9 Arithmetic:MEP Y8 PracticeFractions Book A and Percentages 9.1 Revision of Operations with Fractions In this section we revise the basic use of fractions. Addition a c ac+ += b b b Note that, for addition of fractions, in this way both fractions must have the same denominator. Multiplication a c ac× ×= b d bd× Division a c a d ÷=× b d b c ad× = bc× Example 1 Calculate: 3 4 3 1 (a) + (b) + 5 5 7 3 Solution 3 4 34+ (a) + = 5 5 5 =7 5 2 =1 5 3 1 9 7 (b) + = + (common denominator = 21) 7 3 21 21 = 16 21 142 MEP Y8 Practice Book A Example 2 Calculate: 3 3 (a) of 48 (b) of 32 4 5 Solution 3 3 (a) of 48 = × 48 4 4 × = 348 4 =36 3 3 (b) of 32 = × 32 5 5 × = 332 5 =96 5 1 = 19 5 Example 3 Calculate: 3 3 1 2 (a) × (b) 1 × 4 7 2 5 Solution 3 3 33× (a) × = 4 7 47× =9 28 1 2 3 2 1 2 3 1 2 (b) 1 × = × or 1 × = × 2 5 2 5 2 5 1 2 5 = 6 = 3 10 5 = 3 5 143 9.1 MEP Y8 Practice Book A Example 4 Calculate: 3 3 3 4 (a) ÷ (b) 1 ÷ 7 4 4 5 Solution 3 3 3 4 3 3 13 4 (a) ÷ = × or ÷ = × 7 4 7 3 7 4 7 3 1 = 12 = 4 21 7 = 4 7 3 4 7 4 (b) 1 ÷ = ÷ 4 5 4 5 = 7 × 5 4 4 = 35 16 3 = 2 16 Exercises 1. Calculate: 1 4 3 7 1 7 (a) + (b) + (c) + 7 7 8 8 9 9 3 1 7 9 6 5 (d) + (e) + (f) + 10 10 13 13 7 7 5 3 7 4 11 6 (g) − (h) − (i) − 7 7 9 9 13 13 2. Calculate: 1 1 1 1 1 1 (a)++ (b) (c) + 2 3 5 7 4 5 2 1 7 3 3 4 (d)++ (e) (f) + 3 2 8 10 4 5 3 2 4 2 1 5 (g)++ (h) (i) + 7 3 9 3 4 8 144 MEP Y8 Practice Book A 3. Calculate: 1 1 3 1 3 1 (a)1 +++2 (b)3 4 (c) 2 3 2 2 4 4 5 5 1 1 4 3 4 4 (d)3 +++1 (e)3 2 (f) 5 3 3 2 5 5 7 7 3 5 2 1 5 2 (g)4 ++2 (h)4 3 (i) 2 +3 4 8 7 3 9 3 4. Calculate: 1 1 3 1 3 1 (a)2 −−−1 (b)4 3 (c) 2 2 2 2 4 4 8 4 5 6 5 7 1 1 (d)4 −−3 (e)3 1 (f) 4 −3 7 7 8 8 3 2 2 1 3 1 1 2 (g)2 −−1 (h)5 2 (i) 4 −2 3 9 7 2 4 3 5. Calculate: 1 1 (a) of £20 (b) of 30 kg 4 5 3 4 (c) of £32 (d) of 90 kg 4 5 5 3 (e) of 49 kg (f) of 20 m 7 8 3 7 (g) of £36 (h) of 42 m 5 10 6. Calculate: 1 1 3 1 2 3 (a)×× (b) (c) × 2 4 8 5 3 5 6 2 4 3 4 3 (d)×× (e) (f) × 7 3 5 4 7 5 1 3 4 3 1 4 (g)××× (h) (i) 2 4 9 7 8 5 7. Calculate: 1 1 3 8 3 4 (a)÷÷÷ (b) (c) 2 3 4 9 5 5 7 1 3 3 5 7 (d)÷÷ (e) (f) ÷ 10 2 4 5 9 8 6 2 4 3 5 2 (g)÷÷÷ (h) (i) 7 3 7 4 6 3 145 9.1 MEP Y8 Practice Book A 8. Calculate: 1 3 1 2 1 2 (a)1 ××× (b)3 (c) 1 2 4 2 7 4 3 1 1 1 3 2 4 (d)1 ××× (e)2 (f) 1 2 4 2 4 3 5 9. Calculate: 1 3 1 1 1 2 (a)1 ÷÷ (b)3 (c) 2 ÷ 2 4 2 2 4 3 1 1 1 4 1 2 (d)3 ÷÷÷ (e)4 (f) 3 2 4 2 5 4 3 10. Calculate: 1 3 1 4 12 (a)1 ×× (b)3 1 (c) 1 2 4 2 7 3 11. Calculate: 3 1 1 1 1 3 (a)3 ÷÷÷1 (b)3 1 (c) 3 1 4 2 2 4 3 7 12. Calculate: 4 3 1 3 1 1 (a)+×−1 (b)2 (c) 5 3 7 4 2 7 4 6 1 6 1 2 2 5 (d)6 ÷×1 (e)1 2 (f) 2 −1 2 7 2 3 3 8 9.2 Fractions in Context In this section we consider the use of fractions in various contexts, and how to use the fraction key on a calculator. Example 1 There are 600 pupils in a school. How many school lunches must be prepared if: 3 (a) of the pupils have school lunches, 4 2 (b) of the pupils have school lunches? 3 146 MEP Y8 Practice Book A Solution 3 3 3 3 150 (a) of 600 = × 600 or of 600 = × 600 4 4 4 1 4 1800 = = 450 lunches 4 = 450 lunches 2 2 2 2 200 (b) of 600 = × 600 or of 600 = × 600 3 3 3 1 3 1200 = = 400 lunches 3 = 400 lunches 1 Example 2 2 m 4 The diagram opposite shows a rectangle. (a) Calculate its perimeter. 1 1 m (b) Calculate its area. 3 Solution 1 1 1 1 Perimeter = 2 ++1 2 +1 4 3 4 3 3 4 3 4 =2++1 2 +1 12 12 12 12 14 =6 12 1 = 7 m 6 1 1 1 1 Area = 2 × 1 or Area = 2 × 1 4 3 4 3 3 1 = 9 × 4 = 9 × 4 4 3 1 4 3 1 36 = = 3 m2 12 = 3 m2 147 9.2 MEP Y8 Practice Book A Example 3 3 A loaf of bread requires kg of flour. How many loaves can be made from 4 1 6 kg of flour? 2 Solution 1 3 13 3 6 ÷ = ÷ 2 4 2 4 = 13 × 4 2 3 = 52 6 4 = 8 6 2 = 8 3 8 loaves can be made. b Many calculators have a key marked a c , which can be used to enter fractions. b Pressing 2 a c 3 produces the display 2 3 which represents the 2 fraction . 3 b b Pressing 4 a c 7 a c 9 produces the display 4 7 9 , which 7 represents 4 . 9 Note that you must write the fractions in their correct form, and not just copy the display. (Some calculator displays may be different from this example – check the instruction booklet for your calculator.) Exercises 1. Use your calculator to find answers for the following, making sure that they are written in the correct way: 1 3 5 1 3 1 (a)+− (b) (c) ÷ 4 7 7 3 4 9 1 1 3 7 4 3 (d)÷× (e) (f) × 2 6 4 8 5 8 148 MEP Y8 Practice Book A 1 13 52 (g)1 ××+72 (h) (i) 14 2 24 73 12 13 12 (j)1÷÷−1 (k)6 (l) 53 23 44 25 6 2. (a) Enter the fraction and then press the = key on your calculator. 8 Describe what happens. 8 (b) Enter the fraction and then press the = key on your calculator. 6 Describe what happens. (c) What happens to each of the fractions listed below if you enter it into your calculator and then press the = key: 3 9 4 6 10 3 ,,,, , 7 2 6 4 3 10 3. Calculate the area and perimeter for each of the rectangles below: (a)2 (b) 3 m 2 m 3 5 1 1 m 1 m 2 4 4. A school has 800 pupils. The Headteacher decides to send a questionnaire 2 to of the pupils. How many pupils receive a questionnaire? 5 1 5. A firm that makes floppy discs knows that of the discs they produce 20 have faults. How many faulty floppy discs would you have if you bought: (a) 100 discs, (b) 80 discs, (c) 2000 discs ? 3 6. A cake recipe requires kg of flour. How many cakes could be made with: 8 2 (a) 3 kg flour, (b) 6 kg flour, (c) kg flour, 3 1 1 (d) 1 kg flour, (e) 1 kg flour, (f) 1 kg flour. 2 3 7. The rectangle opposite has an area of 3 3 2 cm2 . cm 5 4 What is the length, x, of the rectangle? x 149 9.2 MEP Y8 Practice Book A 1 8. Sheets of paper are cm thick. Calculate the height of a pile of paper that 80 contains: (a) 40 sheets, (b) 120 sheets, (c) 70 sheets, (d) 140 sheets. 1 How many sheets would there be in a pile of paper 4 cm high? 2 2 1 9. A bottle contains 1 litres of orange squash. To make one drink, of a 5 200 litre of squash is needed. How many drinks can be made from the bottle of squash? 10. Calculate the volume of the following cuboid: 3 2 cm 4 3 3 cm 8 1 4 cm 5 9.3 Conversion of Fractions and Percentages To convert a fraction to a percentage, multiply by 100.