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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Adding and Multiplying Fractions [05/31/2001]

Why do I have to find a common denominator to add fractions, but not to multiply fractions?

Adding and Subtracting Algebraic Fractions [8/24/1996]

How do I add and subtract fractions with the same denominator?

Adding and Subtracting Percents [6/28/1996]

Could you please explain how to add and subtract percents?

Adding Fractions [05/21/2002]

How do you add fractions?

Adding Fractions That Have Variables [03/24/2002]

9a/10 + 2/5. I have the answer in the back of the book but I don't know how to solve it.

Adding Tax and Tip [07/19/1998]

In pricing our hotel luncheons, we charge a base price plus a 6.8% tax and a 20% service charge. How would I find the total in one step?

Algebra and Fractions [08/30/1997]

The sum of two-thirds and one-ninth of a number is 28. Find the number N.

Asking Price of a House [10/14/2001]

If a seller wants to clear $50,000 for his house and the real estate commission is 6%, what should be the asking price for the house?

Averaging Percentages [12/11/1998]

Why can you average percents in the usual way in some cases, and why do you have to use weighted averages in others?

Bar over a Whole Number? [06/05/2001]

What does a bar over a whole number indicate?

Boys Wearing Glasses [07/07/1999]

How many boys in a school wear spectacles if there are 1400 pupils, 1/4 of those wear spectacles, and 2/7 of them are boys?

Calculating Lengthy Repeating Decimals [10/26/2006]

The fraction 355/113 is used as an approximation for pi. A question about converting this fraction to decimal form leads to an interesting discussion of how to calculate long repeating decimals without having to divide them all the way out one number at a time.

Calculating Percentage Increase [07/09/2004]

If my salary increased from 45k to 65k over a period of 10 years, what percentage increase did I receive per year?

Calculating Percentage of Errors [03/21/2002]

You have items to be picked off a shelf every day. You pick one item a day and check it against the order. You wish to asign a percentage to the error in wrong items and/or number of items.

Calculating Percent Increases [10/29/1996]

What's the relation between evaluating 0.05 x 1200 + (1 x 1200) and 1.05 x 1200?

Calculating Sales Tax [09/19/2001]

How do I calculate sales tax? Please describe the steps.

Cancelling Fractions [01/04/1998]

How do you cancel 3/5 x 2/3?

Cancelling Fractions [05/06/2002]

I have to fill in the missing numbers: 2/? x 6/7 x ?/12 = 2/3

Cancelling Fractions [06/03/2003]

I am reading a book on algebra. The author states that cancelling is division too and then shows the following without any explanation of how it's done...

Can Negative Fractions Also Be Proper or Improper? [03/31/2004]

Is a fraction like -3/4 considered a proper fraction? Is -8/3 considered an improper fraction? I've generally thought that all proper fractions lie between 0 and 1 on a number line, but how do the negatives fit in?

Can You Have Zero in the Denominator? [11/7/1994]

My 7th grade math teacher and I are in the midst of an argument over whether any number can be placed over zero in a fraction. I know that a fraction like 10/5 equals 2, and 5*2=10, and that works out for all fractions where the numerator is larger than the denominator, but it doesn't work out for n/0. You'll probably say that it isn't a legitimate fraction, but.. I still say that it is. :)

Changing a Repeating Decimal to a Fraction [09/22/2002]

How do you change 0.75 repeating (0.757575...) to a fraction?

Checking Your Work [09/11/2003]

Our whole class has come up with one answer to a problem, while the teacher's answer book gives a different answer. What have we done wrong?

Clarifying Percentages vs. Percentage Points [11/21/2003]

What is the difference between measuring using percentages versus measuring using percentage points? What is meant by a percentage point?

Clock Hands and Hours Worked [01/29/2003]

A man arrives at work between 8:00 and 9:00 a.m. at exactly the moment the minute hand and hour hand of the clock point in the same direction.... How many hours did the man work?

Comments on Dividing Fractions [03/15/2007]

A question on how to divide fractions leads into comments on how division and subtraction can be thought of as multiplication and addition of an "inverted" number.

Commissions [03/19/2002]

Mildred receives a 5% commission on her sales of exercise equipment and a 6% commission on her sales of weight training equipment...

Comparing Fractions [03/11/1999]

What is the easiest way of telling that one fraction is bigger than another (e.g. 5/9 and 5/6)?

Comparing Individual Discounts to a Collective Discount [07/19/2005]

I am purchasing two books that each have a 10% discount. If the discount is taken on each book first or taken on the total price of the two books, will the result be same or different?

Comparing Ratios and Fractions [01/06/2002]

What are the differences between ratios and fractions?

Converting a Mixed Decimal to a Fraction [11/09/2001]

Write 4.16 2/3 as a mixed number. We know the answer is 4 1/6; we just can't figure out why.

Converting a Repeating Decimal to a Fraction [9/10/1996]

Why does this way of converting a recurring decimal to a fraction work?

Converting Between Mixed Numbers and Improper Fractions [04/08/1999]

Pictures and step-by-step instructions for changing mixed numbers to improper fractions and back again.

Converting Decimals to Fractions [7/10/1995]

A certain fraction is converted to a decimal and the decimal representation is 0.6428571428571428571... What is the fraction?

Converting Fractions and Decimals [02/05/1997]

How do you convert fractions to decimals? How do you convert decimals to fractions?

Converting Fractions to Percents [04/24/2001]

How can I easily convert fractions such as 4/9, 10/9, or 11/12 into percentages?

Converting Repeating Decimals into Fractions [10/22/2003]

I am looking for a rational number with a repeating/non-terminating decimal expansion where the repeating pattern is 12 digits long. How can I find such a number?

Converting Repeating Decimals into Fractions [06/25/2008]

How do you convert a repeating decimal to a fraction when there are some numbers before the part that repeats, like in 0.916666...?

Converting Repeating Decimals to Fractions [12/17/2006]

How do you change a repeating decimal where the first few numbers are not repeating, like 2.41666..., into a fraction?

Cross Products [02/28/1999]

I am having trouble understanding cross-products.

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