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.
- 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?
- 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?
- LCM among Decimals [06/09/2010]
Given two numbers not integers, an adult wonders how to determine their
least common multiple — or even their greatest common divisor.
Doctor Peterson shows how to extend the usual method by shifting
decimal places, and then un-shifting them.
- 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?
- Long Division of Small Numbers [03/26/2014]
A military enlistee struggles to make sense of dividing bigger numbers into smaller ones, as
occurs when expressing fractions as decimals. Applying the distributive property and
multiplicative identity, Doctor Ian steps through the long division algorithm.
- 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?
- Lower Percents: Capacity and Consumption [02/03/2013]
A consumer wants to know how the battery life of her new mobile phone compares to
that of her old one. Doctor Peterson introduces the notion of judiciously selecting the
- 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 Fractions ... Made of Decimals? [06/16/2015]
A student encounters multiplication homework with decimals in the numerator and
denominator of a fraction. Showing equivalent expressions each step of the way,
Doctor Ian lifts the veil separating decimals, fractions, and division.
- 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?