Question

What is `1/2 -: 3/4`?

Answer 1

`color (blue)(2/3)`

Explanation:

Note that `a/b÷c/d=a/b×d/c`

So, `1/2÷3/4 = 1/2×4/3`

`1/cancel2×cancel4^2/3`

`2/3 ~~ 0.66`

In decimal `0.bar6`

Answer 2

`2/3`

Explanation:

`=1/2/3/4`

`=1/2*4/3`

`=1*2/3`

`=2/3`.

Answer 3

`2/3`

Explanation:

Because you use KFC... Keep Flip Change.

You keep the first fraction the same

`1/4`

then you flip the other fraction

`1/4 ÷ 4/3`

Finally, you change the symbol to a times

`1/4 xx 4/3`

You then multiply the fraction getting

`4/6`

Simplified makes

`2/3`

Answer 4

A fraction is actually a division problem so to divide two fractions set it up as a division problem or complex fraction. This makes the most sense.

`1/2/ 3/4 = ( 1/2)/(3/4)`

Now multiply both the top fraction and the bottom fraction by the inverse of the bottom fraction. This makes sense because multiply by `(4/3)/(4/3) = 1` multiplying by one doesn't anything

Also multiplying by the inverse equals one

`(3/4) xx ( 4/3) = 12/12 = 1`

`(1/2 xx 4/3)/ (3/4 xx 4/3) = ( 1/2 xx 4/3)/1` Which leaves.

`1/2 xx 4/3 = 4/6` Divide both top and bottom by 2

`(4/2)/( 6/2) = 2/3`

Dividing a fraction by a fraction makes sense and is easier to remember, even thought it takes longer.

Answer 5

`2/3`

Explanation:

Here is another approach to understand WHY the method of Multiply and Flip works to divide by a fraction, rather than just HOW to do it.

The fraction `3/4` means 'three' quarters.

Quarters are obtained when a whole number is divided into four equal pieces, each is a quarter.

To find the number of quarters there are, multiply a number by `4`

In `1` there will be `1xx4 = 4` quarters
In `2` there will be `2xx4=8` quarters
In `3` there will be `3xx4=12` quarters

In `11` there will be `11xx4=44` quarters

In `1/2` there will be `1/2xx4=2` quarters

However, when dividing by `3/4` we are actually asking "How many groups of `3/4` can be obtained ?"
(or how many times can `3/4` be subtracted?)

That means, once you have the total number of quarters, divide them into groups of three's - each group will be 'Three' quarters.

You do this by dividing the total number of quarters by `3`

In `1` there will be `1xx4 = 4` quarters
`4 div 3 = 1 1/3`, so there are `1 1/3` groups of `3/4`
Hence `3/4` divides into 1, a total of `1 1/3` times

(ie. once with a bit left over.)
.

In `2` there will be `2xx4=8` quarters

`8div 3 = 2 2/3` so there are `2 2/3` groups of `3/4`
Hence `3/4` divides into `2`, a total of `2 2/3` times.

In `9` there will be `9 xx4 = 36` quarters.

`36 div 3 = 12`, so there are `12` groups of `3/4` in `9`
.

In each case we are multiplying by `4` and dividing by `3`.

`4/3` is the reciprocal of `3/4`

Hence the simple rule of Multiply and flip.

`1/2 div 3/4`

`=color(blue)(1/2 xx4) div 3" "larr` change into quarters

`=2color(red)(div3)" "larr` divide into groups of `3`

`=2/3`
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Something like `6div 3/4` can be shown very nicely practically by taking `6` squares, cutting them into quarters and then then making groups of `3/4` ... there will be exactly `8`. which nicely demonstrates:

`6 div 3/4`

`=6xx4 div3`

`=6xx4/3`

`=8`

`3/4` fits into `6` a total of `8` times.
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