Question

How do you divide `5 5/8 div 2/3`?

Answer 1

`8 7/16`

Explanation:

Change the mixed number to an improper fraction

`5 5/8 = 45/8`

Set up a complex fraction to indicate the division

`( 45/8)/(2/3)`

eliminate the bottom fraction `2/3` by multiplying by the inverse.
(Remember that what ever is done to the bottom must always be done to the top. ( fairness)

`{(45/8) xx (3/2)}/{ (2/3) xx (3/2)}`

`2/3 xx 3/2 = 1` so this leaves

`45/8 xx 3/2 = 135/16 = 8 7/16`

Answer 2

`= 8 7/16`

Explanation:

For division of fractions, always change mixed numbers to improper fractions:

`5 5/8 div 2/3`

`= 45/8 xx 3/2" "larr` to divide, multiply by the reciprocal

`= 135/16" "larr` multiply straight across, nothing cancels

`= 8 7/16`

The question was given with mixed numbers, answer in the same form.

Answer 3

A slightly different approach.

`8 7/16`

Explanation:

`color(blue)("An example of the method using numbers")`

I choose: `9-:3` but 9 can be written as `6+3` so we may write the same thing as

`9 -:3->(6+3)-:3`

This is the same as: `(6+3)xx1/3`

Multiply everything inside the brackets by `1/3` giving `6/3+3/3=3`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Writ `5 5/8` as `5+5/8` so now we have: `(5+5/8)-:2/3`

This is the same as `(5+5/8)xx3/2`

Note that `-:2/3` give the same answer as `xx3/2`

Multiply everything inside the brackets by `3/2` giving:

`color(green)(15/2+15/16" "=" "[15/2color(red)(xx1)]+15/16)`

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way the fraction looks without changing its inherent value.

`color(green)(" "=" "[15/2color(red)(xx8/8)]+15/16)`

`" = "120/16 " "+15/16" "=" "135/16`

`" "=" "8 7/16`