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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Greatest Common Factor (GCF) [04/13/1999]

How do you find the greatest common factor?

Hidden Decimal Points [02/04/2002]

I get confused when subtracting 4 from 24.98. I keep coming up with 24.94. Could you explain why whole numbers do not show their decimal point?

How Can Division Result in an Increase? [10/29/2003]

How is it possible for division to give you a larger number, instead of a smaller one?

How Many Days in the Month? [01/22/2004]

There were eleven days of rain one month in Boston. Of the remaining days, two-fifths were sunny, one-fourth were cloudy, and it snowed the other seven days. How many days were in the month?

How Many Significant Digits? [10/17/2001]

Why does 5030 have three significant digits and 5030. four?

How Much of a Total Price Is the Tax? [10/20/2003]

If an item has been purchased and all you know is the total cost for the item and tax, how can you determine how much tax was charged?

How to Divide Decimals by Decimals [03/07/1998]

I don't understand dividing decimals ...

How to Pronounce a Fraction of a Percentage [07/07/2005]

Is it correct to say "one tenth of one percent" as opposed to saying "one tenth percent" for 0.1%? Why or why not?

Ignoring Zeros [09/03/1998]

Are 0.76 and 0.760 equal? When can you ignore the zeros?

Improper Fractions [05/20/2002]

How can 14/9 be a fraction when you can't have 14 parts of something that's been cut into 9 parts?

Improper Fractions and Mixed Numbers [09/10/1997]

What do you do when the numerator of a fraction is bigger than the denominator?

Inches and Feet in Decimal Form [7/16/1996]

How do I convert fractions of inches and feet into a decimal expression of the length in feet?

Introduction to Division with Negative Numbers [05/05/2004]

I don't know how to do division with negative numbers, like +18/-9 or -24/-8 or +21/-3.

Invert and Multiply [11/08/1997]

I am struggling with how to explain to a class WHY we invert and multiply when dividing fractions.

Is Division Sharing? [09/08/2001]

Why in fraction division is the answer larger than the first fraction?

The Joy of Fractions [05/18/2002]

How come fractions are called fractions? How come they can be translated into decimals? Why do they hurt your brain when you first learn them?

Learning Decimals [10/19/1998]

Can you explain decimals to me?

Learning Fractions in the Metric System [11/27/2003]

Since the metric system doesn't use fractions, are math students in metric countries able to skip fractions and work on more useful things?

Longfellow's Bees [08/01/2002]

One-fifth of some bees fly to the rosebush, one-third fly to the apple tree, and three times the difference fly to the acorn tree. One bee is left flying around. How many bees are there altogether?

Meaning of Multiplying Fractions [12/09/1999]

What does it mean to multiply a fraction by a fraction?

Measures of Music and Fractions [01/13/1999]

How can you tell what fraction of a measure a note is? How does it relate to the time signature?

Mixed Numbers [03/20/2001]

I am having trouble with mixed numbers. Is there an easy way to remember how to do them?

Mixed Numerals [2/14/1996]

How can 7/3 be 2 and 1/3?

Moving the Decimal Point [12/04/2002]

When you divide two decimals, what is it called when you move the decimal point?

Multiplication [02/11/1999]

How many decimal places should the product of 3.26 and 0.25 contain?

Multiplication of Fractions [03/22/1999]

What are cancellations?

Multiplying a Fraction by a Decimal [9/5/1996]

How do I simplify and multiply (40/360) by 78.5?

Multiplying and Adding Fractions [04/01/1997]

How do I solve (1/3 + 2/5) * 3/4 ?

Multiplying and Dividing Mixed Numbers [6/5/1996]

How do you divide 1 1/2 by 9/10 or multiply 8 1/4 by 2 2/3?

Multiplying by 1000 [03/10/1997]

What is 2,542 times 1,000?

Multiplying by a Decimal [11/10/1994]

How come when you multiply 0.36 and 88 you get 9.4270, which is less than what it should be?

Multiplying by a Decimal Number [02/28/2001]

I am having trouble understanding why multiplying by decimal numbers gives a product smaller than the factors.

Multiplying by Fractions and Decimals [5/31/1996]

What number is 3/10 more than .025?

Multiplying by the Reciprocal to Divide Two Fractions [05/08/2008]

Why does it work to divide two fractions by multiplying the numerator times the reciprocal of the denominator?

Multiplying Decimal Numbers and Placing the Decimal Point [09/20/2007]

Why does counting up the total decimal places when multiplying decimal numbers work?

Multiplying Decimals and Decreasing Answers [12/02/1998]

Why does multiplying by a decimal decrease the answer? How can you have less than what you started with when you multiply?

Multiplying Decimals by Negatives [03/18/2002]

I can't find decimals on my calculator.

Multiplying Fractions [1/28/1996]

I need help with problems such as this one: 3 1/4 x 3/4 = ?

Multiplying Fractions [01/20/1997]

If multiplication is defined as repeated addition, why is the product of two fractions smaller than either of the fractions?

Multiplying Fractions [07/09/1999]

I need to know how to multiply fractions like 3/5 x 5/8.

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