Ask Dr. Math

Middle School Archive

Browse Middle School Number Sense/About Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    About zero.
    Multiplying by zero.
    Casting out nines.
    Classifying numbers.
    Googol, googolplex.
    Number facts from the Web.
    Significant figures/digits.

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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 numerals?

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 number?

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 square numbers?

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 going wrong?

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.

What Type of Number Are Zero and One? [11/08/2004]

If 1 and 0 are not considered prime or composite numbers, then what are they?

When Casting Out Nines Fails [11/29/2001]

To prove that casting out 9's worked, I intentionally used an incorrect quotient, but was shocked when the problem checked out correctly.

When Percentage Calculations are Inappropriate [02/11/2003]

How do I best calculate the percentage of goal when at least one of the numbers is a negative number?

Where Does Pi Come From? [11/04/1996]

If pi is a ratio of lengths that can be measured only so accurately, how can we know the value of pi so exactly?

Who Invented Integers? [11/29/2001]

And when were integers invented?

Whole Numbers and Multiples [09/11/2001]

My students and I have been trying to figure out what numbers are in the set of "Whole Numbers." Is zero a whole number?

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