Long division is useful when a problem is too large or complicated to solve another way. Long division usually takes more time, but it always work.
Terms to Understand
Dividend
Divisor
Quotient
Remainder
The remainder is whatever part of the divisor is left over after dividing it evenly.
Bring Down
Bringing down is an important step in long division. In this step we bring the next digit in the denominator down to where we can calculate it. By bringing down one digit at a time, this method makes it much easier to divide big numbers.
Place Value
In the decimal number system, number values are aranged in groups of 10. The place value of a digit tell us how many groups of 10 it equals. For example, the in the number means ( groups of ), or ().
Definition of Division
Division is one of the four basic arithmetic operations (+, -, , ). It is the opposite of multiplication. This means that division undoes multiplication, and multiplication undoes division. Division can be thought of as a method for distributing a large group into several equal and smaller groups (or parts).
In multiplication, groups of parts can be combined to become one group of parts:
.
In division, a large group of parts can be divided into equal and smaller groups, each containing parts:
Notation for Division
Symbols for division include a slash, (), a fraction line, , and the division sign (). Each of these expressions is read, “a divided by b”.
Dividends, Divisors, Remainders and Quotients
The first number (or numurator) is the Dividend, and the second number (or denominator) is the Divisor. The result (or answer) is the Quotient, and any left-over amount is the Remainder.
In the below example, the dividend is , the divisor is , the remainder reduces to , and the simplified quotient (or answer) is .
Remainders
Not all numbers divide evenly into other numbers. Sometimes something is left over. That last bit is always less than the divisor, and is called the remainder.
For example, dividing 4 into 6, or , results in a quotient of 1 and a remainder of 2. This is sometimes written as, . But it’s much better to write remainders as either fractions or decimals.
Written as a fraction, the remainder is the numerator, and the divisor is the denominator. It this example, the remainder is written:
Of course this fraction can be simlified. That’s one of the advantages of using fractions in remainders. They make it easy to see the relationship between the remainder and the divisor.
Division of a Fraction
Long Division
Long division is a method used to break harder division problems into a sequence of easier steps.
Note that because there are so many steps in long division, you should always check your work by using multiplication (the inverse operation).
Division by Zero
Because division by zero does not make logical sense, it is considered “undefined”. On most computers and electronic calculators, dividing by zero results in an error.
