Ask Dr. Math

Elementary Archive

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.

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Number Divisibility [11/01/1998]

How many natural numbers under 2,000 are divisible by 5 or 7? What's the quickest way to figure this out?

Order of Numbers in Subtraction and Division [11/09/1999]

Why can you add or multiply numbers in any order, but you cannot switch order when you divide or subtract?

Order of Operations: Parentheses as Packages [10/25/2001]

I need help figuring out the steps in this expression: 5-{-4[2^4-11(-9- 1)]}=

Order of Operations vs. Associative Property [10/10/2002]

Is the associative property an exception to the order of operations, a corollary, or something totally unrelated?

Order of Operations vs. Distributive Property [02/04/2005]

Does the distributive property contradict the rules of order of operations? When we have a(b + c) order of operations says we should add first in the parentheses, then multiply, but the distributive property says we can multiply first to get ab + ac, then add.

Primes and Repeating Unit Numbers [12/09/1998]

How do you prove this statement: For every prime number there exists a repeated unit number that is a multiple of that prime.

Problems with Zero; Writing Remainders [11/07/2001]

When I do long division the answer is correct except for one thing in the middle of the answer when it contains a zero.

Quickly Dividing in Two [7/8/1996]

Are there any quick tricks for figuring out fifty percent of a number such as 14.95 in your head?

Quotient of 65 and 9.4 [2/13/1995]

What is the quotient of 65 and 9.4?

Remainders [07/02/1998]

Can you tell me how to do remainders?

Setting Up a Division Calculation Correctly [12/16/2005]

I get confused about which number goes where when I have to do something like "6 divided by 2". Which number goes in the calculator first? And which number goes on the outside and inside if I am doing it on paper?

Short Division [01/11/2002]

I have math problems that say solve by using "short division." What does this mean?

Three-Digit Numbers [01/27/1997]

If you take a three-digit number, rearrange it two other ways, add the three numbers together, and divide by 3, why do you always get a remainder of zero?

To Multiply or Divide? That Is the Question. [09/02/2003]

In a story problem, how do you know whether to multiply or divide?

Trick for Numbers Divisible by 3 or 9 [02/24/1998]

Proof of a trick for numbers that are divisible by 3 or 9.

Two Division Questions [2/1/1995]

I have a real math challenge for you. There are 9 men. How many cookies would each man get if there were 113 cookies? Also, what is the answer to 1,623,341 divided by 1.632 x 2389?

Ways to Add and Divide More Easily [11/17/2008]

I have to add 2398 and 5752 and then divide by 37. I can do it, but it takes a long time. Is there any faster way to do those calculations?

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 12/18 ? [4/27/1995]

A third grader asks for help with a problem on long division and remainders.

What is 15/11? [4/27/1995]

We are learning division. What is 15/11?

What is 2346 Divided by 56? [4/27/1995]

We are studying Division. 2,346 divided by 56 = ?

What is 25 Divided By 5? [4/27/1995]

I'm studying division at school. Do you know 25 divided by 5?

What is 65 Divided by 3? [4/27/1995]

We just started division. It is pretty simple to me. What is 65 divided by 3?

What Is Trial Division? [02/24/1998]

Trial division is a technique for factoring a number.

Which is the Divisor and Which is the Dividend? [03/01/2002]

I can't remember which number is the dividend and which is the divisor.

Why Decimal Division Works [04/24/2001]

Can you explain why (not how) the procedure of division with decimals works?

Why Is Mental Math Important? [03/25/2004]

How can I convince a 14 year old girl who is in 8th grade the importance of mental math? I think that skills like mentally adding and subtracting 2 digit numbers and being able to estimate multiplying 2 digit large numbers are critical. My daughter's teacher says that such skills aren't needed because of calculators and computers.

Why the Fraction Division Technique Works [11/27/2004]

Why do we need to flip the second fraction when we divide fractions?

Writing a Remainder as a Reduced Fraction [08/29/2001]

I have to solve two division problems and write the remainder as a reduced fraction.

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