Division

Definitions

Division is the process of determining how many times one quantity is contained within another quantity, or of splitting a quantity into equal parts.

The quotient is the result of the operation.

The dividend is the number that is divided. The divisor is the number that divides.

Dividend

Divisor

Quotient

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Two Types of Division

Complete Division

Complete division is an operation between two real numbers. One is called the dividend and the other is the divisor. The quotient will also be a real number.

Example

|24.54\div 2.53=9.69...|

Division With a Remainder

Division with a remainder is an operation consisting of two natural numbers, one called the dividend and the other the divisor, with which two other natural numbers, the quotient and the remainder, are associated.

Definition

The remainder is a number that cannot be divided by the divisor.

Example

Consider the following division. ||37\div4=||

  1. We determine how many times |4| goes into |37|

    The number |4| goes into |37| a maximum of |9| times.

  2. We write the result with the remainder

    Since |4\times9=36,| |1| remains. ||37-36=1||
    The quotient of the whole division is: |9| remainder |1.|

Divisors

Definition

The divisors of a number are the natural numbers by which that number can be divided and which result in an answer without a remainder.

Example

The divisors of |24| are |\left\{1, 2, 3, 4, 6, 8, 12, 24\right\}.|

The number |24| can be divided by each of these numbers and the result is a natural number without a remainder.

Be careful!

The word factor is used incorrectly to denote the divisors of a number.

Factors are the building blocks of multiplication. They can be compared to dividends and divisors in division.

Finding the Divisor

To find a missing divisor between the dividend and the quotient, simply divide the dividend by the quotient.

Example

|56 \div\ ?=8|

|56 \div 8 =\ ?|

|?=7|

Words Used in a Division Word Problem

The following terms are used in a division word problem.

Term

Example

Calculation

Divide

Divide |8| by |4.|

|8\div4|

Quotient

Find the quotient of |32| and |8.|

|32\div8|

Into

What is |9| into |3?|

|9\div3|

Half

What is half of |12?|

|12\div2|

Third

What is a third of |30?|

|30\div3|

Quarter

What is a quarter of |48?|

|48\div4|