Ask Dr. Math

Middle School Archive

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.

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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 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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