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Word Problems

Browse Elementary 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.

Parenthesis [03/09/1999]
Can you help me teach parentheses to a class?

Pattern of Squares [1/08/1998]
Do squares of integers have a pattern? I believe that they do, but I don't know what it is.

Pennies and Remainders [01/13/2003]
Arnie has between 300 and 400 pennies in his collection. When he divides them into groups of 4, 5, or 9, there is always one penny left over. How many pennies does Arnie's collection contain?

Pentagon Puzzle [09/18/2002]
Write the numbers 1 through 10 so each side of the pentagon has a sum of 14.

Percentage of Votes Cast [06/03/2003]
If you have two percentages, say 25% and 50%, can you do a percent change between the two?

Perfect Numbers [9/15/1996]
What is a "perfect number"?

Pi's Last Digit [7/20/1996]
I know pi is a nonterminating decimal, but if there were a last digit wouldn't the last digit be a 0?

Placement of Commas in Writing Numbers [10/22/2003]
Why is the ones period named for the ones place value and why is the thousands period named for the thousands place? Why is there not a hundreds period?

Precise Numbers [10/18/2001]
A precise number occurs when its proper divisors multiplied together equal the number: 6 is a precise number because 1*2*3 = 6. Is there another name or formula?

Prefixes in Math [08/21/2001]
What are the prefixes for 7, 8, 9, and 10?

Prime and Composite Numbers, Sieve of Eratosthenes [01/28/1997]
I need a list of all prime numbers and all composite numbers up to 50.

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.

Problem Solving and Mental Process [10/03/2002]
Two numbers add up to 19. The difference between the two numbers is 3. What are the numbers?

Proof: 2 = 1? [10/03/1997]
a = b is factored to a^2 = ab by multiplying both sides by a...

Proof that 1 + 1 = 1? [09/04/1997]
Can you shed any light on this subject?

Properties, Defined and Illustrated [10/10/2001]
I need a page of information on the commutative, associative, and F.O.I.L. properties.

Rational Numbers and Square Roots [10/07/1998]
Our teacher told us to find all the rational numbers we could containing a sqrt symbol...

The Real Number System in a Venn Diagram [09/08/1998]
How do you construct a Venn diagram that illustrates the real number system?

Reverse Polish Notation in Calculators [09/17/2005]
An introduction to "reverse Polish notation" and the terms "stack", "push", and "pop" in that context.

Roman Numerals [11/13/1997]
What are three ways Roman numerals are used today?

Roman Numerals on Clocks [06/04/2001]
Is the Roman numeral on a clock written as IV, or IIII?

Rounding Round Numbers [10/31/2016]
Two British teachers disagree about how to round 100 to one significant figure. By drawing out different interpretations of how to round such powers of ten, and quantities near them, Doctor Peterson emphasizes purpose and meaning over procedure and mechanical execution.

Rounding to the Nearest Multiple of 5 [01/08/2005]
How do you round to the nearest 5? Would 27 round down to 25 while 28 would round up to 30?

Rounding to the Nearest Tenth [8/29/1998]
Would 6.96 be 7.0 or 6.9?

Saying Numbers Out Loud [03/06/2002]
I have recently been told that the use of "and" is incorrect. Is it "one hundred one" or "one hundred and one"?

Scientific Notation [09/16/1997]
I don't understand how you get the answer: 5x10 to the 3rd power = 5,000; 5x10 to the -3rd power = -5,000.

Scientific Notation of Zero [09/09/2002]
What is the scientic notation of zero?

Short Word Form [10/15/2002]
How is 474,136 written in short word form vs. standard form?

Significant Digits [09/07/1998]
What are significant digits?

Significant Digits and Irrational Numbers [09/24/2005]
How can you determine the signifigant digits of a non-terminating or irrational number like pi?

Significant Digits and Zero [05/19/1999]
When are zeros significant and when are they not significant?

The Size of Infinity [09/03/1998]
What is infinity times 2? Can we measure infinity?

Sizes of Infinities [01/31/1997]
How can you prove that one infinity is larger than another?

Smallest 5-Digit Number [02/05/2002]
My dad says the smallest 5-digit number is 00000, but my teacher says it is 10000. The dictionary says that zero is a digit. What's the right answer?

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 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?

Teaching Children Other Bases [02/20/2002]
Why teach children number systems other than the base 10 number system?

Teaching Elementary Concepts [04/04/1997]
How can I teach rational counting, prime and composite numbers, and square roots at a grade-school level?

Three Consecutive Natural Numbers [09/17/2001]
Why is it that the product of any three consecutive natural numbers is always divisible by six?

Trick for Numbers Divisible by 3 or 9 [02/24/1998]
Proof of a trick for numbers that are divisible by 3 or 9.

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