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Word Problems

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.

Cross Products [02/28/1999]
I am having trouble understanding cross-products.

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?

Decimals Versus Fractions: Pluses and Minuses [08/19/2011]
We already have fraction notation, so what's the point of decimals? A new teacher relaying this question from her middle schoolers wonders if, like other formal representations in math, decimals just amount to another "shorthand." Comparing notational systems to tools, Doctor Ian responds with the various computational advantages and disadvantages of fractions and decimals, before concluding that different tools suit jobs differently.

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

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