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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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- wise.

Percentages in Algebra [12/29/1995]

What number increased by 30% = 260 ? I know the answer, but how did I get it?

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 increased 200%.

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 tax...

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, 4/5, ...

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 luck.

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)

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?

Reducing Fractions [7/4/1996]

How do you reduce fractions with different denominators?

Reducing Fractions [03/17/1997]

How do you know when a fraction is in its simplest form?

Relative Errors [08/03/1997]

How do you find the relative error of a measurement?

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