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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Multiplying Fractions [07/09/1999]

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

Multiplying Fractions and a Whole Number [5/16/1995]

How are problems like 3/5 x 4 done?

Multiplying Fractions by Cancellation [10/09/1998]

I'm trying to multiply fractions by cancelling out numbers...

Multiplying Mixed Numbers [04/06/2004]

Why do you need to convert mixed numbers to improper fractions before multiplying them together? What is the mathematical reason behind this operation?

Multiplying Numbers with Decimals [12/7/1995]

What is 9.4 x 9.6 ?

Multiplying Unlike Fractions [4/1/1996]

What is the fastest way to multiply unlike fractions?

Multiplying Whole Numbers by Fractions [05/31/1999]

How do you multiply whole numbers by fractions?

Name an Equivalent Decimal [08/31/2001]

Examples of problems: 0.3, 3.10, 2.7, 5.00, 87.05, etc.

Name of Bar That Denotes a Repeating Decimal [08/30/2004]

What is the name of the bar that goes over a digit or group of digits that signifies that the digit or group repeats?

Number of Places in Products of Decimals [09/19/2002]

When you multiply decimals, why is there always the same number of decimal places in the answer as in the problem?

Numbers in a Fraction [05/20/2001]

Is a fraction one number or is it two numbers?

Numerator, Denominator: Etymologies [03/25/2002]

Why are the parts of a fraction called the numerator and the denominator?

Numerators and Denominators in Addition [3/3/1996]

Why do we add numerators but not denominators when we add fractions with like denominators?

The Oneths Place [09/29/1998]

In decimal numbers, why is there no oneths place?

Ordering Decimals [10/17/1998]

What is the best way to learn how to compare decimals? For example, is .467 less than, greater than, or equal to .465?

Ordering Fractions [01/17/2003]

How do I order the fractions 2/3, 3/5, and 2/7?

Ordering Fractions by Changing Them to Decimals [12/11/2008]

How can I put the fractions 3/10, 1/2, 7/8, 4/5, 1/6, 3/4, 9/10, 1/3, 3/5, 3/8, 1/4, and 1/10 in order from least to greatest?

Ordering Improper Fractions [10/12/2002]

How can I explain ordering improper fractions?

Order of Decimals [05/18/1999]

How do you order decimals, for instance, 5.9, 6.10, 2.52 ?

Order of Operations [8/21/1996]

How do I solve (8.2 - 3.6)(3 * 3.6 + 6)?

Order of Operations and Fractions [02/22/2002]

Given a+3 and b+5, is 105 / ab 7 or 175?

Origin of the Term "Improper" Fraction [07/28/2006]

Why are fractions with larger numerators than denominators called "improper"? Where did the terms "proper" and "improper" originate in relation to fractions?

Percentage of Votes Cast [06/03/2003]

If you have two percentages, say 25% and 50%, can you do a percent change between the two?

Percent or Percentage? [05/14/2002]

Would you please explain the exact difference between the words percent and percentage?

Picturing Dividing Fractions [04/02/2001]

My fifth graders can divide fractions without a problem, but we can't draw the division problems out to prove our answers...

Placement of the Negative Sign in a Negative Mixed Number [10/25/2004]

When you have a negative improper fraction, can the negative sign be put anywhere in the fraction? For instance, is -1 3/5 the same as 1 -3/5 and 1 3/-5?

Place Value and Similar Numbers [08/15/2003]

How do you read these numbers? Is there a difference? 10.200, 10.00002

Price before Discount [6/3/1996]

A calculator's price is discounted 20 percent. After adding 7 percent tax...

Product of Terms of a Sequence [04/18/2003]

Find the product of the first 99 terms of the sequence 1/2, 2/3, 3/4, 4/5, ...

Proof for Dividing Fractions [01/18/2002]

Could you please send me a proof for dividing fractions?

Putting Fractions in Order [01/24/2001]

I am trying to order fractions from least to greatest, but am having no luck.

Putting Rational Numbers in Order [09/22/2002]

I have to order 4/15, 6/17, and 3/16 from least to greatest, and I can't use a calculator.

Rationalizing the Denominator [05/03/1999]

Why can't you have a square root in the denominator of a fraction?

Reaction Time: Softball, Baseball [04/26/2003]

A baseball pitcher throws at 90mph from 60 feet, and a softball pitcher throws at 60mph from 40 ft. How can I measure reaction time for the batters?

Reciprocal of a Mixed Number [06/01/1999]

What is the reciprocal of 6 and 1/3?

Recurring Decimal Notation [05/12/2003]

What is 0.321 with dots over the 3 and the 1?

Reducing Fractions [03/17/1997]

How do you know when a fraction is in its simplest form?

Reducing Fractions [5/30/1996]

What is the easiest method of reducing fractions to lowest terms?

Reducing Fractions with Large Numbers [03/18/2004]

If you reduced 32/48 to lowest terms, what would the answer be? Those are big numbers, which makes it hard for me.

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...

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