AQA_Bk1_chap02_Layout 1 21/01/2010 16:31 Page 50
2.5
Improper fractions and
mixed numbers
This section will show you how to:
● change improper fractions into mixed numbers
● change mixed numbers into improper fractions
Key words
improper fraction
mixed number
proper fraction
top-heavy
A fraction with the numerator (top number) smaller than the denominator (bottom number) is
called a proper fraction. An example of a proper fraction is –54.
An improper fraction has a bigger numerator (top number) than the denominator (bottom
number). An example of an improper fraction is –59. It is sometimes called a top-heavy fraction.
A mixed number is made up of a whole number and a proper fraction. An example of a mixed
number is 1–43.
EXAMPLE 5
Convert 14
–5 into a mixed number.
14
means 14 ÷ 5.
5
Dividing 14 by 5 gives 2 with a remainder of 4 (5 fits into 14 two times, with –45 left over).
This means that there are 2 whole ones and –45 left over.
So,
14 5 5 4
= + +
5
5 5 5
= 2 –45
EXAMPLE 6
Convert 3 –41 into an improper fraction.
Each whole one is four-quarters.
So, 3 whole ones = 12 quarters
This means that 3 –41 =
50
CORE
( 44 + 44 + 44 )
12 1 13
+ =
4 4 4