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Word Problems

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.

Leaving Answers in Terms of Pi [12/11/2006]
My teacher says it's okay to leave an answer like 600pi, but I think it should be multiplied out as 600(3.14) = 1884 or you haven't finished the problem. What do you think?

Length of Pascal's Triangle [6/13/1996]
How long was Pascal's Triangle?

Line Segment Representing Sqrt(3) [10/07/2002]
Draw a line segment that represents radical 3.

Line under Greater or Less Than Symbol [01/26/2001]
What does it mean when there is a line under the greater or less than symbol?

Locating Pi on a Number Line [08/23/2000]
How can I locate pi on a number line? What number for pi should I use? Should I just use 3.14, or should I go farther?

Mathematical Palindromes [01/17/1997]
Can you tell me about number palindromes?

Mathematics As Analogy [12/16/2003]
How can the ratio of a finite circumference to a finite diameter give an infinite value for pi?

Math Symbols [03/11/2002]
What do these symbols mean in math? ' ~ ! @ # $ % ^ & * ( ) - _ + = /

Meaning of Greater Than, Less Than Symbols [11/07/2002]
Does the meaning of less than and greater than signs depend on location?

The Meaning of Powers, such as Squares and Cubes [3/14/1996]
What does the power mean? Like 5 to the power of 2?

Meaning of the Phrase: Divide by Zero. [01/02/1998]
I want to use 'divide by zero' to indicate a physically impossible task. What does the phrase actually mean?

Memory Aid for Roman Numerals [05/10/2000]
What number is XLIII? Do you have a way of remembering what letter equals what number?

Mental Math [07/25/2003]
I would like to find a trick for multiplying by 3367.

Meters Squared vs. Square Meters [11/18/2001]
Is 12 m^2 better read as 12 square meters or 12 meters squared?

Mnemonic for Less Than and Greater Than [08/11/1999]
What was the old adage for telling how to read the less than and greater than symbols correctly?

Multiples of Four [03/01/1999]
Is zero a multiple of four?

Multiplicand, Multiplier [07/05/2001]
Do you agree with me that in the following mathematical sentence: 456x10, 456 is called the multiplicand and 10 is called the multiplier?

Multiplication's Multiple Meanings: Unified by the Distributive [01/01/2015]
Area? Matrix multiplication? Scaling and rotation? A parent seeks a global understanding — or at least some internal consistency — as to what ties together all the operations called "multiplication." Building up from the natural numbers, where multiplication is repeated addition (MIRA), Doctor Peterson teases out two common threads.

Multiplying a Number by 4 [01/11/1999]
Can you help me find a few numbers that when you multiply them by 4, you will get the original number backwards?

Multiplying by 1 [09/01/1998]
Why doesn't a number change when you multiply it by 1?

Multiplying by Nine [01/10/1997]
Why is the sum of the two digits 9 when you multiply 9 times any number between 1 and 10?

Multiplying by Zero [03/01/2002]
Why does any number times zero equal zero?

Multiplying in Bases Greater Than 10 [10/13/2002]
I need to know how to multiply and divide by bases greater than 10.

My Calculator Gives Wrong Answers for Large Values of x ... [01/20/2010]
Doctor Vogler reveals how a calculator's imprecision leads to increasingly large rounding errors -- and misleads a student trying to make sense of the formula for the base of natural logarithms.

Naming Large Numbers [06/05/2002]
In Rowlett's site for naming large numbers, he seems to take every American prefix and bump its meaning by one to get the corresponding Greek-based prefix. Why?

Naming Nine Things [01/15/2003]
What is the correct name for nine things collectively? I can only find the answer up to 7, septuplet, which has been highly publicized with the McCoy babies.

Napier's Bones [01/20/1997]
How do you use Napier's Bones to do multiplication?

Natural Numbers [6/25/1996]
There are "natural" numbers, but are there "artificial" numbers?

Natural Numbers Problem [5/12/1995]
How would you prove that one added to the product of four consecutive natural numbers is a perfect square?

Negative Absolute Value [6/28/1996]
Is -|8| -8 or 8?

Negative Numbers in Base 2, 16, etc. [01/24/2003]
Are there negative numbers in alternate bases? Our calculator says that 1-2 in base16 is FFFFFFFFFF. This can't be right!

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....

Non-terminating Decimal Representations of Fractions [11/10/1997]
Why when you take a finite, limited quantity like one-third and turn it into a decimal do you get .333... on into infinity?

Not Enough Information about ... Ellipses [12/01/2010]
A student wonders how to interpret the "dot dot dot" notation in decimal expansions. While acknowledging the ambiguity of the ellipsis symbol, Doctor Peterson explains that context often helps.

Nth Term in a Sequence [01/11/2003]
Here is the sequence: 1, 2, 5, 14 ... Find the following 2 terms and a formula for the nth term.

Null Sets [8/23/1996]
Is the null set a proper subset of every set?

The Number Line and Its Contents, Rational and Irrational [07/13/2015]
A teen wonders how to plot irrational numbers on a number line, and why a segment would fail to represent the set of rational numbers. Doctor Peterson draws on several choice examples to get the points across.

Numbers and Digits [09/21/2000]
What is a digit? Why can't we call a digit a number?

Numbers and Numerals [09/06/1997]
What's the difference between a number and a numeral?

Numbers and Numerals [08/29/2002]
15/5 and sqrt(9) both reduce to 3, but is it proper to say that they are integers?

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