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.
- Improper Fractions [05/20/2002]
How can 14/9 be a fraction when you can't have 14 parts of something
that's been cut into 9 parts?
- Inches and Feet in Decimal Form [7/16/1996]
How do I convert fractions of inches and feet into a decimal expression
of the length in feet?
- Increase in Chicken Consumption [8/29/1996]
In 1984 the average American ate 55.7 lbs. of chicken. This was 2.8 lbs.
more than the average in 1982. What was the percent of increase in
- Infinite Geometric Progression [10/02/1997]
How do you go about solving .27 repeating into a fraction?
- Integral Multiples [9/7/1996]
What fraction of the integral multiples of 3, between 1 and 100, are also
integral multiples of 4?
- Introduction to Division with Negative Numbers [05/05/2004]
I don't know how to do division with negative numbers, like +18/-9
or -24/-8 or +21/-3.
- Invert and Multiply [11/08/1997]
I am struggling with how to explain to a class WHY we invert and multiply
when dividing fractions.
- Inverting and Multiplying When Dividing Fractions [9/28/1995]
I have always been taught that to divide fractions I must invert and
multiply. Why does this algorithm work? Is there any other way to divide
- Irwin's Theory [07/06/1998]
How can fractions be added without changing the denominators?
- Is the Fraction N/N Considered Proper or Improper? [10/31/2003]
If a fraction has an equal numerator and denominator, what is it
called? Is it proper, improper, or something else?
- The Joy of Fractions [05/18/2002]
How come fractions are called fractions? How come they can be
translated into decimals? Why do they hurt your brain when you
first learn them?
- LCD, LCM [08/16/1997]
What is the easiest way to find the least common denominator and least
common multiple of two numbers?
- Learning Fractions in the Metric System [11/27/2003]
Since the metric system doesn't use fractions, are math students in
metric countries able to skip fractions and work on more useful things?
- Longfellow's Bees [08/01/2002]
One-fifth of some bees fly to the rosebush, one-third fly to the
apple tree, and three times the difference fly to the acorn tree. One
bee is left flying around. How many bees are there altogether?
- Mark-ups, Merchant Fees, and Multiplication ... or Division? [01/06/2011]
Marking up a price by p percent through division by (1 - p) yields a different result
than does multiplication by (1 + p). Doctor Wallace explains methods for marking up
and for offsetting credit card merchant fees, and along the way distinguishes between markup and
- Mathilda and Matt Share a Pie.... [01/20/2010]
Doctor Ian starts with simpler fractions, and a drawing, to model the
parts, wholes, and parts-as-wholes in this problem of repeated division.
- Meaning of Multiplying Fractions [12/09/1999]
What does it mean to multiply a fraction by a fraction?
- Measures of Music and Fractions [01/13/1999]
How can you tell what fraction of a measure a note is? How does it relate
to the time signature?
- More Than 100 Percent [07/27/1999]
Is there anything larger than 100 percent, like 200 percent or 300
- Mr. Thomas' Salary [9/6/1996]
Mr. Thomas spent 1/12 of his salary to buy a watch and 3/11 of the
remaining to pay for a new television set... what was his salary?
- Multiplying a Fraction by a Decimal [9/5/1996]
How do I simplify and multiply (40/360) by 78.5?
- Multiplying a Fraction by a Variable [08/17/2006]
How do I find the product of something like (1/3) times 'a'?
- Multiplying Decimal Numbers and Placing the Decimal Point [09/20/2007]
Why does counting up the total decimal places when multiplying decimal
- Multiplying Decimals and Decreasing Answers [12/02/1998]
Why does multiplying by a decimal decrease the answer? How can you have
less than what you started with when you multiply?
- Multiplying Decimals by Negatives [03/18/2002]
I can't find decimals on my calculator.
- Multiplying Fractions [4/13/1996]
x over 2y multiplied by 4y over 2 = ?
- Multiplying Fractions by Cancellation [10/09/1998]
I'm trying to multiply fractions by cancelling out numbers...
- Multiplying Fractions, Dividing Common Factors: Why Does It Work? [06/10/2010]
A teacher wonders why, before multiplying fractions, it works to "factor
out." Doctor Ian builds up an explanation about commutativity by walking
through increasingly complicated examples.
- Multiplying Mixed Numbers [04/06/2004]
Why do you need to convert mixed numbers to improper fractions before
multiplying them together? What is the mathematical reason behind
- Multiplying Whole Numbers by Fractions [05/31/1999]
How do you multiply whole numbers by fractions?
- Name of Bar That Denotes a Repeating Decimal [08/30/2004]
What is the name of the bar that goes over a digit or group of digits
that signifies that the digit or group repeats?
- Name of Fraction Bar [7/5/1996]
What is the correct term for the line that separates the numerator and
denominator of a fraction?
- Net Result of Consecutive Percentage Increases [12/11/2003]
Suppose a quantity is increased by some percentage, and then is later
increased again by another percentage. How can I calculate the
overall percentage increase?
- Newton's Method and Continued Fractions [10/06/1999]
Can you clarify some points on Newton's method of finding square roots
without a calculator, and on the continued fraction algorithm (CFA)?
- Non-terminating Decimal Representations of Fractions [11/10/1997]
Why when you take a finite, limited quantity like one-third and turn it
into a decimal do you get .333... on into infinity?
- Number of Places in Products of Decimals [09/19/2002]
When you multiply decimals, why is there always the same number of
decimal places in the answer as in the problem?
- Numbers Containing Whole Number, Decimal, and Fraction at Once [10/19/2004]
If I have a number that contains a whole number, decimal, and fraction
all in one, such as 3.366 2/3, how would I convert all of that to one
fraction in lowest terms?
- Numbers in a Fraction [05/20/2001]
Is a fraction one number or is it two numbers?
- Numerator, Denominator: Etymologies [03/25/2002]
Why are the parts of a fraction called the numerator and the denominator?
- The Oneths Place [09/29/1998]
In decimal numbers, why is there no oneths place?