1. Use fraction strips to calculate of the following. (i) 3 ÷ 1
__ 5
__ 12 ÷ 1
5
__ 4
(ii) 2 ÷ 2 (ii) 5
__ 3
__ 9 ÷ 2
__ 3
(iii) 4 1
2. Find the value of each of the following. (i)
(iii) 3
__ 8 ÷ 4
__ 5
__ 2 ÷ 1
__ 4
(iv) 1
__ 2 ÷ 1
(iv) 1 2
__ 8
__ 3 ÷ 5
__ 6
(v) 1
__ 5 ÷ 1
(v) 2 1
__ 10
__ 2 ÷ 3 3
__ 4
3. Three-fi fths of a bar of chocolate is divided among four friends. What fraction of the bar did each person get?
4. Fiona has a plank of wood that is 7 1 How many pieces will she have?
__ 2 m long. She wants to cut the plank into pieces measuring 5
5. A plumber has a piece of pipe that is 4 3 1 2
6. Suppose you have 11
of the following sizes? (i) 1
__ 4 of the cheesecake
(ii) 1
__ 3 cm long. How many full pieces does she have?
__ 8 cm long. She divides the pipe into pieces that are
__ 12 of a cheesecake. How many servings can you make of each
__ 3 of the cheesecake
(iii) 1
__ 6 of the cheesecake
7. David and Ryan mow lawns to earn money during the summer holidays. On a particular day, David is mowing for 2 3 as long as David.
(i) How long did David spend mowing each lawn? What assumptions do you make?
__ 4 hours and mows 8 lawns. Ryan mows for 1 1
__ 3 times
(ii) How many hours did Ryan spend mowing?
8. Copy the table below and put a tick (✓) in the correct box in each row to show whether each statement is always true, sometimes true, or never true.
Tick one box only for each statement Statement
(i) An improper fraction is greater than 1. (ii) Finding a fraction of something makes it smaller. (iii) A fraction is between zero and one.
(iv) When you multiply a proper fraction by another proper fraction the answer must always be less than one.
(v) Dividing by a fraction makes a number smaller.
(vi) Dividing the top and bottom of a fraction by the same number makes the fraction smaller in value.
9. Find the value of each of the following. (i) (7 __
4 − 2 __
Taking it FURTHER
5 ) × 2 3 __
8 (ii) 1
__ 2 (4
__ 9 + 5
__ 12 )
(iii)
________ 1
2 1
__ 3 (3
__ 4 + 5
__ 4
10. Place one of the numbers 1, 2, 3, or 4 into each space to try to make (a) the largest possible number and (b) the smallest possible answer. Use each number once only.
(i) + (ii) – (iii) × (iv) ÷
__ 3 )
Always true
Sometimes true
Never true
__ 12 m.
(vi) 3
__ 4 ÷ 1
(vi) 2 1
__ 8
__ 5 ÷ 4 2
__ 7
Section A Introducing concepts and building skills