Question

How to make a mixed number a improper fraction ​

Answer 1

A mixed number of the form
`a(b)/(c)` can be turned into an improper fraction by using the fact that a mixed number is really het whole number plus its fraction part, so

`a(b)/(c) = {\displaystyle a + (b)/(c)=(a)/(1)+(b)/(c)}`

Then do the usual procedure for adding fractions via common denominator.

For example, to convert the mixed number
`5 (1)/(4)` into an improper fraction, we have

`5(1)/(4)={\displaystyle 5 +(1)/(4)=(5)/(1)+(1)/(4)}`

To add
`(5)/(1)+(1)/(4)`, we need
`(5)/(1)` to have a denominator of 4, so we multiply the numerator and denominator by 4 to get

`=(5\cdot 4)/(1 \cdot 4)+(1)/(4)=(20)/(4)+(1)/(4) = (21)/(4)`

Therefore,

`5(1)/(4) = (21)/(4)`