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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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Dividing Decimals by Whole Numbers [10/19/2002]

Dividing decimals has been hard for me to learn.

Dividing Fractions [03/16/1999]

Why can't we divide fractions directly? Why do we have to do it by multiplying?

Dividing Negative Numbers in Real Life [03/03/2004]

Why and when do we divide by a negative number in real life? I can't find a convincing example to make my child happy.

Dividing Three Digit Numbers [11/3/1994]

I am in 7th grade. I don't understand how to divide by 3 digit numbers. Can you help me?

Dividing Two Numbers with and without Units [09/15/2004]

We can calculate $500/10 or $500/$10 and get $50 or 50 respectively. What units would the result have if we calculate 500/$10?

Divisibility Algorithm [11/26/2001]

Is there a trick for figuring out multiples of seven?

Divisibility by 11 [02/17/1998]

To check whether a number is divisible by 11, sum the digits in the odd positions counting from the left... Why does this work?

Divisibility by 3 in Three Consecutive Numbers [10/07/2002]

With any combination of consecutive natural numbers, why is one integer divisible by three and why is ONLY one number divisible by 3?

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 Rule for 12 [07/10/2000]

I don't understand why the divisibility rule for 12 does not include 2.

Divisibility Rules [4/29/1995]

We read your rule of divisibility for seven and were quite impressed. We would like to know the rules for the other numbers.

Divisibility Tests in Different Bases [11/16/2008]

How do divisibility tests work in other bases? For example, is there a test to tell if a number in base 9 is divisible by 7?

Division by a Negative and a Definition of Division [09/18/2006]

If 6 is divided by 3 it means that 6 is being divided into 3 equal parts. So what does 6 divided by -3 mean? How do you divide something into -3 equal parts?

Division by Zero [8/27/1996]

What is the value of a number divided by zero?

Division Quotient [11/06/2002]

In a division sentence, when will the quotient be odd? When will it be even?

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?

Divisors [11/07/1997]

What kinds of numbers have exactly 3 divisors? Do bigger numbers necessarily have more divisors? Is there a way to figure out how many divisors 1,000,000 has without actually listing and counting them?...

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.

Egyptian Division [06/23/1998]

How did the ancient Egyptians do division?

Eliminating Fractions in Division [11/20/2003]

How can I change a division involving a fraction to one involving only integers?

Error: Division by Zero [02/12/2001]

How can I explain to my third grader that a number divided by zero is undefined? The school calculator gives the answer 0/E, and the Windows calculator gives positive infinity.

Estimating the Distance to Lightning [08/16/1999]

I've told friends that for every 4.7 seconds between seeing a lightning bolt and hearing the thunder, the lightning is one mile away. Can you explain this?

Etymology of the Word 'Quotient' [11/25/2002]

What is the origin of the word 'quotient'?

Evaluating Parentheses, Brackets, Braces and Grouping Symbols [01/20/2007]

How do I evaluate or simplify an expression with lots of grouping symbols, like (18/2){[(9 x 9 - 1)/ 2] - [5 x 20 - (7 x 9 - 2)]}?

Explaining Order of Operations [09/06/2001]

How would you explain the order of operations to a 5th or 6th grader who has not yet studied the subject?

Explaining the Divisibility Rule for 7 [02/26/2003]

I found the rules for divisibility of a number by 7. Please explain (prove) why the rules work.

Factoring and Cancelling in Long Division [08/29/2003]

How do I perform long division? i.e. 1,002,240,000 / 86400

Find a Four-Digit Number Divisible by 2, 3, and 9 [11/29/2003]

How to determine a possible answer by applying the standard divisibility rules for 2 and 9.

Finding Average Times [02/15/2002]

My son and I have started a physical fitness program, and we are keeping track of our time for the mile. At the end of the week we would like to figure our average time.

Formula for Greatest Common Divisor [01/08/1997]

Is there a formula to get the greatest common factor?

Fraction Division Diagrams [04/21/1999]

Diagram 1 divided by 1 1/2.

Fundamental Idea of Division [03/24/2000]

My 8-year-old daughter had 12 bracelets which she arranged into 4 piles of 3. Did she divide 12 by 3 or by 4?

Galley or Scratch Method of Division [12/08/2002]

In the 15th century, what was the method for performing division?

How Can Division Result in an Increase? [10/29/2003]

How is it possible for division to give you a larger number, instead of a smaller one?

How Much Money? [08/16/2001]

A man has 3 daughters, 4 sons, and a sum of money. If he divides the money equally among his daughters $2 will be left over...

Incorrect Application of PEMDAS and Order of Operations [09/14/2006]

My students think PEMDAS means that all addition should be done before any subtraction is done. How can I show and convince them that they need to do both operations at the same time working from left to right?

Introduction to Division with Negative Numbers [05/05/2004]

I don't know how to do division with negative numbers, like +18/-9 or -24/-8 or +21/-3.

Is Integer Division Associative? [05/14/2002]

Is integer division associative?

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