Mixed Numbers & Top Heavy Fractions
What are mixed numbers & top heavy fractions?
- A fraction that is greater than 1 can be written as either a mixed number or an equivalent top heavy fraction
- A mixed number has an integer part and a fraction part
- has the whole number 3 and the fraction , meaning “three and three quarters”
- A top heavy fraction is a fraction where the numerator is bigger than the denominator
- A top heavy fraction is also known as an improper fraction
- means “fifteen quarters”
How do I convert a mixed number into a top heavy fraction?
- Multiply the integer part by the denominator of the fraction part
- For example, convert into a top heavy fraction
- Add the result to the numerator of the fraction part
- Write the 'new' numerator over the same denominator and ignore the integer part
How do I convert a top heavy fraction into a mixed number?
- Divide the numerator by the bottom
- For example, convert into a mixed number, remainder
- The integer part of the mixed number is the whole number
- The fraction part is the remainder over the denominator
Examiner Tip
- The term 'improper fraction' is frequently used in exam papers.
- Make sure you remember that improper fractions are the same as top heavy fractions.
Worked example
(a) Write as an improper fraction.
Multiply the whole number by the denominator, and add to the numerator
Keep the denominator the same
Simplify
(b) Write as a mixed number
Divide the top by the bottom
17 ÷ 5 = 3 remainder 2
The final answer is 3, with 2 parts still left over
Leave the 3 as the whole number part and put the 2 over the original denominator of 5