Calculations can be carried out using fractions of shapes and quantities. Mixed fractions can be added or subtracted to find the number of fractional parts in a mixed number.
Imagine that there are \(10\) questions in a test and you get \(7\) of them correct. You would say that you got \(\frac{7}{{10}}\), because \(7\) as a fraction of \(10\) is \(\frac{7}{{10}}\).
In the same way, \(4\) as a fraction of \(12\) is \(\frac{4}{{12}}\) or \(\frac{1}{{3}}\)
Similarly \(20\) as a fraction of \(48\) is \(\frac{{20}}{{48}}\) or \(\frac{{5}}{{12}}\).
Seems easy, but just be careful with the units.
For example, \(20p\) as a fraction of \(\pounds20\) is not:
\(\frac{{20}}{{20}}\) but \(\frac{{20}}{{2000}}\) because \(\pounds20\) is \(2000p\).
Similarly, \(30cm\) as a fraction of \(5m\) is \(\frac{{30}}{{500}}\) because \(5m = 500cm\).