Ask Dr. Math

Middle School Archive

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

Selected answers to common questions:
    Dividing fractions.
    Long division.
    Number sentences.
    Order of operations.

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Least Common Multiple [10/26/1999]

What is the smallest number that is divisible by the numbers 1 through 10?

Least Common Multiple [11/5/1995]

A student asks about the least common multiple of 8,12,36.

Least Common Multiple [01/24/1998]

I need to find the LCM of the numbers 16, 20, 9, and 8. I've gone up to 1,000 and still can't find it.

Least Common Multiple [09/29/2001]

What is the least common multiple of 11, 13, and 17?

Making up a Division Word Problem [11/13/2001]

Write a problem that could be solved by using the division sentence 1489/28=n; then write a pair of compatible numbers and estimate the quotient.

Multiplication and Division Equations [11/29/2001]

Solve for x: 17x = 85.

Multiplier, Sum, Difference, Product, Quotient, Dividend [11/25/1997]

What is a multiplier? an addend? a minuend? a product? Why is the number that is being divided the "dividend"?

Multiplying and Dividing Negatives [07/20/1998]

Can you explain multiplication and division with signed numbers? For example what is the sign when you multiply negative numbers?

Name of Division Symbol [7/31/1996]

What is the official name for the division symbol?

Negative Remainders in Arithmetic and Algebra: a Difference of Degrees [05/14/2010]

An algebra teacher wonders how to explain the existence of negative polynomial remainders to students accustomed to positive remainders. Doctor Peterson clarifies the difference between the remainders of arithmetic and those of algebra, underscoring polynomial degree.

New Rule for Divisibility by 7 [11/01/1997]

Multiply the integer excluding the one's digit by 3, and add the one's digit....

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 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.

The Period of 61/97 [01/12/2001]

How can I find the period of 61/97?

Polynomial Division Compared with Long Division [02/01/2009]

I'm having difficulty grasping the concept of polynomial division.

Polynomial Long Division [03/17/2004]

Use long divion to divide (2x - 3) into 4x^4 - x^2 - 2x + 1. I really need help in doing this.

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.

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?

Rationalizing the Denominator [04/09/1997]

Must all fractions have denominators that are rational numbers?

Remainders [07/02/1998]

Can you tell me how to do remainders?

Roman Numerals: Division [11/05/2001]

I have found information on how to add and multiply Roman numerals, but have not found any information on how to divide or subtract.

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?

Sums Divisible by 11 [10/10/2001]

Why is the sum of a number with an even number of digits and that same number written in reverse always divisible by 11?

Synthetic Division [11/13/1997]

Why does synthetic division work?

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?

Total Points from Average Points [03/12/2001]

Mandela's basketball team played six games, with an average or mean of 50 points. How many points did they score?

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

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

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?

Why Decimal Division Works [04/24/2001]

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

Why Does Cross Multiplication Work? [05/09/2002]

Why does the rule a/b = c/d also mean ad = bc? Why can we solve proportions by cross multiplying?

Why Does Long Division Work? [12/22/2006]

I'm curious why the standard long division algorithm works. How do all the "bringing down" and other steps lead to the right answer?

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.

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