20 Arithmetic: Fractions

Transcription

1 MEP Y Practice Book B 0 Arithmetic: Fractions 0. Revision: Whole Numbers and Decimals In this section we revise addition, subtraction, multiplication and division of whole numbers and decimals, before starting to work with fractions. Example Calculate:. 0. (c)...0 (c) Example Calculate: Hence... Example Calculate:... so so..

2 0. MEP Y Practice Book B Exercises. Calculate: (c) 0 (d).. (e).. (f).. (g) 0.. (h).. (i) (j). (k) 0.. (l)... Calculate: (c) 0 0 (d) (e). 0. (f).. (g) (h).. (i).. (j). (k). (l) 0... Calculate: (c) (d) (e) (f) (g) 0. (h). (i). (j).. (k).. (l)... Calculate: (c) (d) (e) (f) (g). (h). (i).. There were people on a bus and got off. How many people were still on the bus?. Floppy disks cost p each. How much would floppy disks cost?. It costs.0 for one adult to go into a theme park. How much would it cost in total for adults to go into the theme park?. Tickets for a show cost each. To cover the cost of putting on the show, is needed. How many tickets must be sold to cover the cost of the show?. An m length of rope is cut into pieces of equal length. How long is each of the pieces? 0

3 MEP Y Practice Book B 0. A PE department has 0 to spend on footballs which cost each. How many footballs can they buy? How much money will they have left? 0. Addition and Subtraction of Fractions In this section we consider how to add and subtract fractions. The key step in this process is to make sure that both fractions have the same denominator. Example Calculate: As the denominator is the same in both fractions, we simply add the numbers on the top of the fraction to give This addition is shown in the diagram below: The denominator is the same in both fractions, so

4 0. MEP Y Practice Book B This is shown in the diagram below: Example Calculate: These fractions do not have the same denominator, so the first step is to change them so that they do. In this case, we can use 0 as the common denominator This is illustrated in the diagram below: In this case we can use a common denominator of.

5 MEP Y Practice Book B This is illustrated in the diagram below: Example Calculate: (c) So Note: It is usually easier to convert the mixed numbers into improper fractions.

6 0. MEP Y Practice Book B (c) Exercises. Calculate: (d) (g) (j) (m) 0 0 (e) 0 (h) 0 (k) (n) (c) (f) (i) (l) (o). Fill in the missing numbers:??? (c) (d) (e)????????????

7 MEP Y Practice Book B. Calculate: (d) (g) (j) (m) (e) (h) (k) (n) (c) (f) (i) (l) (o) 0. A birthday cake is divided into equal parts. Andrew eats and Timothy eats of the cake. What fraction of the cake is left? How many pieces of cake are left? of the cake. A garden has an area of hectare. The owner buys an extra of a hectare of land. What is the area of the garden now? How much more land would the owner need to have a garden with an area of hectares?. Steve and Sheila buy a computer. Steve fills of the hard disk with his programs. Sheila fills of the hard disk with her programs. What fraction of the hard disk is full? What fraction of the hard disk is empty? (c) Steve deletes one of his programs that takes up of the hard disk. 0 What fraction of the hard disk do his programs fill now?. If 0 of all men in the UK own cars, and of all men in the UK own more than one car, what fraction of men in the UK: do not own a car, own only one car?

8 0. MEP Y Practice Book B. Calculate: (d) (g) (e) (h) (c) (f) (i) (j) (k) (l). Ron wins million. He gives million to his daughter and million to his wife. How much does he have left? 0. An old-fashioned gardener measures the height of a plant as inches. A week later the height is measured as grow during the week? inches. How much did the plant 0. Multiplying Fractions In this section we extend the ideas of Unit 0, where you multiplied fractions by numbers, to now include multiplying fractions by fractions. Example Calculate: of, of 0, (c) of m. of

9 MEP Y Practice Book B of 0 0 of 0 or 0 of 0 0 (c) of m m of m m or of m 0 m Example Calculate and illustrate this on a diagram. (c) 0 0 Note that of the small squares are shaded twice, so 0 0. Note that we are using the rule: a b c d a b c d

10 0. MEP Y Practice Book B Example Calculate: (c) (Note: it is usually quicker to cancel down at this stage rather than at the end.) (c) 0

11 MEP Y Practice Book B Exercises. Calculate: (c) (d) (g) (e) (f) 0 (h) (i) (j) (k) (l). Calculate: (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 0. Calculate: (c) (d) (e) (f) (g) (h) (i) (j) (k) (l).. Calculate the area of each of these rectangles: m m m m

12 0. MEP Y Practice Book B. A cake recipe requires kg of flour. How much flour is needed to make: (c) cakes, cakes, 0 cakes?. Jan buys kg cheese. She keeps of it and gives to her sister. What is the weight of: the cheese Jan keeps, the cheese Jan gives to her sister?. A large company makes million profit. They spend of this on new equipment. How much does the company spend on new equipment? How much is left?. Calculate the area of each of these rectangles: m m m m. The diagram shows a small picture frame. The shaded border is cm wide. cm cm What is the area of the shaded border? 0

13 MEP Y Practice Book B 0. A petrol can holds litres. Sanjit fills up a lawn mower and uses of the petrol from the full can. How much petrol does the lawn mower hold? How much petrol is left in the can? Later, Sanjit uses another litres of petrol from the can. (c) How much petrol has he now used? 0. Dividing Fractions In this section we consider how to divide fractions and whole numbers by either whole numbers or fractions. Example Calculate. You can deal with this problem by thinking about the fraction being divided into parts. of the diagram has been divided Divided into parts into parts: Each of these parts is of the whole, so We can also obtain the result in this way: which uses the rule: a b a c b c

14 0. MEP Y Practice Book B Example Calculate:,. The problem is to calculate how many s there are in whole units. The four whole units are shown below, and each is divided into s. The diagram shows s, so We can obtain this result from The problem is to calculate how many s there are in whole units. 0 The diagram shows 0 s, so 0 We can also obtain this result from 0 0 using the rule: a b c a c b

15 MEP Y Practice Book B Example Calculate: (c) 0 These problems can be tackled using the same approach as when a whole number is divided by a fraction. (c) 0 0 [Note: You can cancel only when the nd fraction has been turned upside-down.] We are using the rule: a b c a d b d c Exercises. Calculate: (c) (d) (e) (f) (g) (h) (i)

16 0. MEP Y Practice Book B (j) (k) (l) 0. Calculate: (c) (d) (e) (f) (g) (h) (i) (j) (k) (l). Calculate: (c) (d) (e) (f) (g) (h) (i) (j) (k) (l). By using improper fractions, calculate: (c) (d) (e) (f). Ahmed has kg of sweets. He divides these into equal parts so that he can share them with his two brothers. What fraction of a kg does each boy get?. Sandra has litre of orange squash to make 0 drinks. How much orange squash should she put in each drink?

17 MEP Y Practice Book B. A large cake uses times as much flour as a small cake. A large cake needs kg of flour. How much flour does a small cake need?. A piece of leather is 0 cm wide and cm long. cm 0 cm How many bookmarks, cm wide, can be made if the leather is: cut as shown above, to make bookmarks 0 cm long, cut the other way to make bookmarks cm long?. A recipe for a cake requires kg of sugar. How many cakes can be made with: kg of sugar., kg of sugar, (c) kg of sugar? 0. A car uses litres of petrol for every 0 miles it travels. How far can the car travel on: litres of petrol, litres of petrol, (c) litres of petrol?