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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Cutting An Equal Number of Slices of Cake [07/13/1998]

One cake is 35 slices and another is 42 slices. If the cakes need to have the same number of slices, how many slices should they have?

Cutting a Pipe [06/24/2003]

You have a pipe that is 21 1/8' long. How many 2' segments can be made of this pipe if 1/8' waste is created from each cut?

Decimal Multiplication and Division [11/19/2002]

I'm tutoring a 6th-grade student, and I'm having a hard time explaining to her why you sometimes need to put a zero in the tenths place, in the quotient.

Decimal Numerator? [04/08/2003]

Is there such a thing as .8/1 ?

Decimals: Terminating or Repeating? [01/26/2001]

How can you tell just by looking at a fraction whether, in decimal form, it will terminate or repeat?

Decimal To Fraction Conversion - A Simpler Version [11/25/2002]

A simpler version of the algorithm.

Definition of Repetend [9/17/1995]

What is the definition of repetend? Where can I find its definition on the net?

Denominator = 2 or 1/2 [01/16/1997]

My teacher says that when the denominator is 2, that means I cut the pie (or whatever) in 2....

Deriving Fractions from Decimals [07/19/2001]

I don't understand how to get the fraction for a decimal like 12.5% = 0.125 = 1/8 or 66.7% = 0.667 = 2/3.

The Difference between Calculating Markup and Profit Margin [08/11/2006]

If we have fixed costs of $50,000 on a product and want to have a profit margin of 25%, how much should we charge the customer to buy it?

Difference between Percent and Percentage [04/26/2008]

Is there any difference between percent and percentage?

Displaying Large Repetends on Small Calculators [05/31/2002]

How can I find a 16-digit repetend using an 8-digit calculator?

Dividing 17 Rings [10/22/1996]

How was the inheritance divided?

Dividing Compound Fractions [11/16/1999]

Can you give me a simple step-by-step method to simplify expressions like [(3/y)+(5/zy^2)] / [(5/2y)-(4/y^2)]?

Dividing Decimals by Whole Numbers [10/19/2002]

Dividing decimals has been hard for me to learn.

Dividing Fractions [12/5/1995]

Tell me a shortcut for dividing fractions.

Dividing Fractions [8/4/1996]

Why do you flip the second fraction when dividing fractions?

Dividing Fractions [10/16/1997]

Why do we have to flip the second fraction when we divide?

Dividing Fractions [03/16/1999]

Why can't we divide fractions directly? Why do we have to do it by multiplying?

Dividing Fractions: Why Invert? [01/24/2001]

Why do we have to invert the fraction in dividing fractions?

Dividing Two Numbers with and without Units [09/15/2004]

We can calculate $500/10 or $500/$10 and get $50 or 50 respectively. What units would the result have if we calculate 500/$10?

Dividing with Powers [01/16/2003]

I am having trouble with problems like (6.0 * 10^7)/(3.0 * 10^2).

Does My Fraction 1/1 Story Work? [11/04/2002]

Units in ratios: pitfalls of analogies and stories for understanding math.

Do We Need a Zero before the Decimal? [01/26/2005]

Do I need to use a zero to hold the dollar place if the amount is less than a dollar? I see money amounts written both ways, as $.45 or $0.45. Are both correct? If one is better, why is it better?

Duelling Percentages [06/11/2002]

Why doesn't a decrease of 15%, followed by an increase of 15%, get you back to where you started?

Egyptian Fractions [03/21/1999]

Can you help me understand Egyptian fractions?

Egyptian Fractions [06/11/2001]

The Egyptians wrote all their fractions as a sum of different fractions with a numerator of 1. I need to find a way to work out what fractions should be added together...

Eliminating Fractions in Division [11/20/2003]

How can I change a division involving a fraction to one involving only integers?

Equations Involving Fractions [07/07/2000]

How do I solve equations with fractions and decimals in them?

Equations with Fractions [04/21/1997]

How do you solve x/2 + x/3 = 1/6?

Equations with Fractions: 7y/9+2 = 2y/3 [11/23/1997]

First I moved the variables to one side and the numbers to the other, but I always ended up with -18/13.

Estate Distribution [05/10/1999]

Does 1/10 of the estate go to the church before or after taxes?

Estimating Fractions [12/02/2001]

There is a plate of assorted cookies, 1/6 chocolate chip and 1/5 peanut butter. The rest of the cookies are regular. What fraction do the regular cookies make?

Estimating Fractions/Mixed Numbers [01/10/2002]

I don't understand how to find an estimated sum of 1/6 + 5/8 or 13 1/8 divided by 6 1/5.

Even and Odd Fractions? [01/12/1999]

What rules would we have to have to be able to define a fraction as even or odd?

Examples of Fraction Multiplication and Division [05/14/1998]

I get confused on how to multiply and divide fractions ...

Expressing Percentages [01/26/2004]

Why do we sometimes use phrases like "4 out of 5 dentists"? Wouldn't it be more meaningful just to say 80% instead?

Factoring and Cancelling in Long Division [08/29/2003]

How do I perform long division? i.e. 1,002,240,000 / 86400

Factoring Fractions [05/31/2001]

I am having a major problem trying to figure out how to add fractions that have different denominators.

Figuring Out Fractions [04/28/2004]

I need help with adding and subtracting fractions, especially mixed numbers and equivalent fractions.

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