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.
- Cutting An Equal Number of Slices of Cake [07/13/1998]
One cake is 35 slices and another is 42 slices. If the cakes need to have
the same number of slices, how many slices should they have?
- Cutting a Pipe [06/24/2003]
You have a pipe that is 21 1/8' long. How many 2' segments can be made
of this pipe if 1/8' waste is created from each cut?
- Decimal Multiplication and Division [11/19/2002]
I'm tutoring a 6th-grade student, and I'm having a hard time
explaining to her why you sometimes need to put a zero in the tenths
place, in the quotient.
- Decimal Numerator? [04/08/2003]
Is there such a thing as .8/1 ?
- Decimals: Terminating or Repeating? [01/26/2001]
How can you tell just by looking at a fraction whether, in decimal form,
it will terminate or repeat?
- Decimal To Fraction Conversion - A Simpler Version [11/25/2002]
A simpler version of the algorithm.
- Definition of Repetend [9/17/1995]
What is the definition of repetend? Where can I find its definition on
- Denominator = 2 or 1/2 [01/16/1997]
My teacher says that when the denominator is 2, that means I cut the pie
(or whatever) in 2....
- Deriving Fractions from Decimals [07/19/2001]
I don't understand how to get the fraction for a decimal like 12.5% =
0.125 = 1/8 or 66.7% = 0.667 = 2/3.
- The Difference between Calculating Markup and Profit Margin [08/11/2006]
If we have fixed costs of $50,000 on a product and want to have a
profit margin of 25%, how much should we charge the customer to buy it?
- Difference between Percent and Percentage [04/26/2008]
Is there any difference between percent and percentage?
- Displaying Large Repetends on Small Calculators [05/31/2002]
How can I find a 16-digit repetend using an 8-digit calculator?
- Dividing 17 Rings [10/22/1996]
How was the inheritance divided?
- Dividing Compound Fractions [11/16/1999]
Can you give me a simple step-by-step method to simplify expressions like
[(3/y)+(5/zy^2)] / [(5/2y)-(4/y^2)]?
- Dividing Decimals by Whole Numbers [10/19/2002]
Dividing decimals has been hard for me to learn.
- Dividing Fractions [12/5/1995]
Tell me a shortcut for dividing fractions.
- Dividing Fractions [8/4/1996]
Why do you flip the second fraction when dividing fractions?
- Dividing Fractions [10/16/1997]
Why do we have to flip the second fraction when we divide?
- Dividing Fractions [03/16/1999]
Why can't we divide fractions directly? Why do we have to do it by
- Dividing Fractions: Why Invert? [01/24/2001]
Why do we have to invert the fraction in dividing fractions?
- Dividing Two Numbers with and without Units [09/15/2004]
We can calculate $500/10 or $500/$10 and get $50 or 50 respectively.
What units would the result have if we calculate 500/$10?
- Dividing with Powers [01/16/2003]
I am having trouble with problems like (6.0 * 10^7)/(3.0 * 10^2).
- Does My Fraction 1/1 Story Work? [11/04/2002]
Units in ratios: pitfalls of analogies and stories for understanding
- Do We Need a Zero before the Decimal? [01/26/2005]
Do I need to use a zero to hold the dollar place if the amount is less
than a dollar? I see money amounts written both ways, as $.45 or
$0.45. Are both correct? If one is better, why is it better?
- Duelling Percentages [06/11/2002]
Why doesn't a decrease of 15%, followed by an increase of 15%, get you
back to where you started?
- Egyptian Fractions [03/21/1999]
Can you help me understand Egyptian fractions?
- Egyptian Fractions [06/11/2001]
The Egyptians wrote all their fractions as a sum of different fractions
with a numerator of 1. I need to find a way to work out what fractions
should be added together...
- Eliminating Fractions in Division [11/20/2003]
How can I change a division involving a fraction to one involving only
- Equations Involving Fractions [07/07/2000]
How do I solve equations with fractions and decimals in them?
- Equations with Fractions [04/21/1997]
How do you solve x/2 + x/3 = 1/6?
- Equations with Fractions: 7y/9+2 = 2y/3 [11/23/1997]
First I moved the variables to one side and the numbers to the other, but
I always ended up with -18/13.
- Estate Distribution [05/10/1999]
Does 1/10 of the estate go to the church before or after taxes?
- Estimating Fractions [12/02/2001]
There is a plate of assorted cookies, 1/6 chocolate chip and 1/5 peanut
butter. The rest of the cookies are regular. What fraction do the regular
- Estimating Fractions/Mixed Numbers [01/10/2002]
I don't understand how to find an estimated sum of 1/6 + 5/8 or 13 1/8
divided by 6 1/5.
- Even and Odd Fractions? [01/12/1999]
What rules would we have to have to be able to define a fraction as even
- Examples of Fraction Multiplication and Division [05/14/1998]
I get confused on how to multiply and divide fractions ...
- Expressing Percentages [01/26/2004]
Why do we sometimes use phrases like "4 out of 5 dentists"? Wouldn't it be more meaningful just to say 80% instead?
- Factoring and Cancelling in Long Division [08/29/2003]
How do I perform long division? i.e. 1,002,240,000 / 86400
- Factoring Fractions [05/31/2001]
I am having a major problem trying to figure out how to add fractions
that have different denominators.
- Figuring Out Fractions [04/28/2004]
I need help with adding and subtracting fractions, especially mixed
numbers and equivalent fractions.