Page 81 - Mathematics Coursebook

7.4 Improper fractions and mixed numbers

7.4 Improper fractions and mixed numbers

In a proper fraction the numerator is smaller than the denominator. An improper fraction is sometimes
Example: 2 called a top-heavy fraction.
3
An improper fraction can be
In an improper fraction the numerator is bigger than the written as a mixed number.

denominator. Example: 4
3
An improper fraction can be written as a mixed number. A mixed number contains a
whole number and a fraction.
Worked example 7.4

a Write the fraction shaded in this diagram as:
i a mixed number ii an improper fraction.
2
b i Write 5 as a mixed number. ii Write 4 as an improper fraction.
2 3
1
a i 1 1 complete rectangle and 1 of the second rectangle are shaded.
4 4
5 4 1
ii 4 from the fi rst rectangle and 4 from the second gives a total of
4
5 quarters or 5 .
4
5 1 5
b i = 2 is 5 halves. 4 halves makes 2 whole units and there is 1 half left.
2 2 2
ii 4 2 = 14 Change 4 whole units into thirds: 4 × 3 = 12 so there are 12 thirds.
3
3
Then add the extra 2 thirds: 12 + 2 = 14 thirds.

) Exercise 7.4

1 Write down the fraction shaded in each of these diagrams as:
i a mixed number ii an improper fraction.
a b c

d e f

2 Write each improper fraction as a mixed number. a 7 b 13 c 6
2 4 5
1
1
3 Write each mixed number as an improper fraction. a 4 b 2 c 4 3
2 3 4
4 Sita made 5 cakes for a birthday party. She cut each cake into 12 pieces.
At the end of the party there were 7 pieces of cake that had not been eaten.
Write the amount of cake that was eaten as:
a a mixed number b an improper fraction.

80 7 Fractions