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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100 Percent of Daily Allowance of Iron [09/30/2001]

A common foodstuff is found to contain .00125% iron. The serving size is 87.0 grams. If the recommended daily allowance is 18mg of iron, how many servings would a person have to eat to get 100% of the daily allowance of iron?

2a/5 or 2a Divided by 5? [12/13/2001]

Why, when writing a division problem, do you write 2a over 5 instead of 2a divided by 5?

33 1/3 Percent as a Fraction [08/03/2003]

I need help turning percents like 33 1/3%, 2.5%, and other percents like that into fractions.

(9/2)/(3/4): A Picture [03/27/2003]

We were trying to find a division fraction question and everything we came up with turned into a multiplication fraction problem. Why is that?

Adding and Subtracting Fractions [10/25/1999]

Can you help me learn to add and subtract fractions?

Adding Mixed Numbers [04/13/1999]

How do you add mixed numbers without renaming?

Algebraic Fractions [5/27/1996]

How would you solve for x and find the least common denominator in the equation 2/x = 4/3?

Algebra using Fractions [5/27/1996]

Please show me how to solve this equation: (5/8)X = 9

Cancelling Fractions [03/06/2002]

How do I cancel this problem: 1/5 x 40/1 x 1/2 ?

Changing Decimals to Fractions and Reducing [12/12/2002]

Could you please help me to understand, in the simplest way, how to write a decimal as a lowest-term fraction or mixed number?

Checking Proportions using Square Roots [04/11/2002]

Multiply two fractions, and then take their square root. If it equals one of the fractions you began with, you have a true proportion. Does this always work?

Clarifying Fraction Notation [07/02/1997]

.83 1/3... a trick problem?

Congruent Fractions [04/03/1997]

What are congruent fractions?

Converting Fractions to Decimals [01/08/1997]

How do you convert fractions to decimals? How do you turn decimals into ratios?

Converting Ratios to Percentages [08/03/2003]

How do I convert 1:200 to a percentage?

Converting Repeating Decimals to Fractions [11/19/1997]

I know .333333333333 is 1/3, but what is the trick to it?

Cross-Multiplication [08/04/2002]

Can you explain cross-multiplication?

Diagram Showing Division of Fractions [01/13/2002]

I understand how to divide fractions, but would like to be able to draw this problem in a diagram: (2/3)/(3/4) = 8/9.

Dividing a Fraction by a Fraction [08/11/1997]

Can you help students visualize a problem such as: 1/3 / 1/2 = 2/3 ?

Dividing by a Negative Fraction [01/24/2002]

I understand how to divide fractions, but what if one of them is negative?

Dividing Fractions [7/5/1996]

I always get stuck on dividing fractions.

Dividing Fractions to find Decimals [03/12/2001]

Why does dividing the numerator by the denominator give you the decimal form of a fraction?

Division [11/25/1997]

How do you divide 1,000,000,000,000 by 999,999,999,999,999,999,999?

Employee Pay Schedule [07/12/2003]

For a particular job, Moe should get 40% of the gross pay, Larry should get 30%, and Curly should get 30%, assuming they all work the same number of hours. But how should the money be divided if they work different numbers of hours?

Explaining Division of Fractions [08/11/1999]

Can you give a practical explanation of why the 'invert-and-multiply' rule for division of fractions works?

Explaining Fractions [11/06/2001]

I am a practicum student in a 8th grade math class. The teacher and I don't know how to explain to the students why you can do this manuever. c=d/g; c/d=g; d/c=g.

Figuring a Percentage [5/24/1996]

What percentage is 3 times as many?

Figuring a Tax [05/13/2003]

I work in insurance. We have a premium of $75,329. This premium needs to be increased by a tax of 3.75%...

Figuring Percentage of Increase [09/05/2001]

In 1990, Allen County, Kansas, had 14,385 people. Now, in 2001, it contains 14,905 people. How do I calculate the increase, using a percentage?

Finding a Percentage [01/26/2001]

How do you arrive at a percentage that a number is of a number? Example: what percent of 32000 is 2000?

Finding Percentage of Increase [06/07/2003]

Find the percentage increase: old, $50.50; new $75.75.

Finding Percentages [12/5/1996]

I want to know how to find percents of a number - for example, how to find 13 percent of 29.

Finding the Lowest Common Denominator [12/11/1995]

What is the most efficient way to find the lcd (lowest common denominator)?

Fractional Exponents [08/09/1997]

Is there a proof for X^1/2 = the square root of X?

Fraction Bar Name [12/14/1996]

What is the name of the little line that separates the divisor from the dividend in a standard division question?

Fraction Basics [7/21/1996]

I don't understand how to do fractions.

Fraction Diagrams [03/13/2002]

In an adult condominium complex, 2/3 of the men are married to 3/5 of the women. What fraction of the residents are married?

A Fraction Divided By a Fraction [8/30/1995]

What is 18/6 divided by 2/3?

Fraction Multiplication [7/22/1996]

The meaning of the dot between two fractions.

Fraction Multiplication and Division [02/10/2001]

How do you do calculations like 2 1/10 * 7 5/8 or 27/30 over 75/100?

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