See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Fractions & Percentages
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Finding a least common denominator (LCD).
Comparing/ordering fractions; equivalent fractions.
Improper fractions and mixed numbers.
Converting fractions to/from decimals.
Fractions and repeating decimals.
Finding a percentage.
- Adding Algebraic Fractions, Different Denominators [8/24/1996]
How do I solve 7/2x + (2-x)/(3x^2) + (3 + 5x)/(6x^3)?
- Adding and Multiplying Fractions [05/31/2001]
Why do I have to find a common denominator to add fractions, but not to
- Adding and Subtracting Algebraic Fractions [8/24/1996]
How do I add and subtract fractions with the same denominator?
- Adding and Subtracting Percents [6/28/1996]
Could you please explain how to add and subtract percents?
- Adding Fractions [05/21/2002]
How do you add fractions?
- Adding Fractions That Have Variables [03/24/2002]
9a/10 + 2/5. I have the answer in the back of the book but I don't
know how to solve it.
- Adding Tax and Tip [07/19/1998]
In pricing our hotel luncheons, we charge a base price plus a 6.8% tax
and a 20% service charge. How would I find the total in one step?
- Algebra and Fractions [08/30/1997]
The sum of two-thirds and one-ninth of a number is 28. Find the number N.
- Asking Price of a House [10/14/2001]
If a seller wants to clear $50,000 for his house and the real estate
commission is 6%, what should be the asking price for the house?
- Averaging Percentages [12/11/1998]
Why can you average percents in the usual way in some cases, and why do
you have to use weighted averages in others?
- Bar over a Whole Number? [06/05/2001]
What does a bar over a whole number indicate?
- Boys Wearing Glasses [07/07/1999]
How many boys in a school wear spectacles if there are 1400 pupils, 1/4
of those wear spectacles, and 2/7 of them are boys?
- Calculating Lengthy Repeating Decimals [10/26/2006]
The fraction 355/113 is used as an approximation for pi. A question
about converting this fraction to decimal form leads to an interesting
discussion of how to calculate long repeating decimals without having
to divide them all the way out one number at a time.
- Calculating Percentage Increase [07/09/2004]
If my salary increased from 45k to 65k over a period of 10 years, what
percentage increase did I receive per year?
- Calculating Percentage of Errors [03/21/2002]
You have items to be picked off a shelf every day. You pick one item a
day and check it against the order. You wish to asign a percentage to the
error in wrong items and/or number of items.
- Calculating Percent Increases [10/29/1996]
What's the relation between evaluating 0.05 x 1200 + (1 x 1200) and 1.05
- Calculating Sales Tax [09/19/2001]
How do I calculate sales tax? Please describe the steps.
- Cancelling Fractions [01/04/1998]
How do you cancel 3/5 x 2/3?
- Cancelling Fractions [05/06/2002]
I have to fill in the missing numbers: 2/? x 6/7 x ?/12 = 2/3
- Cancelling Fractions [06/03/2003]
I am reading a book on algebra. The author states that cancelling is
division too and then shows the following without any explanation of
how it's done...
- Can Negative Fractions Also Be Proper or Improper? [03/31/2004]
Is a fraction like -3/4 considered a proper fraction? Is -8/3
considered an improper fraction? I've generally thought that all
proper fractions lie between 0 and 1 on a number line, but how do the
negatives fit in?
- Can You Have Zero in the Denominator? [11/7/1994]
My 7th grade math teacher and I are in the midst of an argument over
whether any number can be placed over zero in a fraction. I know that a
fraction like 10/5 equals 2, and 5*2=10, and that works out for all
fractions where the numerator is larger than the denominator, but it
doesn't work out for n/0. You'll probably say that it isn't a legitimate
fraction, but.. I still say that it is. :)
- Changing a Repeating Decimal to a Fraction [09/22/2002]
How do you change 0.75 repeating (0.757575...) to a fraction?
- Checking Your Work [09/11/2003]
Our whole class has come up with one answer to a problem, while the
teacher's answer book gives a different answer. What have we done wrong?
- Clarifying Percentages vs. Percentage Points [11/21/2003]
What is the difference between measuring using percentages versus
measuring using percentage points? What is meant by a percentage point?
- Clock Hands and Hours Worked [01/29/2003]
A man arrives at work between 8:00 and 9:00 a.m. at exactly the
moment the minute hand and hour hand of the clock point in the same
direction.... How many hours did the man work?
- Comments on Dividing Fractions [03/15/2007]
A question on how to divide fractions leads into comments on how
division and subtraction can be thought of as multiplication and
addition of an "inverted" number.
- Commissions [03/19/2002]
Mildred receives a 5% commission on her sales of exercise equipment and a
6% commission on her sales of weight training equipment...
- Comparing Fractions [03/11/1999]
What is the easiest way of telling that one fraction is bigger than
another (e.g. 5/9 and 5/6)?
- Comparing Individual Discounts to a Collective Discount [07/19/2005]
I am purchasing two books that each have a 10% discount. If the
discount is taken on each book first or taken on the total price of
the two books, will the result be same or different?
- Comparing Ratios and Fractions [01/06/2002]
What are the differences between ratios and fractions?
- Converting a Mixed Decimal to a Fraction [11/09/2001]
Write 4.16 2/3 as a mixed number. We know the answer is 4 1/6; we just
can't figure out why.
- Converting a Repeating Decimal to a Fraction [9/10/1996]
Why does this way of converting a recurring decimal to a fraction work?
- Converting Between Mixed Numbers and Improper Fractions [04/08/1999]
Pictures and step-by-step instructions for changing mixed numbers to
improper fractions and back again.
- Converting Decimals to Fractions [7/10/1995]
A certain fraction is converted to a decimal and the decimal
representation is 0.6428571428571428571... What is the fraction?
- Converting Fractions and Decimals [02/05/1997]
How do you convert fractions to decimals? How do you convert decimals to
- Converting Fractions to Percents [04/24/2001]
How can I easily convert fractions such as 4/9, 10/9, or 11/12 into
- Converting Repeating Decimals into Fractions [10/22/2003]
I am looking for a rational number with a repeating/non-terminating
decimal expansion where the repeating pattern is 12 digits long. How
can I find such a number?
- Converting Repeating Decimals into Fractions [06/25/2008]
How do you convert a repeating decimal to a fraction when there are
some numbers before the part that repeats, like in 0.916666...?
- Converting Repeating Decimals to Fractions [12/17/2006]
How do you change a repeating decimal where the first few numbers are
not repeating, like 2.41666..., into a fraction?