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Browse Elementary Division
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Dividing fractions.
    Flashcards/worksheets on the Web.
    Long division.
    Order of operations.
    Number sentences.

Calculating Percentage Markup Versus Profit [01/23/2004]
In order to figure a profit of 10% I would normally take my cost and then multiply by 1.1 to find the selling price. My employer tells me that in order to find a 10% profit I should divide my cost by 0.9, but I don't understand how this is 10%. Can you please explain?

Cancelling Fractions [06/03/2003]
I am reading a book on algebra. The author states that cancelling is division too and then shows the following without any explanation of how it's done...

Casting Out Nines to Check Arithmetic [08/26/1999]
Can you explain how to use the 'casting out 9's' technique in a way that a 6th grader can understand?

Comments on Dividing Fractions [03/15/2007]
A question on how to divide fractions leads into comments on how division and subtraction can be thought of as multiplication and addition of an "inverted" number.

Commutative Property and Division [02/21/2002]
I am trying to prove that the commutative property following certain rules will work in all circumstances for division...

Compatible Number Estimating [01/31/2002]
My homework is on compatible numbers to estimate quotients - for example, 1,625 divided by 38.

Compatible Number Method for Estimating [09/10/2001]
We are supposed to estimate using compatible numbers. How does one estimate something like 574/8?

Confusion over Interpretation of PEMDAS [03/24/2005]
Students take PEMDAS letter by letter, tending to do all multiplication before any division, rather than working from left to right. Here's a suggestion on how to help avoid that confusion.

Converting Bits to Megabytes [02/12/2001]
The human brain will store 100 trillion bits in its lifetime. How many million megabytes can your brain store?

Counting Days of the Week [02/02/1999]
If today is Thursday, what day would it be 120 days from now?

Deciding How to Express the Answer to a Division Problem [07/22/2006]
When dividing something like 7 by 2, is it best to express the answer as 3 1/2, 3.5, or 3 remainder 1? How do I decide which form to use?

Definition of Quotient [11/13/2008]
If I divide 15 by 2, I always thought that the quotient was 7 and the remainder was 1. But I've seen that the quotient can also be 15/2. How can quotient have different meanings?

Definition of Vinculum [10/21/2004]
Is the bar placed over the set of repeated digits in a repeating decimal called a vinculum? I've heard that but I can't confirm it.

Distributing Division [11/23/2003]
I have a book that says division distributes over addition. Isn't it multiplication that distributes?

Dividing a Large Number by a Small Number [3/25/1996]
How do you divide 7557 by 8?

Dividing and Rounding [08/23/2001]
I have to answer a division problem and then round the quotient to the nearest hundredth...

Dividing a Small Number by a Larger Number [2/6/1996]
What is 7 divided by 22, and what is 2 + 2?

Dividing by Powers of 10 [09/12/1998]
Can you explain how to move the decimal place when you divide by powers of 10?

Dividing by Zero [05/18/2001]
I cannot comprehend that a human being is not able to divide a number by zero...

Dividing Decimal Numbers [7/26/1996]
How do I divide 4.58 into 46.63?

Dividing Decimals with a Remainder [03/30/2001]
What should I do when the directions say to divide and I get a remainder, or if they say round to the hundredths place and there is a remainder?

Dividing Fractions [03/16/1999]
Why can't we divide fractions directly? Why do we have to do it by multiplying?

Dividing Fractions [3/18/1995]
My class would like an explanation on why you invert and multiply when dividing fractions.

Dividing Into or Dividing By? Dividends and Decimal Zeros [01/29/2013]
A student struggles to understand the equivalence of 3/5 and 0.6: three clearly goes into five at least one time; and extending the five into fifty only makes matters worse. Emphasizing the importance of keeping the dividend and divisor in the right order, Doctor Peterson clarifies, first explaining fractions with a sharing scenario, then walking through an example.

Dividing Two Decimals [8/30/1995]
I don't understand dividing one decimal number by another decimal number.

Dividing Two-Digit Numbers [03/01/2002]
How do you divide two-digit numbers?

Divisibility Algorithm [11/26/2001]
Is there a trick for figuring out multiples of seven?

Divisibility by 9 [03/22/2002]
Why is an integer that is rearranged and then subtracted from itself always divisible by nine?

Divisibility of Nine-Digit Numbers [03/08/1998]
Find a nine-digit number such that the first digit is divisible by one, the first two digits are divisible by 2, the first three digits are divisible by 3,..., the whole nine-digit number is divisible by nine.

Divisibility Rules [4/10/1996]
What are some divisibility rules beyond the number 11?

Divisibility Rules, 1-10 [9/11/1996]
Please tell me the divisibility rules for numbers one through ten.

Divisible... [8/27/1996]
Which of these numbers are divisible by {5, 8, 9}... ?

Division as Repeated Subtraction [03/06/1998]
How can you divide one integer by another using only addition and subtraction?

Division by Estimation [11/4/1996]
Estimate the quotient when 716 is divided by 12.

Division by Zero [8/27/1996]
What is the value of a number divided by zero?

Division of 28 by 13 [9/12/1996]
Can you divide seven into twenty-eight thirteen times?

Division Symbols [10/23/1998]
What is the name of the symbol used in long division problems? What about other division symbols?

Division with Roman Numerals [03/02/2004]
I'm having real problems trying to divide using a non place system, like with Roman numerals. The concept of using letters rather than numbers is confusing me. Can you please give me an example of a division calculation?

Does Divisibility by 4 always work? [6/17/1996]
One hundred is divisible by 4 but I don't how 4/00 gets a quotient of 25.

Dollarwise Division [02/20/2013]
What could it mean to divide dollars into dollars? Doctor Peterson provides examples of contexts where it makes sense to see units in a divisor, then introduces dimensional analysis.

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