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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).
Dividing fractions.
Comparing/ordering fractions; equivalent fractions.
Reducing/simplifying fractions.
Improper fractions and mixed numbers.
Converting fractions to/from decimals.
Fractions and repeating decimals.
Finding a percentage.
Percentage increase/decrease.
 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 twothirds or as two thirds. Are both ways
(with a hyphen, without a hyphen) acceptable, or is only one truly
correct?
 Using Common Denominators to Compare Fractions [03/17/1998]

How do you decide which is bigger  3/8 or 4/9  using equivalent
fractions?
 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
they work?
 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
works?
 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?
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