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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Representing Rational Numbers [09/17/2002]

What do fractions, decimals, and percents have in common?

Rounded Fraction of Pi [10/10/2001]

I want to find about 20 digits into pi. What would the fraction (division problem) be for that?

Rounding 3.445 to the Tenths Place [05/24/2001]

In order to round 3.445 to the tenths place, shouldn't it first be rounded to 3.45, then to 3.5? In my daughter's 6th grade math class, they are told to round it directly to 3.5. Is that the preferred way?

Rounding Decimals [8/25/1996]

I'm trying to round 0.03846 to the nearest tenth. Would it be 0.00000 or stay the same?

Rounding Decimals [10/19/1998]

Can you explain how to round decimals?

Rounding Decimals: Even/Odd Issues [05/08/2001]

When do you round down, and when do you round up?

Rounding Fractions to the Nearest Half or Whole [01/10/2003]

How do you round fractions to the nearest half or whole?

Rounding Logic [12/11/1996]

When you have 5.5 why do you always round UP, instead of down?

Rounding Numbers [2/10/1996]

When rounding fractions, would 1/3 be considered 1/2 or 0?

Rounding of Numbers with Decimal Places [5/31/1996]

What is the value of the number 12.4547 rounded up to 2 decimal places? 12.45 or 12.46?

Rounding to the Nearest... [10/15/1997]

I don't know if I'm supposed to round a number (say 451.7576) to 451 or 451.7 or 451.8 when my teacher tells me to round to the nearest tenth.

Rounding to Whole Numbers [04/01/2001]

How do you round to the nearest whole number?

Rounding Up or Down on a 5 [06/13/1999]

If the digit following the one to be rounded is a 5, is rounding up or rounding down determined by whether the original digit is even or odd?

Sales and Taxes [03/11/2001]

I bought $27.97 worth of food. The food tax is 5.5%. I'm trying to find the tax I have to pay, and the total amount that I pay.

Significant Figures in 36 2/3 [11/06/2001]

How many significant figures are there in the area "36 2/3 Acres"?

Simplifying Mixed Fractions [10/01/1999]

How can I simplify 10 3/4 - 8 1/2 + (2 1/2 - 1 1/8)?

Square Roots and Fractions [10/25/1998]

How do you simplify a square root of a fraction?

Subtracting a Larger Fraction from a Smaller Fraction [01/09/1997]

19 4/10 - 6 7/10 = ?

Subtracting Decimals [09/16/1997]

I don't know how to subtract decimals.

Subtracting Fractions [9/6/1996]

I tried to draw a circle and mark out the areas to solve 3/4 - 1/2...

Subtracting Fractions [08/03/2001]

How do you subtract fractions?

Subtracting Fractions with Borrowing [12/17/2002]

When you are subtracting a fraction, do you always take one away from the whole number?

Subtracting Improper Fractions [3/15/1996]

What is: 3 and 4/9 - 2 and 8/7? What is: 4 and 5/3 + 3 and 6/7?

Subtracting Mixed Fractions With Borrowing [01/08/2004]

Two methods for subtracting mixed fractions involving borrowing because the fraction being subtracted is larger than the other one. For example, 5 3/8 - 10 6/8.

Subtracting Mixed Numbers [01/23/1998]

I don't really understand subtracting mixed numbers.

Subtracting Mixed Numbers By Counting On [06/01/1998]

How do you find what to add to 1 and 3 fourths to get 4 and 5 twelfths?

Subtracting Mixed Numbers with Borrowing [03/31/2009]

A question on how to subtract 6 1/8 - 3 1/3 leads to examples of borrowing and regrouping in various contexts, including time, money, liquid volume, and of course mixed numbers. An alternative approach of producing an equivalent but easier problem is also presented.

Teaching Fractions [2/2/1996]

I'm teaching 6th grade math, multiplying fractions, and some of the students don't understand that 5 and 5/1 are the same. Any suggestions?

Teaching Percentages [7/8/1996]

What is an easy way to explain percentages to a 5th grader?

Terminating and Repeating Decimals [04/20/2003]

Which one of these can only be written as a repeating decimal? 3/8; 7/ 16; 1/2; 5/6.

Tips for Simplifying Fractions [06/03/1998]

Can you give my some tips to help me simplify fractions?

Total Number of Pupils [03/21/2001]

In a class, 5/8 of the pupils are boys. There are 8 more boys than girls. What is the total number of pupils in the class?

Understanding Decimal Notation [06/10/2002]

I've been told that you should be able to look at a number like 2 15/100 and know that the decimal equivalent is 2.15. But I don't understand why they're the same.

Undoing Percentage Changes [07/10/2002]

If I increase an initial amount by P percent, by what percentage would I have to decrease it to get back to where I started?

Using Common Denominators to Compare Fractions [03/17/1998]

How do you decide which is bigger -- 3/8 or 4/9 -- using equivalent fractions?

Ways of Adding Fractions [03/19/1999]

Can you help me calculate 1/3 + 1/6?

What Does Cancelling Mean? [01/22/2003]

My teacher says that 2k/4n can be simplified to k/2n. How can one k cancel out 2 n's?

What is 4/5 x 10? [2/10/1995]

What is the answer to this fraction? Please explain.

When to Add or Multiply Denominators? [04/02/2001]

When you multiply fractions, you multiply the numerators and then the denominators. When you add fractions, you add the numerators but not the denominators. Why the difference?

Why Cancel? [02/25/2003]

Why do we have to cancel numbers?

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