Review of Introductory Mathematics
FOUR BASIC ARITHMETIC OPERATIONS
Subtraction can be verified by adding the difference to the subtrahend, which should
result in the minuend.
Multiplying Whole Numbers
Multiplication is the process of counting a number two or more times. It can be considered a
shortened form of addition. Thus, to add the number 4 three times, 4 + 4 + 4, we can use
multiplication terms, that is, 4 multiplied by 3. When numbers are multiplied, the result is called
the product. The numbers multiplied are called factors. One factor is called the multiplicand;
the other is called the multiplier. Multiplication is indicated by the times or multiplication sign
(x), by a raised dot ( ), or by an asterick (*).
In multiplying several numbers, the same product is obtained even if the numbers are multiplied
in a different order or even if some of the numbers are multiplied together before the final
multiplication is made. These properties are called the commutative and associative laws for
The commutative law for multiplication states that numbers can be multiplied in any
order, and the result is the same product. In equation form:
a x b = b x a
Thus, the product of 8 x 3 is the same as 3 x 8.
The associative law for multiplication states that factors can be associated in any order,
and the result is the same product. In equation form:
a x (b x c) = (a x b) x c
Thus, the numbers 2, 3, and 5 can be multiplied by first multiplying 2 x 3 to equal 6 and
then multiplying 6 x 5 to equal 30. The equation may also be solved by first multiplying
3 x 5 to equal 15, and then multiplying 15 x 2 to equal 30. In either case, the product
In multiplying two numbers, one number is placed under the other with the digits arranged in
columns placing units under the units place, tens under the tens place, and so on. Usually, the
larger number is considered the multiplicand and the smaller number is considered the multiplier.
The digit in the units place of the multiplier is multiplied first, the digit in the tens place of the
multiplier next, and so on.