Sophia College Algebra 1. PERFORMING
OPERATIONS WITH REAL NUMBERS | MILESTONE 1
You passed this Milestone
18 questions were answered correctly.
3 questions were answered incorrectly.
1
The Elster family drove 9.25 hours on the first day of their road trip.
How many minutes is this equivalent to?
9,256 minutes
33,300 minutes
555 minutes
154 minutes
RATIONALE
In general, we use conversion factors to convert from one unit to another. A conversion factor is a fraction with equal
quantities in the numerator and denominator, but written with different units. We want to convert hours to minutes.
We know how many minutes are in 1 hour. We will use this fact to set up a conversion factor.
There are 60 minutes in 1 hour so to convert 9.25 hours into minutes, we will multiply by the fraction .
Notice how the fractions are set up. The units of hours will cancel, leaving only minutes. Finally we can evaluate the
multiplication by multiplying across the numerator and denominator.
, In the numerator, 9.25 times 60 equals 555. 9.25 hours is equivalent to 555 minutes.
CONCEPT
Converting Units
2
Perform the following operations and write the result as a single number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
10.8
10
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.
8 times 2 is 16. Next, we add 4 and 16 to complete the operations inside parentheses.
4 plus 16 is 20. Now there is just division and subtraction. Division comes before subtraction in the Order of
Operations, so we divide 20 by 5 next.
, 20 divided by 5 is 4. Lastly, add 4 and 6.
4 plus 6 is 10.
CONCEPT
Introduction to Order of Operations
3
Consider the following expression:
What is the value of this expression when x = -5?
RATIONALE
To find the value of this expression when x = -5, begin by substituting -5 for every instance of x in the expression.
OPERATIONS WITH REAL NUMBERS | MILESTONE 1
You passed this Milestone
18 questions were answered correctly.
3 questions were answered incorrectly.
1
The Elster family drove 9.25 hours on the first day of their road trip.
How many minutes is this equivalent to?
9,256 minutes
33,300 minutes
555 minutes
154 minutes
RATIONALE
In general, we use conversion factors to convert from one unit to another. A conversion factor is a fraction with equal
quantities in the numerator and denominator, but written with different units. We want to convert hours to minutes.
We know how many minutes are in 1 hour. We will use this fact to set up a conversion factor.
There are 60 minutes in 1 hour so to convert 9.25 hours into minutes, we will multiply by the fraction .
Notice how the fractions are set up. The units of hours will cancel, leaving only minutes. Finally we can evaluate the
multiplication by multiplying across the numerator and denominator.
, In the numerator, 9.25 times 60 equals 555. 9.25 hours is equivalent to 555 minutes.
CONCEPT
Converting Units
2
Perform the following operations and write the result as a single number.
[4 + 8 × (5 – 3)] ÷ 5 + 6
10.8
10
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.
8 times 2 is 16. Next, we add 4 and 16 to complete the operations inside parentheses.
4 plus 16 is 20. Now there is just division and subtraction. Division comes before subtraction in the Order of
Operations, so we divide 20 by 5 next.
, 20 divided by 5 is 4. Lastly, add 4 and 6.
4 plus 6 is 10.
CONCEPT
Introduction to Order of Operations
3
Consider the following expression:
What is the value of this expression when x = -5?
RATIONALE
To find the value of this expression when x = -5, begin by substituting -5 for every instance of x in the expression.
