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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Repeating Decimals [04/28/1999]

I am interested in finding longer repeating groups in number tails of repeating decimals.

Repeating Decimals [01/24/2001]

By looking at the denominator, how can you determine if the decimal representation of a fraction will terminate or repeat?

Repeating Decimals and Fractions [11/27/2001]

I have a chart of repeating decimals and their fraction equivalents. The decimal is .71 and they give a fraction of 5/7. I cannot figure out how they came up with this number...

Repeating Decimals as Geometric Series [02/13/2001]

How can you express repeating decimals as geometric series and convert them to fractions using the series sum formula?

Representing Rational Numbers [09/17/2002]

What do fractions, decimals, and percents have in common?

Restoring an Original Price [8/6/1996]

What percent markup do you use to restore a price to its original value after a discount?

Rounded Fraction of Pi [10/10/2001]

I want to find about 20 digits into pi. What would the fraction (division problem) be for that?

Rounding Discounts and Sales Tax [03/20/2002]

Why, when computing sales tax, do we round up before adding it to the price? Why not follow rounding rules?

Rule of Three [06/15/2002]

Please explain to me briefly (and with an example) the concept of the rule of three.

Sales and Taxes [03/11/2001]

I bought $27.97 worth of food. The food tax is 5.5%. I'm trying to find the tax I have to pay, and the total amount that I pay.

The Secret to Mathematics? [09/27/2004]

I understand how to divide fractions--invert and multiply--but what if the dividend or divisor is a variable?

Serving Size, Calories, Daily Values, and Food Labels [05/26/2005]

How do they determine the percent of daily value, calories, and other information shown on food labels?

Shortcut for Comparing Fractions [01/14/2003]

My teacher showed us how to cross multiply to compare fractions.

Shortcut: Repeating Decimals to Equivalent Fractions [03/24/2001]

Is there a shortcut for changing a repeating decimal into its equivalent fraction?

Simplifying Fractions by Factorizing [05/22/1998]

Using factor trees to prime factor and simplify 188/240.

Simplifying Fractions with Radicals [03/09/2006]

How do I simplify 18*sqrt(200) divided by 12*sqrt(500)?

Simplifying Mixed Algebraic Expressions [05/08/1998]

Simplifying fractions such as 2x - (x+y)/y and 4 - 3/(y-1) - 1/(y+1).

Simplifying: Put it Together [4/5/1996]

I am supposed to perform the indicated operations and express the results in lowest terms. Here's the problem: (5/x-1) - (4x/x-1) - (2-x/x-1) = ?

Solve for X [10/09/1999]

How can I solve equations like 4x - (1/2) = -3/2?

Solve for x in a Percentage Equation [2/5/1996]

Express as a function of x. 1) The volume of water that must be added to 5L of antifreeze to make a solution that is x% antifreeze...

Solving a Fraction Problem Using Common Sense [03/21/2004]

When the gun sounded, only two-fifths of the racers began to run. If 460 racers began to run, how many racers were there in all? Can you show me how to figure out what a fraction is without knowing the total number?

Solving Equations with Fractions in Them [12/06/2004]

How do you solve an equation like -5/7 n = 35?

Solving Linear Equations by Using Inverses [08/13/2003]

Solve for a in b = 5/7(a-8).

Solving Two Equations with Mixed Fractions [05/13/1998]

Steps to solving (2 2/3)x - 1 1/4 = 4 1/3 and (4 1/5)x - 2 = 3 1/3.

Splitting Peanuts [08/03/2002]

On a camping trip, the family had brought many bags of peanuts for snacks...

Square Roots and Fractions [10/25/1998]

How do you simplify a square root of a fraction?

Stock Market Fractions [04/05/2002]

Stock closed on Friday at a price of 42 5/8. On Monday stock closed at 39 7/8. How much did the market value of stock drop on Monday?

Subtleties of Rounding [09/24/2003]

There are 480 freshmen at Washington High. If 36% of the freshmen play sports, how many play sports? Is it 172 or 173?

Sum of a Number and Its Reciprocal [01/28/2002]

The sum of a number and its reciprocal is 5 1/5. What is the number?

Techniques for Comparing and Ordering Fractions [07/16/2008]

I'm taking a timed test and need to be able to arrange as many as five or six fractions in order from least to greatest. Do you have any tips on how to do that quickly?

Terminating and Repeating Decimals [04/20/2003]

Which one of these can only be written as a repeating decimal? 3/8; 7/ 16; 1/2; 5/6.

Thinking about the Mediant of Two Fractions [12/10/2009]

One of my students noticed that when given 1/a and 1/b, the fraction 2/(a+b) always seems to be in between 1/a and 1/b. Is this a new fraction rule, or has this been discovered and proved before?

Tips for Simplifying Fractions [06/03/1998]

Can you give my some tips to help me simplify fractions?

Tips on Quickly Converting Fractions to Percents [02/14/2005]

Is there an easy way to turn fractions like 9/60 into a percent without using a calculator?

Two Ways to Change Percents to Fractions [02/21/1998]

How do I change something like 10 1/4% into a fraction?

Undefined Fractions [02/19/2002]

Why is a fraction with a denominator of zero called "undefined"?

Undefined Fractions [06/10/2005]

I am having trouble determining the difference between an undefined fraction and a fraction with no solution. Maybe you can help me determine the difference.

Understanding Decimal Notation [06/10/2002]

I've been told that you should be able to look at a number like 2 15/100 and know that the decimal equivalent is 2.15. But I don't understand why they're the same.

Undoing Percentage Changes [07/10/2002]

If I increase an initial amount by P percent, by what percentage would I have to decrease it to get back to where I started?

Unit Fractions and the Greedy Algorithm [12/27/2000]

How can I represent 2000/2001 as the sum of unit fractions?

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