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?

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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