Question

How do you divide `3\frac { 1} { 2} \div 5`?

Answer 1

`7/10`

Explanation:

The first step is to convert `3 1/2"` into an `color(blue)"improper fraction"`

`rArr3 1/2=7/2`

`rArr7/2÷5" is to be calculated"`

Change the operation to multiplication and 'invert' the 5

`rArr7/2xx1/5`

`=(7xx1)/(2xx5)`

`=7/10`

Answer 2

`7/10` two methods given

Explanation:

Consider the `3 1/2` write as: `3+1/2`

Multiply by 1 and you do not change the value. However,1 comes in many forms so you can change the way a number looks without changing its actual value.

`color(green)([3color(red)(xx1)]+1/2)`

`color(green)([3color(red)(xx2/2)]+1/2)`

`color(green)([6/2]+1/2)" "=" "(6+1)/2=7/2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("So putting it all together")`

`3 1/2-:5" " =" " 7/2-:5`

`color(brown)("Shortcut method")`

Write as `7/2-:5/1 larr" Yes you can write 5 as "5/1`

For divide; turn the `5/1` upside and multiply

`color(blue)(7/2xx1/5 = (7xx1)/(2xx5) = 7/10)`

....................................................................................
`color(brown)("First principle method")`

Fraction `->("count")/("size indicator") ->("numerator")/("denominator")`

You can not `ul("directly")` divide the counts unless the 'size indicators are the same.

`7/2-:5/1" "->" "7/2 -: 10/2`

Now that the size indicators (bottom numbers) are the same we can divide just the counts (top numbers)

`color(blue)(7/2-:10/2 = 7-:10 = 7/10)`