Question

4 1/7÷ 3 1/2-3.5÷0.675-2/9 ÷ -3/8

Answer 1

To divide the given fractions, we first write each of them as improper fractions.

4 1/4 ÷ 3 1/2

Now,

`4(1)/(4)=4+(1)/(4)`
`=(4\cdot4)/(4)+(1)/(4)`
`=(16)/(4)+(1)/(4)=(17)/(4)`
`\therefore4(1)/(4)=(17)/(4)`

And

`3(1)/(2)=3+(1)/(2)`
`=(2\cdot3)/(2)+(1)/(2)`
`\therefore3(1)/(2)=(7)/(2)`

Now the division becomes

`(17)/(4)/(7)/(2)`

Taking the reciprocal of the left-hand fraction and converting division into multiplication gives

`(17)/(4)*(2)/(7)`
`=(17)/(14)`

Hence,

`4(1)/(4)/3(1)/(2)=(17)/(14)`

-3.5 ÷ 0.675

We first convert the decimals to fractions.

`-3.5=-\lbrack3+(1)/(2)\rbrack`

Converting this to an improper fraction gives

`-\lbrack(3\cdot2)/(2)+(1)/(2)\rbrack=-\lbrack(7)/(2)\rbrack`

Now, 0.675 can be written as

`(675)/(1000)`

Therefore, the division can be written as

`-(7)/(2)/(675)/(1000)`

Talking the reciprocal of the right-hand fraction gives

`-(7)/(2)*(1000)/(675)`
`=-7*(500)/(675)=-(140)/(27)`

Hence,

`-3.5/0.675=-(140)/(27)`

-2/9 ÷ -3/8

Taking the reciprocal of the right-hand fraction and converting the division into multiplication gives

`-(2)/(9)*(-8)/(3)`
`=(16)/(27)`
`\therefore-(2)/(9)/(-3)/(8)=(16)/(27)`