nuMber AnD AlgebrA • real numbers
4C
Mixed numbers and improper
fractions
■
An improper fraction has a numerator larger than the denominator; for example 32 .
■
A mixed number is made up of a whole number and a fraction; for example 1 3 , 2 1 .
4
2
Change improper fractions to mixed numbers
■
An improper fraction can be changed to a mixed number by dividing the denominator into the
numerator and writing the remainder over the same denominator.
WorkeD exAMple 9
Draw a diagram to show 54 as parts of a circle, then write the improper fraction as a mixed number.
Think
1
WriTe
Draw a whole circle and divide it into the number of
parts shown by the denominator.
This is 4 quarters or 4 .
4
2
Find the number of parts left over and draw them.
Extra 1 needed.
4
3
Write the improper fraction as a mixed number.
■
5
4
= 11
4
If the improper fraction had a larger numerator, it might be necessary to draw more circles
and the whole number part would then be greater than 1.
WorkeD exAMple 10
Express 11
as a mixed number.
5
Think
WriTe
1
Write the improper fraction.
2
Determine how many times the denominator can be
divided into the numerator and what the remainder is. The
whole number is part of the answer and the remainder
becomes the numerator of the fractional part with the
same denominator as the original improper fraction.
Write the answer.
3
11
5
= 11 ó 5
= 2 remainder 1
= 2 15
Changing mixed numbers to improper numbers
■
102
A mixed number can be changed to an improper fraction by first multiplying the whole
number with the denominator then adding the numerator. The denominator stays the same.
Maths Quest 7 for the Australian Curriculum
nuMber AnD AlgebrA • real numbers
WorkeD exAMple 11
Draw a diagram to show 2 1 as pieces of circle and then write 2 1 as an improper fraction.
3
3
Think
WriTe
1
Draw two whole circles and 1 of a circle.
2
Divide the whole circles into thirds.
3
Count the number of thirds and write the mixed
number as an improper fraction.
3
213 =
7
3
WorkeD exAMple 12
Express 2 3 as an improper fraction.
4
Think
WriTe
1
Write the mixed number.
23
2
Multiply the whole number with the denominator then
add the numerator. The result becomes the numerator
and the denominator stays the same.
=
2×4+3
4
3
Evaluate the top line of the fraction.
=
8+3
4
4
Write the answer.
= 11
4
4
reMeMber
1. An improper fraction has a numerator that is larger than the denominator.
2. A mixed number is made up of a whole number and a fraction.
3. An improper fraction can be changed to a mixed number by dividing the denominator
into the numerator and writing the remainder over the same denominator.
4. A mixed number can be changed to an improper fraction by first multiplying the whole
number with the denominator then adding the numerator. The denominator stays the
same.
eXerCise
4C
Mixed numbers and improper fractions
fluenCy
1 We9 Draw a diagram to show the following improper fractions as pieces of a circle, then
write each improper fraction as a mixed number.
a
5
2
b
4
3
c
11
6
d
13
8
e
12
4
Chapter 4
f
7
6
rational numbers
103