Question

How do you divide `1\frac { 3} { 4} \div 4\frac { 1} { 3}`?

Answer 1

Convert the factors into improper fractions; invert the divisor; and multiply ( to get `21/52`)

Explanation:

`{:(1 3/4=7/4,color(white)("xxx"),4 1/3=13/3):}`

`1 3/4 div 4 1/3`
`color(white)("XXX")7/4 div 13/3`

`color(white)("XXX")=7/4 xx3/13`

`color(white)("XXX")=21/52`

Answer 2

`21/32`

Explanation:

We can make the mixed numbers into improper fractions:

`7/4 -: 13/3`

When we divide by a fraction, we can achieve the same result by multiplying by the reciprocal:

`7/4xx3/13=21/52`

Answer 3

Turn both fractions into improper fractions and divide the fractions as a complex fraction.

Explanation:

A fraction is a division problem so set the problem up as one fraction divided by the second fraction.

First turn both fractions into improper fractions.

`1 3/4 = 7/4`
`4 1/3 = 13/3`

Set up the complex fraction

`(7/4)/(13/3)`

Multiply both the top and bottom fractions by the inverse of the bottom fraction. Multiplying both sides is the same as multiplying by 1 which doesn't change the values. Also multiplying by the inverse makes the bottom fraction one .

`( 7/4 xx 3/13) / ( 13/3 xx 3/13) = ( 7/4 xx 3/13)/1`

Dividing by 1 equals the same number so it leaves only the top.

`7/4 xx 3/13 = 21/52`