How do you convert a fraction like
1
^{
2
}
⁄
_{
3
}
to an improper fraction?

A mixed fraction is made up of a whole number at the front (on the left) followed by a fraction. To convert it to an improper fraction simply multiply the denominator by the whole number and add that number to the numerator.

The new numerator will replace the existing one and will be
**
larger
**
than the denominator.

So how does this work with the mixed fraction
1
^{
2
}
⁄
_{
3
}
?

## Improper Fraction Conversion

Here is the step by step process of converting a mixed fraction to an improper fraction.

Find the denominator in your mixed fraction – this is the number under the fraction bar.

1\ \frac{2}{3}

The denominator for the mixed fraction is the number 3 .

Multiply this number by the whole number (the big number) of the mixed fraction. The big number in this example is the number 1 .

3 \times 1 = 3

Add the result to the numerator.

3 \ + \ 2 \ = \ 5

Replace the current numerator with this new value 5 and remove the whole number altogether:

\xcancel{1} \ \frac{\xcancel{2} \, 5}{3}

The original mixed fraction has now been converted into an improper fraction.

1 \ \frac{2}{3} \ = \ \frac{5}{3}

How can you check your answer?

## Check Your Answer

How can you check if the improper fraction is the correct answer?

Simply divide the numerator by the denominator:

5 \div 3 = 1 \ r2

From the division operation, the quotient 1 is the whole number, and the remainder 2 is the numerator.

5 \div \fcolorbox{red}{lightgrey}{3} = \fcolorbox{blue}{aqua}{1} \ r\fcolorbox{black}{yellow}{2} \rightarrow \fcolorbox{blue}{aqua}{1} \, \frac{\fcolorbox{black}{yellow}{2}}{\fcolorbox{red}{lightgrey}{3}} = 1\,\frac{2}{3}

If you’ve done the right calculation this will match the original mixed fraction.

## Summary

To convert a mixed fraction to an improper fraction simply multiply the denominator to the whole number and add the numberator. The finished number will be the
**
new numerator
**
and the whole number can be removed.

You should finish with a numerator larger than the denominator as the final fraction.

The mixed fraction
1
^{
2
}
⁄
_{
3
}
is
^{
5
}
⁄
_{
3
}
as an improper fraction.