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.
- 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?
- Ordering Fractions [01/17/2003]
How do I order the fractions 2/3, 3/5, and 2/7?
- Ordering Improper Fractions [10/12/2002]
How can I explain ordering improper fractions?
- Order of Discounts and Taxes [04/22/2002]
Why doesn't it matter in determining the cost of an item whether you
take the tax off before or after you take off the discount?
- Order of Operations and Fractions [02/22/2002]
Given a+3 and b+5, is 105 / ab 7 or 175?
- Origin of the Term "Improper" Fraction [07/28/2006]
Why are fractions with larger numerators than denominators called "improper"? Where did the terms "proper" and "improper" originate in relation to fractions?
- Percentage Error [10/24/2002]
Please help me find the percentage error for the following numbers:
5.7 estimated findings, 5.8 actual findings.
- Percentage of Decrease [11/20/1997]
If last year I collected 500 cans and this year I only collected 350
cans, what would be my percentage of decrease for this year?
- Percentage of Increase [07/23/1997]
I need to figure out a percent increase: the figure in 1995 was 50,000
and the estimated figure for 2000 is 325,000.
- Percentage of Votes Cast [06/03/2003]
If you have two percentages, say 25% and 50%, can you do a percent
change between the two?
- Percentages as Comparisons [11/18/1998]
If A is a certain percentage of B, how do A and B relate to each other?
How does this describe percentages?
- Percentages as Fractions [8/25/1996]
What is 57 percent of 93?
- Percentages from Data [4/12/1996]
I have totaled the use of swear words in some newsgroups, by board and by
sex. I want to figure out who's swearing more, men or women, percentage-
- Percentages in Algebra [12/29/1995]
What number increased by 30% = 260 ? I know the answer, but how did I
- Percent Greater Than vs. Increased [11/22/2002]
Is there a difference between the following statements? My profits are
200% greater than they were last year; My profits from last year have
- Percent Increase and "Increase by a Factor of ..." [08/01/2006]
If we start with 1 apple today and tomorrow have 2 apples, then we have
a 100 percent increase. But can't I also say there was an increase by a
factor of 2?
- The Period of 61/97 [01/12/2001]
How can I find the period of 61/97?
- Placement of the Negative Sign in a Negative Mixed Number [10/25/2004]
When you have a negative improper fraction, can the negative sign be
put anywhere in the fraction? For instance, is -1 3/5 the same as 1
-3/5 and 1 3/-5?
- Place Value and Similar Numbers [08/15/2003]
How do you read these numbers? Is there a difference? 10.200, 10.00002
- Price before Discount [6/3/1996]
A calculator's price is discounted 20 percent. After adding 7 percent
- Prime Factors in Unit Fractions [2/29/1996]
Why does the denominator of a unit fraction have to have prime factors of
2 and/or 5 in order to terminate?
- Product of Terms of a Sequence [04/18/2003]
Find the product of the first 99 terms of the sequence 1/2, 2/3, 3/4,
- Profit and Percent Waste [6/13/1996]
A fruit-seller buys 240 apples for $60, but some are bad. Calculate the
percent thrown away.
- Profit on Investment [4/16/1996]
Ann, Bill, Cynthia, and Don invest $2000, $3000, $8000, and $7000 in a
joint business venture...
- Pronunciation of Fractions [03/28/1997]
How do you pronounce fractions with 32, 42... in the denominator...?
- Proof for Dividing Fractions [01/18/2002]
Could you please send me a proof for dividing fractions?
- Proper and Improper Fractions, Mixed Numbers [8/19/1996]
How do you turn a proper fraction into an improper fraction?
- Putting Fractions in Order [01/24/2001]
I am trying to order fractions from least to greatest, but am having no
- Putting Rational Numbers in Order [09/22/2002]
I have to order 4/15, 6/17, and 3/16 from least to greatest, and I
can't use a calculator.
- Rates and Fractions [1/23/1996]
Find each rate as a fraction in simplest form: 1) 24 laps in 12 minutes,
2) 180 miles with 15 gallons...
- Rationalizing the Denominator [04/09/1997]
Must all fractions have denominators that are rational numbers?
- Rationalizing the Denominator [05/03/1999]
Why can't you have a square root in the denominator of a fraction?
- Rationalizing the Denominator [07/10/2003]
1 / ((sqrt)3 + (sqrt)5 + (sqrt)7)
- Ratios and Fractions: A Reconciliation [04/02/2013]
Teachers disagree about whether a fraction can compare part to part.
Doctor Peterson first distinguishes between ratios and fractions before reconciling them
and warning against inflexible thinking.
- Reaction Time: Softball, Baseball [04/26/2003]
A baseball pitcher throws at 90mph from 60 feet, and a softball
pitcher throws at 60mph from 40 ft. How can I measure reaction time
for the batters?
- Reciprocals of Negative Fractions [03/19/2002]
What is a reciprocal, and what is the reciprocal of negative 1/2? What is
the reciprocal of 10?
- Recurring Decimal Notation [05/12/2003]
What is 0.321 with dots over the 3 and the 1?
- Reduced fraction [12/14/1994]
Write .428571428571428571... as a reduced fraction:
- Reducing Algebraic Fractions by Cancelling [03/16/2004]
When reducing fractions, how come you can cancel factors but you can't
cancel terms? Can you please explain, hopefully with examples too?