1. What fraction of each of the following is shaded? (i)
(ii) (iv) (v) (iii) (vi)
2. Name the type of fraction shown. Justify your answer in each case.
(i) 3 (ii) 5
__ 2
__ 7
(i) 7
__ 2
(ii) 14
__ 5
(i) 3 2 (ii) 4 1
__ 5
__ 6
(iii) 6 4 (iv) 2
__ 9
(iii) 25 (iv) 40
__ 7
__ 6
(iii) 1 5 (iv) 2 3
__ 9
__ 8
__ 5
(v) 3 1 (vi) 11
__ 8
3. Write the following improper fractions as mixed fractions.
(v) 19 (vi) 33
__ 4
__ 8
4. Write the following mixed fractions as improper fractions.
(v) 5 2 (vi) 9 1
__ 3
__ 2
5. Decide whether the following pairs of images represent equivalent fractions. Justify your answer in each case.
(i) (ii) (iii) (iv) (v) (vi)
__ 3
6. Copy and fi ll in the missing numbers to fi nd equivalent fractions.
(i) 2 (ii) 3 (iii) 5
__ 5 = __
__ 4 = __
__ 3 = __
10 = 12 __ = __
16 = 18 __ = __
15 = 30 __ = __
40 44 36
(iv) 80 (v) 3 (vi) 8
___ 100 = __
__ 8 = __
__ 40 = __
50 = 20 __ = __
5
24 = 15 __ = __
20 = 2 __ = __
7. A bag contains 60 marbles. 24 of them are yellow, 15 are red and the rest are green.
Rebecca removes one marble at random from the bag. What is the chance the marble is …?
(i) yellow (ii) red (iii) green
Express your answers as a rational number in its simplest form.
8. Use the Venn diagram shown to work out what portion (fraction) of the numbers are …
(i) natural numbers (ii) integers (iii) prime numbers (iv) mixed fractions (v) negative numbers
56 5
–1.75 –3
__ 4
19
–9 1
2
5 2
__ 3
–6 ℕ
15 7
ℤ
ℚ
5.2 Working with fractions
By the end of this section you should be able to: ● add and subtract fractions ● multiply and divide fractions
Adding and subtracting fractions There are three simple steps to add or subtract fractions
1
Check whether the denominators are the same, because we can easily add or subtract fractions when the denominators are the same.
2
If the denominators are not the same, fi nd the lowest common multiple (LCM) of the denominators and convert each fraction into an equivalent fraction with the LCM as the denominator.
3
Add or subtract the numerators. Put the answer over the same denominator. If necessary, you can then
simplify the fraction.
Section A Introducing concepts and building skills