Mixed Numbers & Top Heavy Fractions

A mixed number has an integer part and a fraction part
- $3 \frac{3}{4}$ has the whole number 3 and the fraction $\frac{3}{4}$ , meaning “three and three quarters”
A top heavy fraction is also known as an improper fraction
An improper fraction is a fraction where the numerator is bigger than the denominator
- $\frac{15}{4}$ means “fifteen quarters”
Any fraction that is greater than 1 can be written as either a mixed number or an equivalent improper fraction

Multiply the integer part by the denominator of the fraction part
- For example, convert $4 \frac{6}{7}$ into a top heavy fraction
- $4 \times 7 = 28$
Add the result to the numerator of the fraction part
- $28 + 6 = 34$
Write the 'new' numerator over the same denominator and ignore the integer part
- $4 \frac{6}{7} = \frac{34}{7}$

Divide the numerator by the bottom
- For example, convert $\frac{22}{3}$ into a mixed number, $22 \div 3 = 7$ remainder $1$
The integer part of the mixed number is the whole number
The fraction part is the remainder over the denominator
- $\frac{22}{3} = 7 \frac{1}{3}$

The term 'improper fraction' is frequently used in exam papers
- Make sure you remember that improper fractions are the same as top heavy fractions

(a) Write $5 \frac{3}{4}$ as an improper fraction.

Multiply the whole number by the denominator, and add to the numerator

Keep the denominator the same

$\frac{(5 \times 4) + 3}{4}$

Simplify

$\frac{23}{4}$

(b) Write $\frac{17}{5}$ 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

$3 \frac{2}{5}$

Mixed Numbers & Top Heavy Fractions (CIE IGCSE Maths: Core)