OBJECTIVE: Convert improper fractions to mixed numbers and
mixed numbers to improper fraction
Preliminary
What is a fraction? What is an improper fraction? What is a mixed number?
A fraction is written using two whole numbers, one on top and the other at the bottom with a line
separating them; the bottom number cannot be zero. The top number is called the numerator and
the bottom number is called the denominator. The following are examples of fractions:
a.
b.
1
2
c.
5
2
7
3
d.
e.
25
27
111
100
Example 1.
The above examples consist of three improper fractions, which are fractions that have a
numerator that is greater than its denominator. Can you identify those improper fractions?
Examples 1.b, 1.c and 1.e are the improper fractions.
A mixed number is written using three whole numbers. One of the whole numbers is placed to
the left of the other two which are written as a fraction that is not improper. The following are
examples of mixed numbers:
a.
2
b.
1
2
2
1
3
c.
1
11
100
Example 2.
The process of converting from an improper fraction to a mixed number begins by determining
how many times the fraction’s denominator can be taken from the numerator. Examples 1.b, 1.c
and 1.e are reproduced below to illustrate this process:
Email [email protected] to request the answer key for this worksheet.
© www.caribbeanexams.com
Page 1
1.b.
1.c.
5
2
7
3
1.e.
111
100
In the case of Example 1.b, the denominator 2 can be taken from 5 a maximum of 2 times
leaving 1 as the remainder. Now all the required intermediate results are available to write the
corresponding mixed number. The remainder 1 becomes the numerator of the fractional part
whose denominator is 2 – the same denominator of the original improper fraction. The number of
times (2 times) the denominator was able to be taken from the original mixed fraction’s
numerator becomes the number that is written to the left of the new fractional part. This answer
is exactly what is given as Example 2.a. Likewise, the answers to the conversion of Examples 1.c
and 1.e to mixed fractions are respectively Examples 2.b and 2.c.
To convert a mixed number to an improper fraction the steps described previously are followed
in the reverse order. Using Example 2.c as the starting point, the steps are as follows. First,
multiply the denominator by the whole number part – this gives 100 × 1 = 100. Second, add the
numerator to the result of the previous step – this gives 11 + 100 = 111. Finally, write the
improper fraction using the result of the second step as the numerator and reusing the
denominator of the original mixed number – this gives Example 1.e.
Exercises
1. Convert the following improper fractions to mixed numbers:
a.
8
5
b.
11
4
c.
23
3
d.
121
25
Email [email protected] to request the answer key for this worksheet.
© www.caribbeanexams.com
Page 2
2. Convert the following mixed numbers to improper fractions:
a.
b.
c.
d.
4
2
5
11
8
10
13
6
7
123
11
12
Email [email protected] to request the answer key for this worksheet.
© www.caribbeanexams.com
Page 3