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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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?

Do We Need a Zero before the Decimal? [01/26/2005]

Do I need to use a zero to hold the dollar place if the amount is less than a dollar? I see money amounts written both ways, as $.45 or $0.45. Are both correct? If one is better, why is it better?

Duelling Percentages [06/11/2002]

Why doesn't a decrease of 15%, followed by an increase of 15%, get you back to where you started?

Egyptian Fraction [3/29/1996]

Why did the Egyptians use a special symbol for the fraction 2/3?

Eliminating Fractions in Division [11/20/2003]

How can I change a division involving a fraction to one involving only integers?

Equivalent Fractions [12/19/1996]

What are equivalent fractions and how do you use them?

Equivalent Fractions [05/07/1999]

I am trying to understand equivalent fractions like 6/12 = 1/2.

Equivalent Fractions [6/11/1996]

I don't understand equivalent fractions -- I understand how to do it, but I don't understand how you would know if it is right.

Estimating Fractions [12/02/2001]

There is a plate of assorted cookies, 1/6 chocolate chip and 1/5 peanut butter. The rest of the cookies are regular. What fraction do the regular cookies make?

Estimating Fractions/Mixed Numbers [01/10/2002]

I don't understand how to find an estimated sum of 1/6 + 5/8 or 13 1/8 divided by 6 1/5.

Even and Odd Fractions? [01/12/1999]

What rules would we have to have to be able to define a fraction as even or odd?

Examples of Fraction Multiplication and Division [05/14/1998]

I get confused on how to multiply and divide fractions ...

Explaining Rounding Using a Number Line [7/29/1996]

What is the best way to introduce and explain the term "rounding" to a student who speaks limited English?

Expressing a Fraction as a Decimal [8/19/1996]

How do you write 3/8 as a decimal?

Expressing Percentages [01/26/2004]

Why do we sometimes use phrases like "4 out of 5 dentists"? Wouldn't it be more meaningful just to say 80% instead?

Factoring and Cancelling in Long Division [08/29/2003]

How do I perform long division? i.e. 1,002,240,000 / 86400

Figuring Out Fractions [04/28/2004]

I need help with adding and subtracting fractions, especially mixed numbers and equivalent fractions.

Finding a Common Denominator [02/21/2002]

Find a common denominator for each pair of fractions: 3/4,5/8; 3/4,7/ 10; 5/6,3/5; them write equivalent fractions.

Finding a Fraction that Equals an Unending Number [07/08/2003]

Is there a way to find if there is a fraction that equals 0.777777...?

Finding Common Denominators [06/25/2001]

What is the best way to find a common denominator?

Finding Fractions between Fractions [01/08/2002]

What are four fractions between 1/3 and 1/2?

Finding Fractions on a Ruler [08/16/1999]

How can I find measurements like 7/8" or 5/16" on a ruler?

Finding Numbers Between Decimals [08/13/1998]

Find 3 decimals greater than 3.71 but less than 3.72.

Finding the Digit of a Decimal Expansion [11/14/1998]

What digit will appear in the 534th place after the decimal point in the decimal representation of 5/13?

Finding What Cancels [03/26/2003]

(1 1/2)(1 1/3)(1 1/4)(1 1/5)... Find how many factors it will take to reach the product of 1000.

Flipping and Switching Fractions [01/18/2002]

I need to solve the following: n/2=5/10; 1/n=5/10; 1/2=n/10; 1/2=5/n.

Fraction Division Diagrams [04/21/1999]

Diagram 1 divided by 1 1/2.

Fraction Operations Explained [11/23/2003]

Addition, subtraction, multiplication and division of fractions are explained through examples and helpful comments.

Fraction or Decimal? [06/23/1998]

Which is more precise, a fraction or a decimal - for instance, 1/3 or 0.33?

Fractions and Adding Zeros [08/26/2001]

I am having problems with doing fractions on the calculator.

Fractions and Cross Multiplication [07/14/1998]

When do you cross-multiply in solving fractions?

Fractions and Decimals [02/15/1999]

How do you make 17/11 a proper fraction?

Fractions and School Enrollments [02/26/2003]

The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School is exactly the enrollment of the Language School. The sum of 1/5, 1/6, 1/7, and 1/8 of the enrollment of the Business School is exactly that of the Design School. What are the enrollments of these three schools, assuming no school has more than 1000 pupils?

Fractions for 3rd and 4th Graders [2/13/1996]

I need to come up with creative and effective ways to teach fractions to some 3rd and 4th graders.

Fractions for Repeating Decimals [5/14/1996]

Convert 3.04050505.... into a fraction.

Fractions in Simplest Form - When? [11/29/2001]

Should fractions always be reduced to their simplest form? Why or why not?

Fractions of a Cup [04/15/2003]

A diagram: for a mixture of 3 cups concentrate and 4 cups water, how much water and concentrate would you need to make 1 cup of mix?

Fractions or Decimals? [05/18/1999]

Why do we use both decimals and fractions to represent amounts less than one?

Fractions Table [06/20/1998]

Could you help me locate a math table for fractions to the 16th's?

Fraction Tutorials [04/28/1997]

Do you know of tutorials for multiplying fractions, adding improper fractions, and working with mixed number fractions?

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