Question

How do you divide `\frac { 4} { 245} -: \frac { 8} { 343}`?

Answer 1

`7/10`

Explanation:

Notes:
`color(white)("XXX")245=7xx7xx5`
`color(white)("XXX")343=7xx7xx7`
`color(white)("XXX")`To divide by a fraction, invert the fraction and multiply.

`4/245div 8/343`
`color(white)("XXX")=4/245 xx 343/8`

`color(white)("XXX")=4/(7xx7xx5) xx(7xx7xx7)/8`

`color(white)("XXX")=4/(cancel(7)xxcancel(7)xx5) xx(cancel(7)xxcancel(7)xx7)/8`

`color(white)("XXX")=4/5 xx7/8`

`color(white)("XXX")=cancel(4)/5 xx7/cancel(8)_2`

`color(white)("XXX")=7/10`

Answer 2

`4/245-:8/343=7/10`

Explanation:

Dividing a fraction `a/b` by another fraction `c/d` means multiplying former by the reciprocal or multiplicative inverse of latter i.e. `c/d`.

Reciprocal or multiplicative inverse of `c/d` is obtained by reversing the numerator and denominator. Hence reciprocal or multiplicative inverse of `c/d` is `d/c` and `a/b-:c/d=a/bxxd/c`.

Hence `4/245-:8/343=4/245xx343/8`

As `4` and `8` are divisible by `2` and `245` and`343` are divisible by `7`, this become

`(cancel4^1)/(cancel245^35)xx(cancel343^49)/(cancel8^2)`

= `1/35xx49/2` and as `35` and `49` are again divisible by `7`,

this becomes `1/(cancel35^5)xx(cancel49^7)/2`

= `7/(5xx2)`

= `7/10`