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.
- Filling a Pool [07/28/1997]
It takes 2 hours to fill a pool with one hose, and 5 hours with another.
How long does it take to fill the pool with both hoses?
- Finding 465 Percent [9/14/1996]
What is 465 percent of 12?
- Finding a Common Denominator [02/21/2002]
Find a common denominator for each pair of fractions: 3/4,5/8; 3/4,7/ 10;
5/6,3/5; them write equivalent fractions.
- Finding a Fraction that Equals an Unending Number [07/08/2003]
Is there a way to find if there is a fraction that equals 0.777777...?
- Finding Common Denominators [06/25/2001]
What is the best way to find a common denominator?
- Finding Fractions between Fractions [01/08/2002]
What are four fractions between 1/3 and 1/2?
- Finding Fractions on a Ruler [08/16/1999]
How can I find measurements like 7/8" or 5/16" on a ruler?
- Finding Percentages on a Calculator [06/22/2006]
How does the percent key on a calculator work? How do I use it to find
a percent of a number?
- Finding Sale Price [03/01/2002]
We are studying how to find the sale price by subtracting the discount
from the regular price.
- Finding the Digit of a Decimal Expansion [11/14/1998]
What digit will appear in the 534th place after the decimal point in the
decimal representation of 5/13?
- Finding the LCM of Several Numbers [11/06/2003]
Do the numbers 65, 55, 25, and 35 have a common denominator?
- Flipping and Switching Fractions [01/18/2002]
I need to solve the following: n/2=5/10; 1/n=5/10; 1/2=n/10; 1/2=5/n.
- Formula to Calculate Percent Increase [01/31/2005]
I want to compare two figures and show the percent increase that has
been made. For example, if 55 has increased to 75, what percentage
increase is that?
- Fraction: Algebra without the Equations [8/23/1996]
I have come up with a way to solve fraction problems like "2/3 of ? =
66", but I have no idea why it works.
- Fraction Division Diagrams [04/21/1999]
Diagram 1 divided by 1 1/2.
- Fraction Equivalents of Decimals that Repeat ... Mostly [05/04/2010]
How do you find the fraction equivalent of a repeating decimals that also includes
digits that do not repeat? Doctor Greenie tweaks a student's formal algebraic
approach, introduces another wrinkle grounded in the base ten number system, then
shares two algorithms based on his work with high school students who take part in
- Fraction Operations Explained [11/23/2003]
Addition, subtraction, multiplication and division of fractions are
explained through examples and helpful comments.
- Fraction or Decimal? [06/23/1998]
Which is more precise, a fraction or a decimal - for instance, 1/3 or
- Fraction or Decimal Form? [07/30/2002]
Is it better to write 1/2(6x-3(2x-1)) or 0.5(6x-3(2x-1)), and why?
- Fractions and Common Denominators [06/04/2001]
Why do you need a common denominator to add fractions, but not to
- Fractions and Cross Multiplication [07/14/1998]
When do you cross-multiply in solving fractions?
- Fractions and School Enrollments [02/26/2003]
The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School
is exactly the enrollment of the Language School. The sum of 1/5, 1/6,
1/7, and 1/8 of the enrollment of the Business School is exactly that
of the Design School. What are the enrollments of these three schools,
assuming no school has more than 1000 pupils?
- Fractions for Repeating Decimals [5/14/1996]
Convert 3.04050505.... into a fraction.
- Fractions in Simplest Form - When? [11/29/2001]
Should fractions always be reduced to their simplest form? Why or why
- Fractions: On the Order of Operations and Simplifying [02/27/2010]
A student wonders if the vinculum and solidus grouping symbols
obviate the need for the order of operations.
- Fractions Table [06/20/1998]
Could you help me locate a math table for fractions to the 16th's?
- Fractions with Exponents [01/29/2001]
I need help with questions like (-3x^2 y^2)^-2/(xyz)^-2.
- Fraction Tutorials [04/28/1997]
Do you know of tutorials for multiplying fractions, adding improper
fractions, and working with mixed number fractions?
- From Infinite Decimals to Mixed Fractions [10/09/1998]
Write this fraction as a mixed number: (.151515...+.555...)/ (.161616...-
- Greatest Common Factor (GCF) [04/13/1999]
How do you find the greatest common factor?
- History of the Fraction Bar [09/01/2005]
What is the original name of the fraction bar? I know it is called the
vinculum, but was that the original name? If not, what was it
- How Can Division Result in an Increase? [10/29/2003]
How is it possible for division to give you a larger number, instead
of a smaller one?
- How Many Boys Are in the Seventh Grade? [05/20/1999]
In a seventh grade of 360 students, 80 percent can swim...
- How Many Days in the Month? [01/22/2004]
There were eleven days of rain one month in Boston. Of the remaining
days, two-fifths were sunny, one-fourth were cloudy, and it snowed the
other seven days. How many days were in the month?
- How Many Freshmen Originally Tried Out? [01/15/2003]
Some freshmen were trying out for the school track team... The 10 who
remained became the track team.
- How Much of a Total Price Is the Tax? [10/20/2003]
If an item has been purchased and all you know is the total cost for
the item and tax, how can you determine how much tax was charged?
- How Old Did This Man Live to Be? [02/23/1998]
A word problem involving fractions.
- How to Divide Fractions? [11/6/1994]
When dividing fractions, for example: 3/11 divided by 5, I know that you
reciprocate the "5" and multiply, but I don't understand why except that
it works! Can you explain it?
- How to Multiply Fractions [9/6/1996]
I'm having trouble multiplying fractions.
- How to Pronounce a Fraction of a Percentage [07/07/2005]
Is it correct to say "one tenth of one percent" as opposed to saying "one tenth percent" for 0.1%? Why or why not?