an
equation keeps the equality. Ex: If 2 + 3 = 5 (both are 5), then (2 + 3) - 1 =
(5) -1 (both are 4).
,Mia can subtract 8 from both sides. On the left, 8 - 8 is 0, leaving ? alone on
the left. On the right, 11 - 8 is 3. So the unknown value (the drink's cost) was
$3.
The operation applied to both sides can be addition, subtraction,
multiplication, or division. As long as the same operation is applied to both
sides, the equality is kept. Ex: 4 × 10 = 40 because both sides are 40. So (4
× 10) / 4 = (dividing both sides by 4) because both sides are 10.
Though the sides looked different, both were 40, so dividing 40 by 4 yields
10.
Example:
This problem asks what 10 gallons of gas costs at 4 dollars per gallon. In
other words, 4 × 10 = ?
The ? is an unknown value. To find the value, a person can evaluate the left
side: 4 × 10 is 40. Thus, for the equation to be correct, the unknown value
must be 40.
Often, the unknown value is inside an expression. If Mia paid $40 for gas,
and gas is $4 per gallon, how many gallons did she buy? The equation is 4
× ? = 40.
The unknown value in 4 × ? = 40 can be found by dividing both sides by 4.
On the left, multiplying by 4 and then dividing by 4 is like doing nothing, so
just the ? remains.
On the right, is 10. Thus, the unknown value equals 10. And indeed, 4
× 10 = 40.
Variable: A variable is a symbol, usually a letter, representing an unknown
number. For example, in the equation x + 5 = 10, x is the variable.
Constant: A constant is a fixed value that does not change. In the
equation, x + 5 = 10, the numbers 5 and 10 are constants because their
values are always the same.
Coefficient: A coefficient is a number that is multiplied by a variable. For
example, in 3x, the number 3 is the coefficient because it is multiplied by the
variable x.
,An expression is a mathematical phrase that combines variables,
coefficients, and constants to represent a specific value, but it does not
include an equal sign. In contrast, an equation asserts the equality between
two expressions, connected by an equal sign, and establishes a relationship
that can be solved to find the values of the variables. The charts below
(Figures 1.5.2 and 1.5.3) offer further explanation and examples of the
differences.
, Writing ? in equations is awkward, so people usually use a letter like x, as in
8 + x = 11. x is called a variable: A letter used to represent a value. The
name "variable" is due to the value "varying" depending on the problem: x
(MATH 101) Final Exam
Comprehensive Study Guide | New
2026 Update | 100% Correct.
Quantitative Literacy
An equation is a math statement where each side of the equal sign =
evaluate to the same value (the word "equation" comes from making
"equal"). Each side of an equation is an expression: Numbers and possibly
operators like +, -, ×, or /, like 2 + 3, or like 5, that evaluate to a value.
To evaluate an expression means to determine the expression's value, as in
2 + 3 evaluates to the value 5.
Commonly, a real-life problem can be written as an equation, with an
"unknown" value that should be determined. Ex: If a sandwich costs $8 and a
drink costs $3, how much is a meal? In other words, 8 + 3 = ?.
Often, the unknown value is not alone on a side, but rather in the middle of
an expression. Ex: If a sandwich costs $8 and the meal's bill was $11, how
much was the drink? The equation is 8 + ? = 11. A person can "guess"
values for the unknown until the sides are equal. 8 + 1 would be 9, too low. 8
+ 2 would be 10, too low. 8 + 3 is 11, so the drink cost 3 dollars.
A more methodical approach is to apply the same operation to both sides of
an equation, which maintains the equality, and can be done to make the
unknown value alone on one side, thus "solving" for that unknown value.
Example:
Some problems have an unknown value alone on one side. If a sandwich is
$8 and a drink is $3, what is the meal's cost? 8 + 3 = ?
A person simply evaluates the other side to determine the unknown value: 8
+ 3 is 11. So the unknown value is 11. And indeed, 8 + 3 = 11.
But sometimes the unknown value is inside an expression. Mia is asked how
much a drink costs. She remembers her meal was $11 and her sandwich was
$8. So 8 + ? = 11.
What is the unknown value? Applying the same operation on both sides of an
equation keeps the equality. Ex: If 2 + 3 = 5 (both are 5), then (2 + 3) - 1 =
(5) -1 (both are 4).
,Mia can subtract 8 from both sides. On the left, 8 - 8 is 0, leaving ? alone on
the left. On the right, 11 - 8 is 3. So the unknown value (the drink's cost) was
$3.
The operation applied to both sides can be addition, subtraction,
multiplication, or division. As long as the same operation is applied to both
sides, the equality is kept. Ex: 4 × 10 = 40 because both sides are 40. So (4
× 10) / 4 = (dividing both sides by 4) because both sides are 10.
Though the sides looked different, both were 40, so dividing 40 by 4 yields
10.
Example:
This problem asks what 10 gallons of gas costs at 4 dollars per gallon. In
other words, 4 × 10 = ?
The ? is an unknown value. To find the value, a person can evaluate the left
side: 4 × 10 is 40. Thus, for the equation to be correct, the unknown value
must be 40.
Often, the unknown value is inside an expression. If Mia paid $40 for gas,
and gas is $4 per gallon, how many gallons did she buy? The equation is 4
× ? = 40.
The unknown value in 4 × ? = 40 can be found by dividing both sides by 4.
On the left, multiplying by 4 and then dividing by 4 is like doing nothing, so
just the ? remains.
On the right, is 10. Thus, the unknown value equals 10. And indeed, 4
× 10 = 40.
Variable: A variable is a symbol, usually a letter, representing an unknown
number. For example, in the equation x + 5 = 10, x is the variable.
Constant: A constant is a fixed value that does not change. In the
equation, x + 5 = 10, the numbers 5 and 10 are constants because their
values are always the same.
Coefficient: A coefficient is a number that is multiplied by a variable. For
example, in 3x, the number 3 is the coefficient because it is multiplied by the
variable x.
,An expression is a mathematical phrase that combines variables,
coefficients, and constants to represent a specific value, but it does not
include an equal sign. In contrast, an equation asserts the equality between
two expressions, connected by an equal sign, and establishes a relationship
that can be solved to find the values of the variables. The charts below
(Figures 1.5.2 and 1.5.3) offer further explanation and examples of the
differences.
, Writing ? in equations is awkward, so people usually use a letter like x, as in
8 + x = 11. x is called a variable: A letter used to represent a value. The
name "variable" is due to the value "varying" depending on the problem: x
