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.
- Thinking about the Mediant of Two Fractions [12/10/2009]
One of my students noticed that when given 1/a and 1/b, the fraction
2/(a+b) always seems to be in between 1/a and 1/b. Is this a new
fraction rule, or has this been discovered and proved before?
- Tips for Simplifying Fractions [06/03/1998]
Can you give my some tips to help me simplify fractions?
- Tips on Quickly Converting Fractions to Percents [02/14/2005]
Is there an easy way to turn fractions like 9/60 into a percent
without using a calculator?
- Two Ways to Change Percents to Fractions [02/21/1998]
How do I change something like 10 1/4% into a fraction?
- Undefined Fractions [02/19/2002]
Why is a fraction with a denominator of zero called "undefined"?
- Undefined Fractions [06/10/2005]
I am having trouble determining the difference between an undefined
fraction and a fraction with no solution. Maybe you can help me
determine the difference.
- Understanding Decimal Notation [06/10/2002]
I've been told that you should be able to look at a number like 2
15/100 and know that the decimal equivalent is 2.15. But I don't
understand why they're the same.
- Undoing Percentage Changes [07/10/2002]
If I increase an initial amount by P percent, by what percentage would I
have to decrease it to get back to where I started?
- Unit Fractions and the Greedy Algorithm [12/27/2000]
How can I represent 2000/2001 as the sum of unit fractions?
- Unit Fractions Summing to 1 [07/15/2001]
Find seven different unit fractions whose sum is 1.
- Use of Hyphen When Writing Fractions with Words [01/20/2004]
I have seen 2/3 written as two-thirds or as two thirds. Are both ways
(with a hyphen, without a hyphen) acceptable, or is only one truly
- Using Common Denominators to Compare Fractions [03/17/1998]
How do you decide which is bigger -- 3/8 or 4/9 -- using equivalent
- Ways of Adding Fractions [03/19/1999]
Can you help me calculate 1/3 + 1/6?
- Weird Fraction [06/11/2003]
Factoring in order to cancel terms.
- What are Compound Fractions? [11/23/2002]
I often get confused by compound fractions. What are they, and how do
- What Does Cancelling Mean? [01/22/2003]
My teacher says that 2k/4n can be simplified to k/2n. How can one k
cancel out 2 n's?
- What Exactly is a Fraction? [10/15/2001]
What is a fraction? Is 3/1 a fraction? Is 5/sqrt(2) a fraction?
- What Percent is 0.7? [6/12/1996]
Is it 70 percent?
- When Percentage Calculations are Inappropriate [02/11/2003]
How do I best calculate the percentage of goal when at least one of
the numbers is a negative number?
- When to Add or Multiply Denominators? [04/02/2001]
When you multiply fractions, you multiply the numerators and then the
denominators. When you add fractions, you add the numerators but not the
denominators. Why the difference?
- Which Fractions Repeat? [07/21/1998]
How do you know whether a fraction will be a repeating or terminating
decimal? If repeating, how many decimal places?
- Why Are All Repeating Decimals Classified Rational? [11/12/1997]
Please explain how .6 repeating can be a rational number when expressing
it over 10's, 100's, etc.
- Why Cancel? [02/25/2003]
Why do we have to cancel numbers?
- Why Decimal Division Works [04/24/2001]
Can you explain why (not how) the procedure of division with decimals
- Why Does Cross Multiplication Work? [05/09/2002]
Why does the rule a/b = c/d also mean ad = bc? Why can we solve
proportions by cross multiplying?
- Why Does Division Convert a Fraction to a Decimal? [01/04/2009]
Why do you divide the denominator into the numerator to turn a
fraction into a decimal? What is the math behind that process?
- Why Does OF Mean Multiply? [12/04/2001]
I wanted to know why the word "of" means multiplication.
- Why Do We Rationalize Fractions? [11/29/2005]
Why do we have to simplify fractions that have a radical in the
denominator to remove that radical and rationalize the denominator?
Why is that important?
- Why Find the LCM? [10/07/1998]
Where do you use LCMs? How do they apply to real life?
- Why Learn Fractions? [8/13/1996]
What is the point of learning fractions?
- Why the Decimal Point Goes Where It Does [09/21/2003]
My daughter is having trouble understanding why the first place before
the decimal point is 'ones', and the first one after is 'tenths'.
- Why Were Fractions Invented? [11/26/2007]
An overview of the history of fractions and the purpose they serve.
- Writing a Percent as a Fraction and Reducing the Result [05/03/2004]
I just can't seem to figure out how to convert a percent into a
fraction, such as 20% = 20/100 = 1/5. All I know is that you put it
into a fraction like 20/100 but after that I get stuck and I just
don't know how to get the answer.
- Writing Ratios [06/03/1999]
How can I write a ratio in three different ways?
- Writing Repeating Decimals as Fractions [11/8/1995]
When you are expressing a repeating decimal as a fraction, why do you use
9, 99, 999, or 9999 etc. in the denominator? For example, 0.5555...(5
repeating) equals 5/9.
- X is What Part of Y? [11/01/2001]
2/5 is what part of 4/5? What part of 2/3 is 4/5? What part is 4/5 of 3?
2/3 is what part of 2?
- Zero Before the Decimal Point? [10/06/2000]
What is the merit of writing the zero before the decimal point in numbers
less than one, for example 0.25?
- Zero in the Denominator [8/14/1996]
What is the value of 4/0 * 0/4?