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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Fraction Problems [4/25/1995]

I am having trouble with some fractions and fractional equations.

Fractions, Improper Fractions, Mixed Numbers [02/01/1997]

How do you turn an improper fraction into a mixed number?

Fractions in the SI System? [11/07/2001]

When using metric can 4 cm and 5 mm be written as 4 1/2 mm?

Fractions of Musical Notes [10/14/1997]

How many notes are in two sixteenth notes plus eighth notes with five quarter notes?

Fractions with Repeating Decimals [02/24/1997]

How do you know if a fraction will have a repeating decimal or if it will terminate?

Fraction to Decimal to Percent Conversions [10/29/2001]

My teacher requires us to be able to convert fractions, percents, and decimals all together rather than converting a percent to a fraction OR a decimal...

How Many Boxes? A Diagram [03/20/2003]

There were juice boxes in a cooler. Jared took 1/6 of them. Sara took 1/4 of what was left. Now there are 15 boxes. How many boxes were there to start with?

Improper Fractions [04/15/1999]

I need help making improper fractions into mixed numbers.

Inches, Feet, Yards, Miles, and Unit Fractions [01/29/2002]

I need to know if you multiply or divide in changing feet to inches, feet to yards, miles to yards, feet to miles, yards to miles, yards to feet.

Least Common Multiple [3/29/1996]

I have a question about how to find the least common multiples from a set of numbers.

Making Fractions into Percentages [04/30/2003]

What percentage is 3/5?

Markups and Discounts [02/12/2002]

What is the correct way to mark up or discount a product?

Multiplying and Dividing Fractions [01/23/2001]

We are trying to figure out how to understand division and multiplication of fractions.

Multiplying Fractions [04/11/1999]

The basics, with a step-by-step example.

Multiplying Fractions [02/06/2001]

I need help solving 8/9 * 3/5. What is cross-cancelling?

Multiplying Mixed Numbers [05/28/1998]

Explaining and illustrating how to multiply fractions and mixed numbers.

Origin of the Percent Symbol [02/12/2002]

Where did the percent symbol originate?

Percentage as Standard for Comparison [05/12/2003]

How can you have more than 100% of something?

Percentage Increase in Cost of Eggs [8/4/1996]

When eggs went from 17 to 39 cents, by what percent did the price increase?

Percentage Increase vs. Percentage [05/13/2003]

If there were 10,000 claims in 2001, and that is a 300 percent increase since 1999, how many claims were there in 1999?

Percentage of Increase [7/23/1996]

What is the percent of increase when you go from 96 to 256?

Percentage Problems [01/20/1998]

What number is 25 percent of 24? 24 is what percent of 25? 24 is 25 percent of what number?

Percentages to or from Fractions [04/04/1997]

How do you convert between percents and fractions?

Percentage Target (Projection) [07/24/2003]

I am trying to work out percentage difference between a given figure and a projected figure in the future.

Percent Change, Increase, Difference [07/15/1997]

How do you find the percent difference between two numbers? What about percent change and percent increase?

Percent Problem [5/21/1995]

What percentage of 76 is 27?

Percent vs. Percentage [08/17/2002]

What's the difference between percent and percentage?

Ratios as Fractions [01/26/1997]

How do you put ratios into simplest form?

Reciprocals [12/19/1996]

What is the use of reciprocals?

Simplifying Expressions with Fractions [9/2/1996]

How do I simplify 9(-1/7)(1/3)(-28) ?

Simplifying Fractional Equations [4/4/1996]

I am supposed to perform the indicated operations and express results in lowest terms: 1: ((x^2 - 2xy + y^2) / 6xy) * ((3x^2y^2) / (x^2 - y^2)) = ?

Simplifying Fractions [12/08/2002]

Finding and eliminating (cancelling) prime factors.

Turning a Repeating Decimal into a Fraction [10/18/2002]

How do I make a decimal like .063490634906... into a fraction?

Unit Analysis and Conversion Factors [02/01/2003]

How to convert the following? 7.5 x 10^4 nm to kilometers; 3.9 x 10^5 mg to decigrams; 2.21 x 10^-4 dL to microliters.

What is a Significant Digit? [12/25/2001]

I came across a question asking for an answer with no more than "2 significant digits" - can you please explain what a significant digit is?

Why Divide Fractions? [11/5/1994]

Where, in this wide world of ours, would one divide fractions? For example: 3 2/5 / 7/8. Can you give me a real life example?

1/x = x% [04/16/2001]

For what value of x does 1/x = x% ?

34 is 51 Percent of J [11/12/2001]

A hint about problems that use the word "of."

3 Methods for Finding Least Common Denominator [02/04/1998]

My fifth graders are having a very difficult time understanding how to get the least common denominator. Any shortcuts?

Adding Algebraic Fractions, Different Denominators [8/24/1996]

How do I solve 7/2x + (2-x)/(3x^2) + (3 + 5x)/(6x^3)?

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