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Browse Elementary Multiplication
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Flashcards/worksheets on the Web.
    Learning to multiply.
    Least common multiple, Greatest common factor.
    Number sentences.
    Order of operations.



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

Multiplying by 1000 [03/10/1997]
What is 2,542 times 1,000?

Multiplying by 11 [09/16/1997]
We said: 568 x 11 and after about 5 seconds she said the answer was 6248. How did she do it so quickly?

Multiplying by a Decimal [11/10/1994]
How come when you multipy 0.36 and 88 you get 9.4270, which is less than what it should be?

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 Decimal Numbers and Placing the Decimal Point [09/20/2007]
Why does counting up the total decimal places when multiplying decimal numbers work?

Multiplying Decimals and Decreasing Answers [12/02/1998]
Why does multiplying by a decimal decrease the answer? How can you have less than what you started with when you multiply?

Multiplying Fractions [01/20/1997]
If multiplication is defined as repeated addition, why is the product of two fractions smaller than either of the fractions?

Multiplying Huge Numbers [5/9/1996]
8541 * 4372 = 37340252 - How can I check my answer?

Multiplying Mixed Numbers [06/02/2003]
Can you multiply mixed numbers without changing them into improper fractions?

Multiplying Mixed Numbers [04/06/2004]
Why do you need to convert mixed numbers to improper fractions before multiplying them together? What is the mathematical reason behind this operation?

Multiplying Negative Integers [11/07/2001]
Multiplying negative integers by breaking each negative number into a positive number multiplied by -1.

Multiplying Negatives [1/13/1995]
An adult ponders his elementary school lessons of multiplication and negative numbers. We can rewrite -2*3 as -2 + -2 + -2, but how can we re- write -2 * -3?

Multiplying Sets [11/28/1994]
If you are multiplying three sets of 8 do you write the problem 3x8 or 8x8?

Multiplying Small Numbers [6/15/1996]
I don't know what 6 times 6 is.

Multiplying Two-Digit Numbers [06/04/1998]
Can you show me how to multiply two-digit numbers like 39 x 98?

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

Napier's Rods [03/05/1999]
How do Napier's bones work?

Negative Two Kids [09/27/2002]
Let's say 3 x 2 = 6. Three is how many kids there are in a 'group.' Two is how many 'groups' there are, and six is the answer. Now let's say 3 x (-2) = -6. How can you have negative two 'groups' of three kids?

Number of Places in Products of Decimals [09/19/2002]
When you multiply decimals, why is there always the same number of decimal places in the answer as in the problem?

Number Properties [01/26/1998]
What are the definitions for addition and multiplication of: closure, commutative, associative, and identity?

Number Puzzle Based on Multiplication Ideas [08/07/2005]
Find the smallest possible natural number that ends in 6 such that if the 6 is erased and placed in front of the remaining digits, the resulting number is 4 times as large as the original number.

Numbers Bigger Than 12 [03/22/1997]
How do you do problems like 14 x 7?

One Billion as Product of Two Numbers with No Zeros [12/12/2001]
Write 1,000,000,000 as the product of two numbers, neither of which contains any zeros.

Ordering the Operations [11/10/1998]
Why does the order of operations have to be in that order? Who set that specific order of operations?

Order of Digits in Multiplication [03/27/2001]
Why do we learn to multiply starting with the least significant digits in the ones place, instead of starting with the larger place values?

Order of Operations [01/25/1998]
Evaluate the expression: 30 - 5^2 + 4^3.

Order of Operations [8/21/1996]
How do I solve (8.2 - 3.6)(3 * 3.6 + 6)?

Order of Operations and Fractions [02/22/2002]
Given a+3 and b+5, is 105 / ab 7 or 175?

Order of Operations: Parentheses as Packages [10/25/2001]
I need help figuring out the steps in this expression: 5-{-4[2^4-11(-9- 1)]}=

Order of Operations vs. Associative Property [10/10/2002]
Is the associative property an exception to the order of operations, a corollary, or something totally unrelated?

Order of Operations vs. Distributive Property [02/04/2005]
Does the distributive property contradict the rules of order of operations? When we have a(b + c) order of operations says we should add first in the parentheses, then multiply, but the distributive property says we can multiply first to get ab + ac, then add.

Paperless Multiplication [07/23/2002]
How can I do two-digit multiplications (e.g., 99*98) without having to use paper?

Parts of a Subtraction Problem [04/09/2001]
What are the numbers 4 and 1 called in the subtraction 4 - 1 = 3?

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

Proving That (-1) * (-1) = 1 [01/30/2006]
At the high school level it is difficult to prove that -1 x -1 = 1. Is there a published proof somewhere that is appropriate for kids that age?

Rapid Multiplication ... Diagonally? [02/24/2010]
Doctor Vogler describes the "accumulator" method for finding products of two multi-digit terms, then works through an example.

Rectangular Arrays to Teach Multiplication [11/10/1994]
I teach fourth grade math. Are rectangular arrays the best way to teach multiplication?

Russian Peasant Multiplication [08/19/1997]
I have a project to do on "Russian" or "peasant" multiplication.

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