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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Filling a Pool [07/28/1997]

It takes 2 hours to fill a pool with one hose, and 5 hours with another. How long does it take to fill the pool with both hoses?

Finding 465 Percent [9/14/1996]

What is 465 percent of 12?

Finding a Common Denominator [02/21/2002]

Find a common denominator for each pair of fractions: 3/4,5/8; 3/4,7/ 10; 5/6,3/5; them write equivalent fractions.

Finding a Fraction that Equals an Unending Number [07/08/2003]

Is there a way to find if there is a fraction that equals 0.777777...?

Finding Common Denominators [06/25/2001]

What is the best way to find a common denominator?

Finding Fractions between Fractions [01/08/2002]

What are four fractions between 1/3 and 1/2?

Finding Fractions on a Ruler [08/16/1999]

How can I find measurements like 7/8" or 5/16" on a ruler?

Finding Percentages on a Calculator [06/22/2006]

How does the percent key on a calculator work? How do I use it to find a percent of a number?

Finding Sale Price [03/01/2002]

We are studying how to find the sale price by subtracting the discount from the regular price.

Finding the Digit of a Decimal Expansion [11/14/1998]

What digit will appear in the 534th place after the decimal point in the decimal representation of 5/13?

Finding the LCM of Several Numbers [11/06/2003]

Do the numbers 65, 55, 25, and 35 have a common denominator?

Flipping and Switching Fractions [01/18/2002]

I need to solve the following: n/2=5/10; 1/n=5/10; 1/2=n/10; 1/2=5/n.

Formula to Calculate Percent Increase [01/31/2005]

I want to compare two figures and show the percent increase that has been made. For example, if 55 has increased to 75, what percentage increase is that?

Fraction: Algebra without the Equations [8/23/1996]

I have come up with a way to solve fraction problems like "2/3 of ? = 66", but I have no idea why it works.

Fraction Division Diagrams [04/21/1999]

Diagram 1 divided by 1 1/2.

Fraction Equivalents of Decimals that Repeat ... Mostly [05/04/2010]

How do you find the fraction equivalent of a repeating decimals that also includes digits that do not repeat? Doctor Greenie tweaks a student's formal algebraic approach, introduces another wrinkle grounded in the base ten number system, then shares two algorithms based on his work with high school students who take part in math competitions.

Fraction Operations Explained [11/23/2003]

Addition, subtraction, multiplication and division of fractions are explained through examples and helpful comments.

Fraction or Decimal? [06/23/1998]

Which is more precise, a fraction or a decimal - for instance, 1/3 or 0.33?

Fraction or Decimal Form? [07/30/2002]

Is it better to write 1/2(6x-3(2x-1)) or 0.5(6x-3(2x-1)), and why?

Fractions and Common Denominators [06/04/2001]

Why do you need a common denominator to add fractions, but not to multiply them?

Fractions and Cross Multiplication [07/14/1998]

When do you cross-multiply in solving fractions?

Fractions and School Enrollments [02/26/2003]

The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School is exactly the enrollment of the Language School. The sum of 1/5, 1/6, 1/7, and 1/8 of the enrollment of the Business School is exactly that of the Design School. What are the enrollments of these three schools, assuming no school has more than 1000 pupils?

Fractions for Repeating Decimals [5/14/1996]

Convert 3.04050505.... into a fraction.

Fractions in Simplest Form - When? [11/29/2001]

Should fractions always be reduced to their simplest form? Why or why not?

Fractions: On the Order of Operations and Simplifying [02/27/2010]

A student wonders if the vinculum and solidus grouping symbols obviate the need for the order of operations.

Fractions Table [06/20/1998]

Could you help me locate a math table for fractions to the 16th's?

Fractions with Exponents [01/29/2001]

I need help with questions like (-3x^2 y^2)^-2/(xyz)^-2.

Fraction Tutorials [04/28/1997]

Do you know of tutorials for multiplying fractions, adding improper fractions, and working with mixed number fractions?

From Infinite Decimals to Mixed Fractions [10/09/1998]

Write this fraction as a mixed number: (.151515...+.555...)/ (.161616...- .2222...).

Greatest Common Factor (GCF) [04/13/1999]

How do you find the greatest common factor?

History of the Fraction Bar [09/01/2005]

What is the original name of the fraction bar? I know it is called the vinculum, but was that the original name? If not, what was it originally called?

How Can Division Result in an Increase? [10/29/2003]

How is it possible for division to give you a larger number, instead of a smaller one?

How Many Boys Are in the Seventh Grade? [05/20/1999]

In a seventh grade of 360 students, 80 percent can swim...

How Many Days in the Month? [01/22/2004]

There were eleven days of rain one month in Boston. Of the remaining days, two-fifths were sunny, one-fourth were cloudy, and it snowed the other seven days. How many days were in the month?

How Many Freshmen Originally Tried Out? [01/15/2003]

Some freshmen were trying out for the school track team... The 10 who remained became the track team.

How Much of a Total Price Is the Tax? [10/20/2003]

If an item has been purchased and all you know is the total cost for the item and tax, how can you determine how much tax was charged?

How Old Did This Man Live to Be? [02/23/1998]

A word problem involving fractions.

How to Divide Fractions? [11/6/1994]

When dividing fractions, for example: 3/11 divided by 5, I know that you reciprocate the "5" and multiply, but I don't understand why except that it works! Can you explain it?

How to Multiply Fractions [9/6/1996]

I'm having trouble multiplying fractions.

How to Pronounce a Fraction of a Percentage [07/07/2005]

Is it correct to say "one tenth of one percent" as opposed to saying "one tenth percent" for 0.1%? Why or why not?

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