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# Multiplying Numbers

It is easiest to think of multiplication as a method to sum similar items efficiently. It is the process of finding the quantity obtained by repeating a specified quantity a specified number of times based on repetitive addition. Multiplying is the opposite of dividing.

## Properties of Multiplication

1. Multiplication Sign:

- The letter-like “x” is the most common sign,

- Instead of “x” a dot, •, is often used as a multiplication sign,

- A sign is often omitted; instead numbers are enclosed by parenthesis

or brackets: [ (5) (2) = 5 x 2 = 10 ].

2. Any number or quantity multiplied by zero equals zero: (5 x 0 = 0).

3. Any number or quantity multiplied by 1 equals that same number: (5 x 1 = 5).

4. Math Signs:

- A positive number multiplied by a positive number is positive,

- A positive number multiplied by a negative number is negative,

- A negative number multiplied by a negative number is positive.

5. The result of multiplying 2 or more numbers together is the product.

6. The number of digits of a product can never exceed the sum of digits of

all multiplied numbers.

The math sign “*” (asterisk) is often used in computer programming to designate multiplication.

## Long Multiplication

The basic multiplication method is long multiplication.

Suppose we have five baskets and each basket has one dozen apples.

To determine the total number of apples using simple addition we could write:

12 + 12 + 12 + 12 +12 = 60

Using simple multiplication we write:

5 x 12 = 60

5 • 12 = 60

(5) (12) = 60

5 * 12 = 60

5 is the multiplicand, 12 is the multiplier and both are factors. In mathematics all quantities multiplied are factors.

We want to multiply 5 and 12.

12 can be written as 10 + 2:

(carry 1 to the next left column as 10)

Using the carry method each column that produces a number greater than 9, is 2 digits, carries the left-most digit to the next left column and is added to that column. In the middle example , 5 x 2 = 10, the 10 is greater than 9. Write the zero (above right) in the column and carry the 1 to the next left column. The carry method is a common form of long multiplication.

67 = 60 + 07

x 46 = 40 + 06

Cross Multipliers of 67 and 46:

06 x 07

06 x 60

40 x 07

40 x 60

Although multiplication can be written more efficiently than addition it is sometimes necessary to use long multiplication to simplify the math problem into addition to find the product. A difficult multiplication of 2 numbers each having 2 digits is reduced to addition of 4 numbers.

Using the above method there is no need to carry digits. After all multiplications have been completed the resulting numbers are added together to obtain the total. 60 x 6 and 40 x 7 are by cross multiplication where a numeric digit of one column is multiplied by a numeric digit from a different column.

Cross multiply to find the product of 583 and 75, one number is 3 digits:

583 =

x 75 =

15 =

400 =

2,500 =

210 =

5,600 =

+ 35,000 =

500 + 80 + 3

70 + 5

(5) (3)

(5) (80)

(5) (500)

(70) (3)

(70) (80)

(70)(500)

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