Converting between mixed numbers and improper fractions
Convert a mixed number to an improper fraction
You can write the whole number part as a fraction, with the same denominator as the other fraction, and then add the fractions together.
Example
\(1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\)
Question
What is \(2 \frac{1}{4}\) as an improper fraction?
\(2 \frac{1}{4}\)
\(= 1 + 1 + \frac{1}{4}\)
\(= \frac{4}{4} + \frac{4}{4} + \frac{1}{4}\)
\(= \frac{9}{4}\)
Convert an improper fraction to a mixed numbers
There are two ways to convert an improper fraction to a mixed number:
- Method 1 - separate an improper fraction into as many whole numbers as possible, with a smaller remaining fraction.
- Method 2 - divide the numerator by the denominator to find how many whole numbers there are and add the smaller remaining fraction
Example
Express \(\frac{17}{5}\) as a mixed number.
Method one
\(\frac{17}{5}= \frac{5}{5} + \frac{5}{5} + \frac{5}{5} + \frac{2}{5} = 3 \frac{2}{5}\)
Method 2
\({17}\) divided by \({5}\) is \({3}\) remainder \({2}\).
So the whole number part is \({3}\), and the remainder \({2}\) means there are \(\frac{2}{5}\) left over.
So the answer is \(\frac{17}{5} = 3 \frac{2}{5}\)
Question
Write \(\frac{20}{7}\) as a mixed number.
Method 1:
\(\frac{20}{7} = \frac{7}{7} + \frac{7}{7} + \frac{6}{7} = {2}\frac{6}{7}\)
Method 2:
\(\frac{20}{7} = 20 \div 7 = 2\) remainder \({6}\), so:
\(\frac{20}{7} = 2 \frac{6}{7}\)