Math Division Fraction

Introduction to math division fraction:

As division of whole numbers shows how often one integer is contained in another integer, to division of fraction shows how often one fraction is contained in another. If the numerator of any fraction be made a denominator, and the denominator a numerator, the fraction of made is called the reciprocal of the former. Thus `4 / 3` is the reciprocal of `3 / 4.`

In division * as the divisor is to the dividend, of is a unit of the quotient (both in whole numbers and fraction).


Math division fraction – Steps and methods:


To dividing algebraic fraction, follow these steps:

Write the given fractions.
Change the division sign to a multiplication sign and invert the second fraction.
Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.
We will get final answer.
Math division fraction – Methods:

Dividing common fraction
Dividing a fraction and a whole number
Dividing mixed number

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Math division fraction– Three methods and example problems:


Dividing common fractions:

To divide common fraction, follow these steps:

Invert the divisor.
Then multiply the numerator by the numerator and the denominator by the denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

(`4 / 6` ) `-:` (`5 / 8` )

Solution:

(`4 / 6)` `-:` (`5 / 8` ) (divisor)

= (`4 / 6` ) * (`8 / 5` )

= `(4 * 8) / (6 * 5)`

= `32 / 30`

= `16 / 15`

Example 2:

Find the dividing fraction

(`5 / 9` ) `-:` (`4 / 9` )

Solution:

(`5 / 9` ) `-:` (`4 / 9` ) (divisor)

= (`5 / 9` ) * (`9 / 4` )

= `(5 * 9) / (9 * 4)`

= `45 / 36`

= `5 / 4`

Math division fraction and a whole number:

To divide a fraction and a whole number, follow these steps:

Change the whole number to a fraction by the placing the whole number over one.
Invert the divisor.
Then multiply the numerator by  numerator and  denominator by denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

12 `-:` (`3 / 7` )

Solution:

12 `-:` (`3 / 7` )

= (`12 / 1` ) `-:` (`3 / 7)`

= (`12 / 1` ) * (`7 / 3` )

= `(12 * 7) / (1 * 3)`

= ` 84 / 3`

= 28

Example 2:

Find the dividing fraction

8 `-:` (`12 / 5` )

Solution:

8 `-:` (`12 / 5` )

= (`8 / 1` ) `-:` (`12 / 5` )

= (`8 / 1` ) * (`5 / 12` )

= `(8 * 5) / (1 * 12)`

= `40 / 12`

= `10 / 3`

Dividing mixed number fraction:

To divide mixed numbers, follow these steps:

Change the mixed number to an improper fraction
Invert the divisor.
Then multiply the numerator by numerator and denominator by denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

(2 `6/5` ) `-:` (`7 / 2`

Solution:

(2 `6/5` ) `-:` (`7 / 2` )

= (2 `6/5` ) = `((2 * 5 + 6) / 5)` = `16 / 5`

= (`16 / 5` ) `-:` (`7 / 2` )

= (`16 / 5` ) * (`2 / 7` )

= `(16 * 2) / (5 * 7)`

= `32 / 35`

Example 2:

Find the dividing fraction

(4` 7/3` ) `-:` (`6 / 5` )

Solution:

(4 `7/3` ) `-:` (`6 / 5` )

= (4 `7/3` ) = `((4 * 3 + 7) / 3)` = `19 / 3`

= (`19 / 3` ) `-:` (`6 / 5` )

= (`19 / 3` ) * (`5 / 6` )

= `(19 * 5) / (3 * 6)`

= `95 / 18`