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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Fractions of Musical Notes [10/14/1997]

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

Help With Multiplication and Percents [11/11/1996]

Can you help me with multiplication so that I can better understand percents?

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.

Making Fractions into Percentages [04/30/2003]

What percentage is 3/5?

Multiplication of Decimals [01/02/2002]

When numbers after decimal points are added together the decimal place can then be placed that number of places from the right. Why? How does this work?

Multiplying and Dividing Decimals [6/27/1996]

Would you please explain multiplication and division of decimals?

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 Fractions and Mixed Numbers [03/12/1997]

How do you multiply fractions and mixed numbers like 1 1/3 x 1/4 = ?

Multiplying Mixed Numbers [06/02/2003]

Can you multiply mixed numbers without changing them into improper fractions?

Multiplying Mixed Numbers [05/28/1998]

Explaining and illustrating how to multiply fractions and mixed numbers.

Reciprocals [12/19/1996]

What is the use of reciprocals?

Reducing Fractions [3/7/1996]

How do you bring a fraction like 5/8 to its lowest term? Please explain the procedure.

Reducing Fractions [02/25/1997]

How do you reduce fractions?

Reducing Fractions with Large Numbers [01/30/1998]

Is there a "trick" for going through the possibilities before declaring that 4,5,6,7,8,9, digit number fractions may or may not be reduced?

Relating Decimal Answers to Remainders [02/15/2002]

How did you divide 457/5 and get the answer 91.4, and why is it a decimal?

Renaming Fractions [05/22/2000]

Can you explain renaming fractions in a way I can understand?

Rounding Decimals [06/14/1999]

Is 1.9949 rounded to 2 decimal places 2.00 or 1.99?

Simplifying Expressions with Fractions [9/2/1996]

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

Simplifying Fractions [12/08/2002]

Finding and eliminating (cancelling) prime factors.

Subtracting Decimals with Borrowing [10/09/2001]

How do you subtract 488.354 from 536.30?

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

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

Understanding Common Denominators [07/16/1997]

What is a common denominator?

Unit Conversions: mph to fps [03/06/2003]

How can I find out how many feet per second I could travel driving 55 miles per hour?

Using Fractions to Read Decimals [08/29/2001]

Can you please tell me how to read in words, decimals such as: .02, .20, etc.?

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?

3/4 of _____ Is 90 in Three Ways [03/24/2010]

In a multiplication problem like "Three-quarters of _____ is ninety," how do you fill-in- the-blank with the factor that satisfies the equality? Doctor Ian presents three different methods: guess-and-improve; the equivalency between multiplication and division; and multiplying through by a reciprocal.

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 a Zero When Multiplying a Decimal [06/21/2001]

I don't understand why you add a zero when multiplying decimals.

Adding Fractions [6/5/1996]

Can you help me with this question? 1 1/2 + 4 3/2.

Adding Fractions [7/26/1996]

How do you add fractions?

Adding Fractions [11/10/1997]

How do you add 4 2/3 + 3 1/6?

Adding Fractions [05/21/2002]

How do you add fractions?

Adding Fractions [01/13/2003]

2/25 + 2/15 equals what?

Adding Fractions Without Using the LCD [11/18/1999]

I think I've found a new way of adding fractions that doesn't require finding the LCD. Can you tell me whether or not my method works, and if it is a new discovery?

Adding Mixed Numbers [12/10/1995]

3 1/4 + 5 3/12

Adding Tax and Tip [07/19/1998]

In pricing our hotel luncheons, we charge a base price plus a 6.8% tax and a 20% service charge. How would I find the total in one step?

Bar over a Whole Number? [06/05/2001]

What does a bar over a whole number indicate?

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