Help: Examples of multiplication
Here are some examples of typical expressions involving multiplication. This
table shows you what they would look like in a textbook and how they would
need to be entered for QuickMath.
Multiplication of Whole Numbers
The product of two whole numbers a and b is defined to be the whole number a
* b, which is another name for the sum
b+b+b+ ..... +b a terms
of b
The a and b are called factors of the product.
EXAMPLE 3·4 = 4+4+4 3 terms of
4
MULTIPLICATION BY ZERO
For any number a E W,
a*0 = 0 + 0 + 0 a terms of 0, thus a*0 = 0
EXAMPLE 6*0 = 0
The product of two specific numbers such as 5 and 3 is denoted by
5 *3, 5 x 3, 5(3) or (5)(3)
The product of a specific number and a literal number such as 3 and a is denoted
by
3*a, 3 x a, 3(a), (3)(a) or simply 3a
When we multiply a specific number and a literal number, we write the specific
number as the first factor.
The product of two literal numbers such as a and b is denoted by
a*b, a x b a(b), (a)(b), or simply ab
The commutative law of multiplication
For any two numbers a, b E W,
The following are laws of multiplication of whole numbers:
ab = ba
The associative law of multiplication
For any three numbers a. b, c E W,
a(bc) = (ab)c
Example: 5 x (8 x 7) = (5 x 8) x 7
The identity for multiplication
There is a unique number l, called the multiplicative identity, such that for
any number a E W,
a x l = 1 x a = a
Example 9 x l = l x 9 = 9
The distributive law of multiplication over addition
For any three numbers a, b, c E W,
(b + c)a = a(b + c) == ab + ac
Example: 4(a + b) = 4a + 4b
Note Although multiplication is a binary operation, it can be extended to
find the product c three or more numbers as was done for addition.
Example: 6 x 5 x 3 = (6 x 5) x 3 = 30 x 3 = 90
Or 6 x 5 x 3 = 6 x (5 x 3) = 6 x 15 = 90
Note When an expression involves additions and multiplications without
grouping symbols. we perform multiplications before additions.
Example 1. 7 x 8 + 2 = 56 + 2 = 58
Note When an expression involves grouping symbols with only specific numbers
inside them it is easier to perform the operations inside the grouping symbols
first.
Example 7(3 + 8) + 9 = 7(11) + 9 = 77 + 9 = 86