See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Number Sense/About Numbers
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Multiplying by zero.
Casting out nines.
Number facts from the Web.
- Sizes of Infinities [01/31/1997]
How can you prove that one infinity is larger than another?
- Small Base, Long Division [10/06/2015]
An adult struggles to divide numbers in bases other than ten. Starting with a list of
divisor multiples, Doctor Peterson steps through a similar long division before
checking his work.
- Spaces and the Number Line [02/26/2003]
If you say, 'How many degrees are there between -2 and 4?' would you
count the 0 degrees and answer 7 degrees or would you not count the
nought and answer 6 degrees?
- Square and Composite Numbers [9/5/1996]
Is it possible for a number to be a square number and a composite number?
- Square Numbers End in 0 1 4 5 6 9 [10/15/2002]
Why do all square numbers end in 0 1 4 5 6 9?
- Square Roots and Irrational Numbers [10/08/1997]
Will every square root of a positive number that is not a perfect square
be an irrational number?
- Subscripts [09/30/2002]
How are subscripts used?
- Subtracting Roman Numerals [03/14/1999]
What are the rules for the "subtraction components" in writing Roman
- Summing Three Consecutive Numbers [12/03/1998]
How many natural numbers from 10 to 40 can also be written as a sum of
three consecutive natural numbers?
- Sum of Consecutive Prime Numbers [6/29/1996]
Why is the sum of two consecutive prime numbers always twice a composite
- Sum of Integers Not an Integer [02/20/2003]
I need to pick a set of 9 integers with a mean of 3.5.
- Sum of the Digits of Multiples of 9 [04/08/2001]
Why do the digits of nine times a single-digit number add up to 9?
- Sums of Consecutive Integers [08/18/1999]
Is there a way of finding a series of consecutive integers whose sum is a
given number? For example: 3=1+2, 5=2+3, 6=1+2+3, etc.
- Sums of Odd and Even Numbers [02/04/2002]
I have to prove why the sum of two even numbers is an even number, and
why the sum of an even and an odd number is an odd number.
- Sum Twice the Difference [10/18/2002]
What number can you add to and subtract from 129 such that the sum
is twice the difference?
- Syllables from One to One Million [03/12/2003]
How many syllables are there when counting from one to one million?
- Talking About Zero, Absolute Zero and Negative Numbers [11/12/2003]
Are there any useful strategies other than temperature to introduce
negative numbers, and also to teach about zero, its properties, and
how they differ from those of absolute zero?
- Teaching Children Other Bases [02/20/2002]
Why teach children number systems other than the base 10 number system?
- Teaching Rounding Rules [10/17/2002]
I was taught that when one rounds numbers like 3.5 or 4.5 to the
nearest even integer, so that 3.5 should be rounded up, and 4.5 should
be rounded down. Is there any good reason why grade-schoolers are
taught to always round up?
- Testing for Triangular Numbers [06/09/1999]
How do I figure out whether 12456, 1225, or 13456 are triangular or
- Three Consecutive Natural Numbers [09/17/2001]
Why is it that the product of any three consecutive natural numbers is
always divisible by six?
- Triangular Numbers [07/07/1998]
How do you know a number is triangular? How is n/2(n+1) derived?
- Triangular Numbers [4/11/1996]
What is a triangular number?
- Trick for Numbers Divisible by 3 or 9 [02/24/1998]
Proof of a trick for numbers that are divisible by 3 or 9.
- Trilogy, Tetralogy... [05/28/2003]
Why isn't there a numbering system for groups like trilogies?
- Types of Numbers [10/30/1998]
How are the different types of numbers related? For example, what about
counting, whole, rational, irrational, integers, prime, ... ?
- Use of Plural with Decimal Numbers [02/27/2002]
What are the rules for 1.0001, 1.1, 1.5 or 1.999 ? Should we write
1.0001, 1.1, 1.5, 1.999 point or 1.0001, 1.1, 1.5, 1.999 points ?
Differences between plurals in English and French.
- Uses of Bases Other Than Base 10 [09/28/2004]
Why are there different math bases and what would they be used for?
- Uses of the Distributive Property [02/25/2002]
I have to write a paragraph describing the distributive property and what
it is used for.
- Using Estimation to Check Your Answer [03/28/2008]
I had to find the percent increase in population from 38,000,000 to
515,000,000 and I got 1,255%. But that seems way too big. Where am I
- Using Integers [01/05/1999]
I need some real-life examples of integers to show my students that they
need to be able to use them in math class.
- What are Like Terms? [11/20/2001]
Examples of like terms.
- What Exactly is a Fraction? [10/15/2001]
What is a fraction? Is 3/1 a fraction? Is 5/sqrt(2) a fraction?
- What is an Integer? [10/03/2002]
Why isn't -1/2 considered an integer?
- What is a Number Base? [04/19/2003]
The base eight number 7n3 is equal to the base 7 number 1n35.
What digit does n stand for?
- What is a Parenthesis? [07/17/2000]
What does the mathematical term "parenthesis" mean?
- What is a Reciprocal? [10/10/2002]
Can you clarify what the reciprocal is?
- What is Expanded Notation? [08/22/2001]
My daughter was asked to rewrite each number as expanded notation. What
is expanded notation?
- What is Number Sense and How Can You Improve It? [08/29/2007]
What does the term 'number sense' refer to on standardized math test
results? Is there any way to increase your number sense?
- What is the Largest Named Number? [12/08/2004]
A discussion of various large numbers and how they are defined,
including google, googleplex, and Moser, Skewes, and Graham numbers.