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2.6 Summary of key concepts

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module summarizes the concepts discussed in the chapter "Multiplication and Division of Whole Numbers."

Summary of key concepts

Multiplication ( [link] )

Multiplication is a description of repeated addition.
7 + 7 + 7 + 7 ︸ 7 appears 4 times
This expression is described by writing 4 X 7.

Multiplicand/multiplier/product ( [link] )

In a multiplication of whole numbers, the repeated addend is called the multiplicand , and the number that records the number of times the multiplicand is used is the multiplier . The result of the multiplication is the product .

Factors ( [link] )

In a multiplication, the numbers being multiplied are also called factors . Thus, the multiplicand and the multiplier can be called factors.

Division ( [link] )

Division is a description of repeated subtraction.

Dividend/divisor/quotient ( [link] )

In a division, the number divided into is called the dividend , and the number dividing into the dividend is called the divisor . The result of the division is called the quotient .
quotient divisor dividend

Division into zero ( [link] )

Zero divided by any nonzero whole number is zero.

Division by zero ( [link] )

Division by zero does not name a whole number. It is, therefore, undefined. The quotient 0 0 size 12{ { {0} over {0} } } {} is indeterminant.

Division by 2, 3, 4, 5, 6, 8, 9, 10 ( [link] )

Division by the whole numbers 2, 3, 4, 5, 6, 8, 9, and 10 can be determined by noting some certain properties of the particular whole number.

Commutative property of multiplication ( [link] )

The product of two whole numbers is the same regardless of the order of the factors. 3 × 5 = 5 × 3 size 12{3 times 5=5 times 3} {}

Associative property of multiplication ( [link] )

If three whole numbers are to be multiplied, the product will be the same if the first two are multiplied first and then that product is multiplied by the third, or if the second two are multiplied first and then that product is multiplied by the first.
( 3 × 5 ) × 2 = 3 × ( 5 × 2 ) size 12{ \( 3 times 5 \) times 2=3 times \( 5 times 2 \) } {}
Note that the order of the factors is maintained.

Multiplicative identity ( [link] )

The whole number 1 is called the multiplicative identity since any whole number multiplied by 1 is not changed.
4 × 1 = 4 size 12{4 times 1=4} {}
1 × 4 = 4 size 12{1 times 4=4} {}

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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