Multiplication of Real Numbers
- Some Definitions
When multiplying two numbers such as
2 x 3 = 6
The numbers on the left (the 2 and the 3) are called factors
and the result (the 6) is called the product.
- Properties of Multiplication
- The Zero Property
If you receive one million dollars exactly zero times, how much
money do you get? Clearly the answer is zero. In general any
number times zero is zero.
The Zero Property of
Any number times zero is zero.
3 x 0 = 0 55 x
0 = 0 0 x 4 = 0
0 x 0 = 0
- The Identity Element for Multiplication
Just as it is easy to multiply a number by zero, multiplying by one is
also very simple. If you buy twelve eggs exactly one time, then you
have bought a total of twelve eggs. In general, any number times one
is the original number.
The Identity Property of
Any number times one is one.
3 x 1 = 3 55 x
1 = 55 1 x 4 =
4 1 x 1 = 1 0 x 1
- The Commutative Property of Multiplication
For multiplication, it does not matter what order
the factors appear. Two six packs of beer has the same number of
bottles as six two packs of beer.
The Commutative Property of
Numbers multiplied in different orders give
2 x 6 = 6 x 2 43 x
12 = 12 x 43 1 x 7 = 7 x
1 0 x 5 = 5 x 0
- The Associative Property of Multiplication
When we multiply three numbers, we can multiply
the product of the first two by the third or we can multiply the first by
the product of the last two. The result will always be the
Suppose you have three books, each having
two chapters such that every chapter has ten pages. There are two
ways of determining the total number of pages in the books.
Since there are three books with two chapters each, there are
3 x 2 = 6 chapters. Each
chapter has ten pages so there are 6 x
10 = 60 total pages.
Since each book has two chapters each with ten pages, each book has
2 x 10 = 20 pages. There
are three books each with 20 pages, so there are 3 x
20 = 60 total pages.
The Associative Property of
When three numbers are multiplied, the
multiplication can be grouped in any way.
3 x (2 x 10) = (3 x 2) x 10
= 60 (12 x 1) x
3 = 12 x (1 x 3) = 36
- The Distributive Property
There is a property that relates to when multiplication and addition
are combined. If two people have ten fingers and four limbs each,
then we can determine the total number of fingers and limbs by either of
the following two methods:
Method 1: Each
person has ten fingers and four limbs, hence
10 + 4 = 14
body parts. Since there are two people, the total number of body
2 x 14 = 28
Method 2: The
are two people with ten fingers each, hence there are
2 x 10 = 20
total fingers. Similarly, there are two people with four limbs each,
hence there are
2 x 4 = 8
total limbs. Adding the body parts gives
20 + 8 = 28
total body parts.
The Distributive Property
Multiplication can be distributed over addition
without changing the result.
2 x (10 + 4) = 2 x 10 + 2 x 4
= 28 3 x (5 +
6) = 3 x 5 + 3 x 6 = 33
- Practice with Multiplication
x 7 = 1015)
(245 x 3 = 435) Remember to
place an extra 0 in the right digit
- 423 x 27 =
(Hold mouse over the yellow rectangles to check
- 314 x 103 =
- You own a bicycle rental shop near the lake. Your bikes rent for
$29 per rental and you had 327 customers in the first week of
July. What was your total revenue for bicycle rentals during the
first week of July?
Revenue = price
x number of customers
x 9 = 2943)
(327 x 2 = 6540) Remember
to place an extra 0 in the right digit
Your total revenue during the first week of
July was $9,483.
- Your computer screen measures 13 inches by 9 inches. What is the
total area of your computer screen?
Area = Width x Height
The area of the computer screen is 117
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