Sophia College Algebra
MM212 Final Milestone
20/25 that's 80%
20 questions were answered correctly.
5 questions were answered incorrectly.
1
Geri runs a total of 3.1 miles in a cross-country race.
How many feet is this equivalent to?
•
5,280 feet
•
16,368 feet
•
4,989 feet
•
15,840 feet
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 miles to feet. We know how many
feet are in 1 mile. We will use this fact to set up a conversion factor.
There are 5280 feet in 1 mile. To convert 3.1 miles into feet, multiply by the fraction
.
Notice how the fractions are set up. The units of miles will cancel, leaving only feet.
Finally we can evaluate the multiplication by multiplying across the numerator and
, denominator.
In the numerator, 3.1 times 5280 equals 16368. 3.1 miles is equivalent to 16,368 feet.
CONCEPT
Converting Units
2
Perform the indicated operations and write your result as a single number.
R
ATIONALE
For this expression, there is a lot to consider here. Follow the order of operations, and
evaluate anything inside parentheses and other grouping symbols first. There are two
groups. First, the radical symbol groups (11 × 2 – 6), and a set of parentheses groups .
Let's evaluate what is under the radical first.
Under the radical, there is multiplication and subtraction. Multiplication comes before
subtraction in the order of operations, so we multiply 11 by 2 to get 22. Next, evaluate the
subtraction.
22 minus 6 is 16. Now we can take the square root of 16.
, The square root of 16 is 4. This is the simplified expression underneath the radical. Next,
we have to evaluate the operations in the set of parentheses. Exponents comes before
subtraction in the order of operations, so we square 4 first.
4 squared equals 16. Next, we subtract 9 from 16.
16 minus 9 equals 7. Now that we have eliminated the grouping symbols, we can evaluate
the multiplication of 5 and 7.
5 times 7 equals 35. Finally, we can add 4 and 35.
4 plus 35 is equal to 39. The expression simplifies to 39.
CONCEPT
Order of Operations: Exponents and Radicals
3
, RATIONALE
When given a rectangle with unknown measurements, we can find the area of the rectangle
by multiplying the length and the width. We need to express the length and width by
adding the partial dimensions of each side.
MM212 Final Milestone
20/25 that's 80%
20 questions were answered correctly.
5 questions were answered incorrectly.
1
Geri runs a total of 3.1 miles in a cross-country race.
How many feet is this equivalent to?
•
5,280 feet
•
16,368 feet
•
4,989 feet
•
15,840 feet
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 miles to feet. We know how many
feet are in 1 mile. We will use this fact to set up a conversion factor.
There are 5280 feet in 1 mile. To convert 3.1 miles into feet, multiply by the fraction
.
Notice how the fractions are set up. The units of miles will cancel, leaving only feet.
Finally we can evaluate the multiplication by multiplying across the numerator and
, denominator.
In the numerator, 3.1 times 5280 equals 16368. 3.1 miles is equivalent to 16,368 feet.
CONCEPT
Converting Units
2
Perform the indicated operations and write your result as a single number.
R
ATIONALE
For this expression, there is a lot to consider here. Follow the order of operations, and
evaluate anything inside parentheses and other grouping symbols first. There are two
groups. First, the radical symbol groups (11 × 2 – 6), and a set of parentheses groups .
Let's evaluate what is under the radical first.
Under the radical, there is multiplication and subtraction. Multiplication comes before
subtraction in the order of operations, so we multiply 11 by 2 to get 22. Next, evaluate the
subtraction.
22 minus 6 is 16. Now we can take the square root of 16.
, The square root of 16 is 4. This is the simplified expression underneath the radical. Next,
we have to evaluate the operations in the set of parentheses. Exponents comes before
subtraction in the order of operations, so we square 4 first.
4 squared equals 16. Next, we subtract 9 from 16.
16 minus 9 equals 7. Now that we have eliminated the grouping symbols, we can evaluate
the multiplication of 5 and 7.
5 times 7 equals 35. Finally, we can add 4 and 35.
4 plus 35 is equal to 39. The expression simplifies to 39.
CONCEPT
Order of Operations: Exponents and Radicals
3
, RATIONALE
When given a rectangle with unknown measurements, we can find the area of the rectangle
by multiplying the length and the width. We need to express the length and width by
adding the partial dimensions of each side.
