Ask Dr. Math

Elementary Archive

Browse Elementary Fractions & Decimals
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Adding and subtracting fractions.
    Finding a least common denominator (LCD).
    Dividing fractions.
    Comparing/ordering fractions; equivalent fractions.
    Reducing/simplifying fractions.
    Improper fractions and mixed numbers.
    Dividing decimals.
    Converting fractions to/from decimals.
    Rounding fractions and decimals.
    Fractions and repeating decimals.

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Borrowing in Subtraction in Various Contexts [10/25/2006]

An explanation of using borrowing to calculate 12 5/11 minus 2 6/11 is extended to borrowing when subtracting times, liquid measures, and other wholes and parts in general.

Canceling and Reducing When Multiplying Several Fractions [01/25/2008]

I need help when multiplying three or more fractions. How can I cancel numbers out when they are not next to each other?

Canceling Instead of Multiplying and Dividing [09/25/2003]

Find the value of the product 3/5 x 5/7 x 7/9 x 9/11 x 11/13 x 13/15.

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...

Changing Decimals to Whole Numbers when Dividing [12/10/2001]

Why does a decimal need to be a whole number before you can divide?

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?

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.

Common Denominators [2/8/1996]

Why do fractions need common denominators in order to be added?

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)?

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 Clock Time to a Decimal [06/04/1999]

How can you convert a time range to a decimal?

Converting Decimals to Fractions [06/07/1998]

How do you convert decimals to fractions?

Converting Fractions and Decimals [02/05/1997]

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

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 to Fractions [01/20/1998]

Change the sum of the decimals to a fraction for 0.77777......., 0.4; change each decimal to a fraction and add the fraction; compare the answers.

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?

Counting Decimal Places [05/22/2001]

When multiplying decimals, why does placing the decimal in the answer by counting the number of decimal places in the problem and counting from the right the same number of places work?

Creating Improper Fractions [02/28/1998]

How do you change a mixed number into a improper fraction?

Cross Products [02/28/1999]

I am having trouble understanding cross-products.

Decimal Division [09/02/1997]

How do I divide with numbers that have decimals in them?

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 by Numeric Value [03/12/2001]

Arrange from least to greatest: 0.1, 0, 0.01, 1.0.

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....

Denominators [12/31/1997]

I have a problem with different denominators... 4/5+5/6+7/16 = ? What is the best and fastest way to find the LCD?

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.

Difference between Percent and Percentage [04/26/2008]

Is there any difference between percent and percentage?

Different Techniques for Rounding Off Decimal Numbers [01/28/2006]

A discussion of some alternatives to the traditional rounding technique.

Dividing by a Fraction [6/7/1995]

Why is it when dividing fractions you have to multiply by a reciprocal?

Dividing Decimals with a Remainder [03/30/2001]

What should I do when the directions say to divide and I get a remainder, or if they say round to the hundredths place and there is a remainder?

Dividing Fractions [7/5/1996]

I always get stuck on dividing fractions.

Dividing Fractions [03/16/1999]

Why can't we divide fractions directly? Why do we have to do it by multiplying?

Dividing Fractions [3/18/1995]

My class would like an explanation on why you invert and multiply when dividing fractions.

Dividing Fractions [8/17/1996]

What is one-half divided by three-fourths?

Dividing Fractions: Why Invert? [01/24/2001]

Why do we have to invert the fraction in dividing fractions?

Dividing Two Decimals [8/30/1995]

I don't understand dividing one decimal number by another decimal number.

Does My Fraction 1/1 Story Work? [11/04/2002]

Units in ratios: pitfalls of analogies and stories for understanding math.

Do Fractions Have to be Equal? [05/09/2003]

A textbook defines fractions as 'one or more of the equal parts of a whole.' Is this true? Do the parts of the whole have to be equal?

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