Equivalent fractions 95

Example 13

How many sixths are equivalent to ~?

Multiply the top and bottom by 2: x2/'

.>: - '1

1 23 6

x2So i is equivalent to t

Example 14

Who h' 1 3 7?IC IS arger, 5 or 10'

Find an equivalent fraction in tenths for ~:

x2/~~- - 1-/ '---l3 65 10<>~)

<, --------

x2

3' . I 6 7' I h 3-r- IS equiva ent to 10' so 10 IS arger t an 5'

Exercise 6E

1 Find an equivalent fraction for:(a) ~ in sixths (b) ~ in tenths

2 Find the missing numbers that make these fractionsequivalent:

1 D 1 D 1 D(a) - = - (b) - - (c) - -2 4 3 9 10 201 2 2 1 3 1

(d) - (e) - (f) -6 D 8 D 15 D2 D 4 D 12 D(g) - = - (h) 8 = 16 (i) - -3 6 15 5

96 Fractions

3 Who h i I 1 3?IC IS arger'"5 or 10'

4 Sangeeta and Ryan each win the same amount ofmoney in a prize draw. Ryan spends one fifth of hismoney. Sangeeta spends four twentieths of hers.Who spends the most? Explain your answer.

5 Find the pairs of equivalent fractions in this box. Writethem down like this: != 162

1 4 12 1 5 3~ 5 4 ~ 310 7 30 5

~ 4~20 14 1225 12

6 Which of these fractions are less than ]?3 1 2 9 30"5 20 10 20 100

~ 75 l 2510 ~ 100 10 100

10 10 5020 100 1 100 1100 4 4

Hint:lx25= 252 x 25 = 503 x 25 = 754 x 25 = 100

7 Find the pairs of equivalent fractions in this box:

8 Write these fractions in their simplest form:(a) 186 (b) ~ (c) i6 (d) 1BJlO

Remember:The simplest form isthe equivalentfraction with thesmallest numberspossible on top andbottom.

6.6 Adding and subtracting fractions

It is easy to add or subtract fractions with the samedenominator (bottom).

98 Fractions

Exercise 6F_1 ~. If ,,- "..,

1 Add these fractions:(a) ~ +~ (b) ~+~ (c) fo + 1~ (d) l~o + 19o

2 Work out these subtractions:(a) 1-~ (b) ~ - ~ (c) {2 - 1

62 (d) 1

2000- 160

3 Add these fractions and write each answer in itssimplest form.(a) i+~ (b) ~+t (c) f2+{2 (d) lO+13

0

There is more aboutsimplest form onpage 94.

4 Do these subtractions and write your answers insimplest form.(a) ~ - ~ (b) 1~ - 120 (c) 1 - ~~ (d) 1 - 1~

5 Kay had ~metres of silk. She gave ~metres to Aisling.How much did she have left?

6 On his way to school Selim spends ~ ofthe journey in a bus and ~ of the journeyin a train.Then he walks the rest of the way.(a) What fraction of the journey is

spent altogether on the train andthe bus?

(b) What fraction did he walk?

7 Surmey bought lo kg of grapes,fo kg of apples and 120 kg of plums.How much did the fruit weigh altogether?

Summary of key points

1 You can use numbers to represent a fraction:3 window panes .s->: The topare clean. ------------3 .i->: number is

4 the numerator.The window has ~ ~4 equal panes. The bottom

number is thedenominator.

88

4.11 Questions on Pie ChartsQl At a University there were 180 students in the Media Studies department.

Country-------Number of students

UK Malaysia Spain Others

90 35 10 45

To show this on a Pie chart you have to work out the angle of each sector.Complete the table showing your working. The UK is done for you.

, ,

' I I ", .COUNTRY WORKING

ANGLEin degrees

UK 90 +- 180 x 360 = 180°

MALAYSIA

SPAIN

OTHERS

Now complete the Pie chart using an angle measurer. The UK sector is donefor you.

Q2 On TV, programmes of different types have the amount of air time as shown inthe table.

Programme I Hours I Angle

24

NewsSportMusicCurrent AffairsComedyOther

532329

Other

Sport

Current Affairs

Total

Complete the table by finding the size of the angle represented by each typeof programme. Use an angle measurer or calculation method.

~The full circle (that's all 3600 of it) represents the total of everything - so~ you shouldn't find any gaps in it. basically.

SECTION FOUR - STATISTICS AND GRAPHS

89

4.11 Questions on Pie Charts

3 Pupils at a school were asked about their activities at weekends. The resultsare shown in the table. Complete the table and then draw the pie chart usingan angle measurer.

Just follow the working in the questions - then LEARN THE METHOD.

ACTIVITY I HOURS I WORKING I ANGLE

Homework 6 6 + 48 x 360 = 45Sport 2

TV 10

Computer games 2

Sleeping 18Listening to music 2Paid work 8Total 48

4 A family spends £540 each week on various items which are listed in the tableand shown as sectors on the pie chart. Using an angle measurer or bycalculation find the angle of each sector and enter it in the table

Item I e I Angle

Mortgage 150Heat/light 30Food 90Clothes 30 Heat/light

Car 45General 195 Clothes

SECTION FOUR - STATISTICS AND GRAPHS