2.6: Summary of Key Concepts
Summary of Key Concepts
Multiplication
Multiplication
is a description of repeated addition.
\(\begin{matrix} \underbrace{7 + 7 + 7 + 7} \\ {\text{7 appears 4 times}} \end{matrix}\)
This expression is described by writing \(4 \times 7\).
Multiplicand/Multiplier/Product
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
In a multiplication, the numbers being multiplied are also called
factors
. Thus, the multiplicand and the multiplier can be called factors.
Division
Division
is a description of repeated subtraction.
Dividend/Divisor/Quotient
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
.
\(\begin{array} {r} {\text{quotient}} \\ {\text{divisor} \overline{)\text{dividend}}} \end{array}\)
Division into Zero
Zero divided by any nonzero whole number is zero.
Division by Zero
Division by zero does not name a whole number. It is, therefore, undefined. The quotient \(\dfrac{0}{0}\) is indeterminant.
Division by 2, 3, 4, 5, 6, 8, 9, 10
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
The product of two whole numbers is the same regardless of the order of the factors. \(3 \times 5 = 5 \times 3\)
Associative Property of Multiplication
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.
\((3 \times 5) \times 2 = 3 \times (5 \times 2)\)
Note that the order of the factors is maintained.
Multiplicative Identity
The whole number 1 is called the
multiplicative identity
since any whole number multiplied by 1 is not changed.
\(4 \times 1 = 4\)
\(1 \times 4 = 4\)