See also the
Dr. Math FAQ:
order of operations
3D and higher
Browse Middle School Division
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Selected answers to common questions:
Order of operations.
- 2a/5 or 2a Divided by 5? [12/13/2001]
Why, when writing a division problem, do you write 2a over 5 instead of
2a divided by 5?
- (9/2)/(3/4): A Picture [03/27/2003]
We were trying to find a division fraction question and everything we
came up with turned into a multiplication fraction problem. Why is
- Basic Real Number Properties [07/31/1997]
I need information about basic real number properties: associative,
commutative, closure, identity, inverse, distributive.
- Division [11/25/1997]
How do you divide 1,000,000,000,000 by 999,999,999,999,999,999,999?
- Division by Zero [11/2/1994]
Why can't you divide a number by 0?
- Explaining Fractions [11/06/2001]
I am a practicum student in a 8th grade math class. The teacher and I
don't know how to explain to the students why you can do this manuever.
c=d/g; c/d=g; d/c=g.
- Least Common Multiple Puzzle [03/24/2003]
What is the smallest number divisible by 1,2,3,4,5,6,8,9,10 that is
- Least Common Multiple Word Problem [12/10/1996]
Each of three businesses receives different sized cartons of glasses. If
all three receive the same number of glasses and none of them receive
more than a thousand glasses, how many glasses and cartons are in each
- Long Division [08/23/1998]
My biggest problem is long division. For example, what is 73/4?
- Manipulating Positive and Negative Numbers [8/9/1996]
Could you explain the rules for adding, subtracting, multiplying, and
dividing positive and negative numbers?
- Multiples of 9 Number Puzzle [03/23/2003]
If you take a two-digit number, add the digits, and subtract the sum
from the original number, why is the answer always a multiple of 9?
- Order of Operations: Math vs. English; Calculators [11/13/1996]
What is 144 divided by 3(8+4)? 4 or 576?
- Probability of Sky Falling is 0/0? [3/3/1995]
When asked the probability that the "sky will fall" one student responded
"0/0". What should we have told this 8th grade student about dividing by
- Reciprocals [12/19/1996]
What is the use of reciprocals?
- Restrictions on Variables in Division [8/4/1996]
What are the restrictions on the variables in (y^3+8)/(y^2+3y+2)?
- Wording Division Problems [08/10/1998]
How would you clarify the wording of division problems like "divide into"
or "divide by"?
- Working with Integers [01/12/1999]
Could you explain how to divide, multiply, add, and subtract integers?
- 1 Divided by Very Small Number [8/6/1996]
1/0.00000000000000000000000000000000001 = ?
- Adding and Subtracting Roman Numerals [10/26/1999]
How can I add and subtract Roman Numerals without converting them to
regular numbers? What did the Romans do to solve this kind of problem?
- Are Subtraction and Division Commutative and Associative Operations? [05/15/2008]
I don't agree that subtraction and division are not commutative
operations. If we define a - b as a + (-b), then it commutes correctly
into (-b) + a. So why does everyone say subtraction is not commutative?
- Brackets [01/29/2001]
Please explain how brackets  work.
- 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?
- Counting Techniques [12/29/1997]
Find the number of positive divisors of 17640, inclusive of 1 and 17640
itself. Find the number of odd integers between 2000 and 7000 that do not
have repeated digits.
- Cutting An Equal Number of Slices of Cake [07/13/1998]
One cake is 35 slices and another is 42 slices. If the cakes need to have
the same number of slices, how many slices should they have?
- 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.
- Determining If a Large Number is Divisible by 11 [10/22/2003]
I just learned a trick to decide whether a large number is divisible by
11 or not. Why does the trick work?
- Determining Which Number to Divide by Which [10/04/2004]
Julia plans to use a recipe that yields 15 pounds of fudge. She
intends to wrap the fudge she makes in 3/4 pound boxes and give one
box to each of her friends and relatives for gifts. How many gifts
will she have? Should I divide 15 by 3/4 or 3/4 by 15?
- Dividing by Powers of 10 [09/12/1998]
Can you explain how to move the decimal place when you divide by powers
- Dividing by Zero [05/18/2001]
I cannot comprehend that a human being is not able to divide a number by