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Fractions

Fractions


5HSERIES TOPIC

1Fractions

Mathletics Passport © 3P Learning

Q Foroneparticularschool: There are 256 studentsinYear7. TheYear8, 9and10groupsallhavehalfthenumberofstudentsthantheyearjustbelowthem. HowmanystudentsarethereatthisschoolinYears7to10?

Work through the book for a great way to do this

Give this a go!

Fractionsallowustosplitthingsintosmallerequalsizedamounts.

Writedowntwooccasionswhereyouhavehadtosplitsomethingupevenlybetweenfamilymembersorfriends.Describehowyoumadesurethiswasdonefairlyeachtime.

2 Fractions


5HSERIES TOPIC

FractionsHow does it work?

Proper fractions

Proper fractions represent parts of a whole number or object.

(ii) Shade these to match the fraction:

Let’s look at some equally sized shaded shapes.

Split into 2 equal parts

Two halves = 1 whole

(i) Write a fraction for the shaded parts of the squares below:

Split into 3 equal parts Split into 4 equal parts1 whole square

The number of equal parts shaded

(iii) Include at least two half-shapes when shading these to match the fraction:

11 1=

The total number of equal parts

42

32

21

83

125

2516

85

numeratordenominator

number of equal parts you havetotal number of equal parts

The numerator is always smaller than or equal to the denominator in proper fractions.

Shaded partsTotal equal parts

Larger denominator = smaller equal parts

21

5HSERIES TOPIC

3Fractions


How does it work? Your Turn Fractions

Proper fractions

1 What fraction of these equal-sized shapes have been shaded?

b ca

e f g h

d

Shade these to match the given fraction:

b c da e

125

88

b c da e

1611

104

73

259

103

107

41

65

2

3 Shade these to match the given fraction, including at least one pair of half-shapes:

4 Fractions


5HSERIES TOPIC


Proper fractions

Drawandshadediagramswithequalsizedshapestorepresenteachofthesefractions: (i) Shadingwholeshapesonly. (ii) Includingatleastonepairofhalf-shadedshapes.

PROPER FRACTIONS PROPER FRACT

IONS

..../...../20...

45

b

c d

(ii)

(i)

(ii)

(i)

(i)

(ii) (ii)

(i)

53

92

d85

74

4

a

5HSERIES TOPIC

5Fractions


How does it work? Fractions

PROPER FRACTIONS PROPER FRACT

IONS

..../...../20...

45

Equivalent proper fractions

These are fractions with different numbers that represent the same amount. For example, two fitness teams do three sessions of training in the same park.

Session 1: Grouped in pairs Session 2: In groups of four Session 3: Grouped as a whole team

84

Fraction of training groups wearing striped (or plain) shirts in each session.

The groups change size but the total number of people training remains the same

84

42

21` = = = Equivalent fractions

21

42

We find equivalent fractions by dividing/multiplying the numerator and denominator by the same number.

(ii)(i)53 3

53

159

33

#

#

#=

6 @

53

159` =and equivalent fractions

3212

44

3212 4

83

'

'' =

6 @

Simplify = Find the smallest equivalent fraction.

3212

83` =and equivalent fractions

(ii)(i)93

93

2418

31` is the simplest equivalent fraction to

43` is the simplest equivalent fraction to

93

31

33`

'' =

2418

6 436`

'' =

2418

GCF for 3 and 9 is: 3 GCF for 18 and 24 is: 6

GCF: the largest number that divides into both exactly

Write an equivalent fraction for each of these using the multiplication or division given in square brackets

Simplify these fractions by dividing the numerator and denominator by the greatest common factor (GCF)

6 Fractions


5HSERIES TOPIC



1 Writetheequivalentfractionsrepresentedbytheseequally-sizedshadedareas:

b

2 Writeanequivalentfractionforeachoftheseusingthemultiplicationordivisiongiveninsquarebrackets:

a

3 Simplifythesefractionsbydividingthenumeratoranddenominatorbythegreatestcommonfactor(GCF).

a

4 Simplifythesetwofractions.

a

5 Arethefractions2114 and

2416 fromquestion4equivalentfractions?Brieflyexplainyouranswer.

b

b

b

a== == =

41 5#6 @

108 2'6 @

c d53 3#6 @

2412 6'6 @

2016

328

2114

2416

5HSERIES TOPIC

7Fractions




6 Match the pair of equivalent fractions below by joining them with a straight line. Solve the puzzle by matching the letter with the number each straight line passes through.

EQ

UIVAL

ENT PROPER FRACTIONS EQUIVALENT PROPER

FRACTIONS

..../...../20...3510

54

128

43

156

246

21

108

155

51

1612

3015

83

53

31

32

306

148

41

72

7227

52

106

74

8 Fractions


5HSERIES TOPIC

How does it work? FractionsHow does it work? Fractions

Mixed numbers to improper fractions

Improper fractions to mixed numbers

23

2 means ‘bigger than’

Improper fractionsnumerator 2denominator

Mixed numbers are simplified improper fractions.

45

121 Mixed numbers

A ‘mix’ of whole numbers and proper fractions.141

(i) 132

(ii) 251

r

414

27 7 2

3 1

321

'= =

=

=

remainder

same simplified denominatorWhole number answer

Simplify if possible picture form

132

33 1 2

35

#= +

= same denominator

251

55 2 1

511

#= +

= same denominator

#

+

#

+

Improper fractions and mixed numbers

An improper fraction has a bigger numerator (top) than denominator (bottom)

Mixed numbers have a whole number and a proper fraction.

Simplify these

(i) 35

(ii) 414

r

35 5 3

1 2

132

'=

=

=

numeratordenominator

= numerator 'denominator

remainder

same denominatorWhole number answer

5HSERIES TOPIC

9Fractions




b

2 Simplify these improper fractions by writing them as mixed numbers.

a

3 Write these fractions in simplest form first, then change to the mixed numbers.

a

4 Write the equivalent improper fraction for these mixed numbers.

a

5 Write the equivalent improper fraction for these mixed numbers after first simplifying the fraction parts.

a

b

a=

512

314 c

223

1 Write the mixed numbers represented by these shaded diagrams:

b915

1421 c

1618

b121 2

43 c 4

54

b4122 2

246 c 25

7224

c d

e f

=

=

=

=

=

IMPROPER FRACTION

S AND MIXE

D NUMBERS

..../...../20...

Make sure you write the fraction in simplest form where possible.

10 Fractions


5HSERIES TOPIC


Fractions on the number line

Proper fractions represent values between 0 and 1 on a number line.

(ii)

Display the fractions and on these number lines

Mixed numbers

21 number of equal steps taken between 0 and 1

total number of equal steps between 0 and 1

Mark equal-sized steps matching the denominator between 0 and 1, then plot the fraction using the numerator.

21

,21

53

32

2 equal steps between 0 and 1

1 step taken

53


3 steps taken

32


2 steps taken

= =10 10 10

For mixed numbers, plot the fraction between the given whole number and the next whole number.

321 number of equal steps towards the next whole number ‘4’

total number of equal steps between ‘3’ and the next whole number ‘4’Start from this whole number

Display and read these fractions on a number line

421


1 step taken towards 5 252


2 steps taken towards 3

237

31=


1 step taken towards 3

54 32

32

21Start

(i)

(ii)(i)

Write down the fraction displayed on these number lines

1218

23 1

21= =


1 step taken towards 2

2121Start

31







10 43 54

42

21=

10 43 54(i) (ii) (iii)

Simplest form 332 4

64 4

32= Simplest form

Start

52Start

=

Improper fractions – simply change to the equivalent mixed number first then show on the number line

5HSERIES TOPIC

11Fractions



Fractions on the number line

1 What proper fraction do the following points on the number line represent?

2 Display these fractions on a number line:

3 Write and display the fraction of equal shapes shaded on a number line for these diagrams:

a

4 Write the mixed number and equivalent improper fraction for the dots plotted on these number lines:

a

5 Display these improper fractions on the number line:

41

1542

1027

10a b c

10 10

10a b c

10 10

33

158

b c

32 21b c

65

a211

522b c

6 Display these on the number line after changing to equivalent fractions in simplest form first.

a == b c1863 ==

25110 ==

21 43 5

32 54 6

= = =

= = =

10

FRACTIONS ON

THE NUMBER LINE FRACTIONS ON

..../...../20...

THE NUMBER LINE

10 10

12 Fractions


5HSERIES TOPIC


Reciprocal fractions

Original fraction 52 swap

25 Reciprocal fraction

Write the reciprocal of these fractions

(i) 43

(ii)

43

43

34

For mixed numbers, change to an improper fraction first then write the reciprocal.

Whole/mixed number examples: Always write as a fraction first.

Reciprocal fraction

818

swap

818

49

49

94= swap Reciprocal fraction

Simplified

Write the reciprocal of these

(i) 3

(ii)

313

13

31= Reciprocal fraction

243

swap

243

411

411

114swap Reciprocal fraction

Improper fraction

Mixed number 321

27

27 swap Reciprocal fraction

Whole number as a fraction

(iii) 4159

4159 4

53

523

523

235swap Reciprocal fraction

Improper fractionSimplified fraction

We will see why we find the reciprocal a little later on in this booklet.

It is used when dividing an amount by a fraction.

Improper fraction72

5HSERIES TOPIC

13Fractions



Reciprocal fractions

1 Write the reciprocal for these fractions:

2 Write the reciprocal, then simplify these fractions:

3 Write the reciprocal of these:

4 Write the reciprocal of these mixed numbers:

a

5 Write the reciprocal of these mixed numbers after first writing as a fraction:

6 Write the reciprocal of these fractions as a simplified mixed number:

a

a

a

a

a

b c d32

711

196

415

b c d106

814

1812

1025

b c d2 451

91

b c2 3 131

52

95

b c3 1 2102

1210

219

b c4810

6612

11515

RECIPROCAL FRACTIO

NS

RECIP

ROCAL FRACTIONS

..../...../20...

43

43

14 Fractions


5HSERIES TOPIC

FractionsWhere does it work?

Comparing fractions

This is where we see which fractions are larger than others.

21

31or

Write equivalent fractions by changing the denominators to their LCM.

Since they have the same denominator, now just compare their numerators.

21

63

33

#

#

62

31

22

#

#or

Lowest Common Multiple (LCM)The smallest value that appears in both times tables

bigger 1 smaller63

62

21

31

2

2

Compare the size of these fractions

(i) ,32

43

125

(ii) 411

513

and,

32

43

125and LCM of denominators = 12

Compare numerators

Order fractions by size

32

128

44

#

#

129

4 33 3

125

#

#, and

125

128

129

125

32

43

1 1

1 1`

If comparing improper fractions, use the same method but leave the answer as a mixed number.

and,

411

513

411

55

2055

#

#

513

44

2052

#

#,

2055

2052

243 2

53

2

2`

LCM of denominators = 20

Compare numerators

Write in simplest form

`

5HSERIES TOPIC

15Fractions


Where does it work? Your Turn Fractions

Comparing fractions

1 Comparethesizeofthesefractions:

2 Comparethesizeofthefractionsineachofthesegroups:

3 Comparethesizeoftheseimproperfractions:

a

a

a

b

b

b49

716

,53

21

2011and

and

,129

32

65and

,314

415

821and

52

31and

43

75and

COMPARING FRACT

IONS

COM

PARING FRACTIONS

..../...../20...

12

31

16 Fractions


5HSERIES TOPIC

Where does it work? Fractions

Adding and subtracting fractions with the same denominator

one quarter and two quarters equals three quarters

41

42

two thirds less one third equals one third

Simplify these fractions with the same denominator

(i) 92

95+

92

95

92 5

97

+ = +

=

(ii) 76

72-

76

72

76 2

74

- = -

=

(iii) 32

35+

32

35

32 5

37

231

+ = +

=

=

(iv) 53

51

54- +

Add the numerators only

Subtract the numerators only


Simplify

Subtract/add the numerators only

Simplify

+ =

43

If the denominator (bottom) is the same, just add or subtract the numerators (top).

32

-

31

+ =

=

53

51

54

53 1 4

56

151

- + = - +

=

=

Always write answers in simplest form

-

=

31

5HSERIES TOPIC

17Fractions



Adding and subtracting fractions with the same denominator

1 Simplifythesewithouttheaidofacalculator:


3 Simplifythesewithouttheaidofacalculator,rememberingtowritetheanswerinsimplestform:


a b c31

31+

53

51-

95

92+

d e f118

116-

1511

154-

83

85+

a b c21

24+

58

52-

32

35+

d e f410

41-

711

74+

215

28-

a b c411

45-

613

619+

89

813+

a b c94

91

92+ +

320

310

34- -

21

21

21+ -

d e f51

54

52+ -

78

74

76- +

613

611

69+ -

ADDING AND SUBTRACTIN

G FRACTIONS WI

TH THE SAME DENOMINATOR

..../...../20...

18 Fractions


5HSERIES TOPIC


Adding and subtracting fractions with a different denominator

one quarter and one half equals ?

41

21

one quarter and two quarters equals three quarters

Simplify these expressions which have fractions with different denominators

(i) 32

51+ For

32

51

(ii) 87

21

43- + For ,

87

21

43

Denominators are different

The LCM of the denominators is 15

Equivalent fractions with LCM denominators


Denominators are all different

The LCM of all the denominators is 8

Equivalent fractions with LCM in the denominators

Simplify the numerator

Simplify to mixed number

41

42

43

+ =

=

32

51

32

51 3

1510

153

1510 3

1513

55

3#

#

#

#+ = +

= +

= +

=

+

and

and

21

43

44

22

87

21

43

87

87

84

86

87 4 6

89

181

#

#

#

#- + = - +

= - +

= - +

=

=

?

21

22

42

#

#=

Multiply top and bottom by the number used to make the denominator equal to the LCM

+ =

+ =

`

5HSERIES TOPIC

19Fractions




1 Fillinthespacesforthesecalculations:


a b31

61+

74

51-

a b

c

31

21+

65

21-

52

41- d

e f

61

43+

76

32-

53

83+

TheLCMofthedenominatorsis: TheLCMofthedenominatorsis:

31

61

31

61

#

#` + = +

=

=

=

75

51

75

51

77

#

#

#

#` - = -

=

=

-

simplestform

simplestform

61+

20 Fractions


5HSERIES TOPIC



3 Simplifytheseexpressionswithouttheaidofacalculator,rememberingtowritetheanswerinsimplestform.

a b

c

21

54+ 8

1353-

21

83

41+ - d

e f32

41

65- +

53

103

43+ -

127

31

2411- +

ADDING AND SUBTRA

CTING FRACTIONS W

ITH THE DIFFERENT DENOMINATOR ..../...../20...

5HSERIES TOPIC

21Fractions



ADDING AND SUBTRA

CTING FRACTIONS W

ITH THE DIFFERENT DENOMINATOR ..../...../20...


The same rules apply for questions with a mix of whole numbers and fractions. Here are some examples:

a b

c

221+ 1

43+

132- d

e f

183-

253- 4

41-

Simplify these expressions which have a mix of whole numbers and fractions

4 Simplify these expressions:

g h

(i) 341+

(ii) 152-

(iii) 472-

152

55

52

53

- = -

=

472

728

72

726

375

- = -

=

=

Write the fraction after the whole number

Write the whole number as a fraction with same denominator

Subtract the numerators only

Write the whole number as a fraction with same denominator

Simplify fraction

335- 5

25-

341 3

41+ =

22 Fractions


5HSERIES TOPIC


Multiplying and dividing fractions

31

52

31

52

3 51 2

152

##

#= = =

Remember: A flipped fraction is called the reciprocal fraction

Simplify these:

We can use shaded diagrams to calculate the multiplication of two fractions

(i) 32

54

If whole numbers are involved, write them as a fraction

(ii) 2872

'

3

2872 28

27

128

27

2196

198

98

#

#

' =

=

=

=

=

To multiply fractions, just remember: Multiply the numerators (top) and the denominators (bottom)

3 21 5

31

52

31

25

65

#

#

#

' =

=

=

Change the ‘' ’ to a ‘# ’

of

32

54

158

#` =

5

Draw a grid using the denominators as the dimensions

Use the numerators to shade columns/rows

Write where they overlap as a fraction

Flip the second fraction and change sign to ‘# ’

Write the whole number as a fraction

Simplify

3

5

2

4

158=

`

To divide an amount by a fraction, just remember: flip the second fraction then multiply

Only flip the second fraction

ofof = ‘# ’

5HSERIES TOPIC

23Fractions




1 Calculatethesefractionmultiplicationsbyshadingthegivengrids:

a b51

43of

32

74of

c d

e f

5

=

54

54of

52

83of

43

97of

43

65of

simplified

54

54of

52

83of =

32

74of` =

`

51

43of` =

4

3

7

5

5

=`

5

8

=of of =`

9

==`

4

43

97

6

4

43

65

simplifiedsimplified

24 Fractions


5HSERIES TOPIC




a b

c

21

31

#53

41

#

32 2

` j d

e f31

23'

112

41'

53 2

` j

g h

i

65 4'

43 8'

1054

# j

k l1253

' 2132

'

2483

#

psst:thisisjust3

2

3

2#



a b

c

21

31

#53

41

#

32 2

` j d

e f31

23'

112

41'

53 2

` j

g h

i

65 4'

43 8'

1054

# j

k l1253

' 2132

'

2483

#

psst:thisisjust3

2

3

2#

#

' MULTIPLYIN

G ANDDIVIDING FRACTIONS

MULTIPLYING ANDDIVIDING

FRACTIONS

..../...../20...

5HSERIES TOPIC

25Fractions




3 Simplifythesewithouttheaidofacalculator,rememberingtowritetheanswerinsimplestform.

a b

c

82 2

` j43

23

#

83

45' d

e f109

58'

43

32

21

# #

32

35'

g h52

63

31

# # 421

21' '

4 Is32

64 exactlythesameas

32

812' ?Explainyouranswer.

psst:sameastheothers!

psst:worklefttoright!

of

#

' MULTIPLYIN

G ANDDIVIDING FRACTIONS

MULTIPLYING ANDDIVIDING

FRACTIONS

..../...../20...

26 Fractions


5HSERIES TOPIC


Operations with mixed numbers

Just change to improper fractions then use the same methods as shown earlier.

Simplify these calculations involving mixed numbers

Addition and subtraction

(i) 1 232

61+

(ii) 4 151

21-

Multiplication and division

(iii) 1 243

31

#

(iv) 161 2'

132 2

61

35

613

610

613

623

365

+ = +

= +

=

=

451 1

21

521

23

1042

1015

1027

2107

- = -

= -

=

=

Change to improper fractions







Multiply tops and bottoms together



Flip second fraction and change to multiply

Multiply numerators and denominators together

143 2

31

47

37

1249

4121

# #=

=

=

1 261

67

12

67

21

127

#

' '=

=

=Remember

, ,2 31

2

1

3= = etc

Or just add the whole numbers and the fractions separately.

1 2 33

2

6

1

6

5+ = + =

5HSERIES TOPIC

27Fractions



Operations with mixed numbers

1 Simplify these additions and subtractions without the aid of a calculator:

2 Simplify these without the aid of a calculator:

3 Simplify these divisions without the aid of a calculator:

a b

c

2 441

32+ 2 1

41

52-

5 253

21- d 3 1

61

51+

a b

c

4 152

# 473 2#

143 3

21

# d 5 131

54

#

a b3 221' 1

32 3'

252 1

21

' 1521

32

'

..../...../20...#+ OPERATIONS WITH

MIX

ED NUMBERS OPE

RATIONS WITH MIXED NUMBERS

#+

c d

28 Fractions


5HSERIES TOPIC


Combining all the operations

Earn yourself an awesome passport stamp by trying these trickier questions without using a calculator.

1 Simplify 6 171

53

21

#+

2 Simplify 4 3 521

65

31

#'

3 Simplify this shaded diagram into a single fraction.

psst: remember your order of operations

psst: work left to right… so do the division first

psst: write as fractions, then work left to right

# +

* AW

ESOME *

..../...../20...

* AWESOME *

5HSERIES TOPIC

29Fractions


FractionsWhat else can you do?

Fractions of an amount

How many links are there in 52 of a chain made using a total of 20 links?

Here are some questions that calculate fractions of an amount.

(i) Juliet lost 41 of the 116 songs she had downloaded when a computer virus infected the files.

How many songs were not affected by the virus?

(ii) How long is 107 of 1 hour?

41 116

41 116

41

1116

4116

#=

= +

=

107

107

107

160

10420

#

=

=

=

Change to smaller units if possible

Answer the question

Simplified, this question is just: Find 2052 .of

52 20

52 20

52

120

540

8

#

#

=

=

=

=

of

of songsIf 4

1 are gone, then 4

3 remain.

So finding 4

3 of 116 will get

the same answer. Try it!

Remember: ‘of’ = ‘# ’

* AW

ESOME *

..../...../20...

* AWESOME *

songs not affected by the virus

of 1 hour of 60 minutes

29

116 29 87

=

- =

42

42

=

=107` of 1 hour minutes

52` of the 20 links = 8 links

`

` Answer the question

30 Fractions


5HSERIES TOPIC

What else can you do? Your Turn Fractions


1 Calculate the amount for each of these, showing all working:

2 Calculate the amount for each of these by first making the mixed number an improper fraction:

3 Calculate these fractions of quantities, showing all working:

a b

c

2051

d

a b

c d

a b

of43 32of

How many hours is 43 of 1 day? How many grams is

103 of 2 kilograms?

1 day = 24 hours 1 kg = 1000 grams

232 4of 2

65 4of

221 4of 1

54 15of

372 14of 34

32 6of

psst: the answers will be bigger than the given whole number

FRACTIONSOF ANAMOUNT

FRACTIONS

OF ANAMOUNT

..../.....

/20...

5HSERIES TOPIC

31Fractions




4 Inanorchestraof60musicians,51 wereinthebrasssection.Howmanybrasssectionplayerswerethere?

psst:remembertoincludeastatementansweringthequestionattheend

5 Kristaandherteammateseachreceive51 ofa$900prizeforwinningacompetition.

HowmuchdoesKristareceive?

6 Hankbought72 ofthe28towelsthatwereonsaleinashop.HowmanytowelswerenotboughtbyHank?

3 Howlongis65 of2hours? Howfaris

51 of3kilometres?

1 hour= 60minutes 1 km = 1000 metres

c d

7 TheleadinonebrandofHBpencilis118 graphite.

Howmanygramsofnon-graphitematerialarethereinthisbrandifeverypencilcontains33gramsoflead?

32 Fractions


5HSERIES TOPIC



Amani used 250 g of one ingredient, which was 52 of the total ingredients used in the recipe she

was following. What is the total weight of ingredients used in this recipe?

Here is what to do if you already have the fraction amount and need to find the original whole amount.

8 The letter ‘e’ is used twenty one times in this question. If this is 81 of all the letters used to write

this question, work out how many letters there are in total (show all working and check your amount by counting).

9 During a performance by Jolly Rob, 280 members of the audience found his jokes funny. If this was

74 of the total audience members at the performance, how many people were watching Jolly Rob?

10 By 3:00 pm, Juan had been waiting 30 minutes for his bus to arrive. If this is 65 of the total time he

spent waiting, at what time did his bus arrive?

Divide the amount by the numerator

Multiply answer by the denominator

of the total ingredients used

of the total ingredients

(the total ingredients)

250

250 2

125

125 5

625

#

'

=

=

=

=

=

52

51`

55`

` Total weight of ingredients used in the recipe 625=

g

g

g

grams

grams

grams

A short-cut way is to multiply 250 g by the reciprocal.

g g2502

5625# =

5HSERIES TOPIC

33Fractions


What else can you do? Fractions

Two amounts as a fraction

(i) Alltheboxesinthepictureweighatotalof40kg.Theboxbeingcarriedis2000 g. Whatfractionofthetotalweightisbeingcarried?

Writetheseamountsasfractionsofoneanotherinsimplestform

thefractionofthetotalweightbeingcarried

40 40000

400002000

201

=

=

=

`

Sometimesweneedtocomparetwoamountsbywritingoneasafractionoftheother.Forexample,write14outof36asafractioninsimplestform

Theseexamplesshowhowbothamountsmustbeinthesameunitsbeforewritingasafraction.

3614

22

3614

187

36187

''=

=

=

DividetheamountbytheGCF

Simplestform

FirstamountSecond‘outof’amount

14` outof

kg Needbothweightsinthesamesmallerunits

Simplifyfraction

Answerquestion

1hour= 60minutes

Needbothtimesinthesamesmallerunits

Simplifyfraction

Answerquestion

Needbothamountsinthesamesmaller units

Simplify

Answerquestion

(ii) Whatfractionof221 hoursis15minutes?

(iii) Ifonereamofpapercontains500sheets,whatfractionis240sheetsoutof4reams?

g

Firstsmalleramounttotalamount

` theboxbeingcarriedis201 ofthetotalweight

221 2

21 60

150

15015

101

#=

=

=

` 15minutesis101 of2

21 hours

minuteshours

4 4 500

2000

2000240

253

#=

=

=

reams

` 240sheetsis253 of4 reams

sheets

sheets

Firstsmalleramounttotalamount

1kg= 1000 g

minutes

34 Fractions


5HSERIES TOPIC


Two amounts as a fraction

1 Writethefirstamountasafractionofthesecondforeachoftheseinsimplestform

2 Inaschoolof800students,240wereinYear7.WhatfractionoftheschoolareYear7students?

3 After100testrolls,adiedisplayedthenumber5sixteentimes.Whatfractionoftherollswere5?

a b

c d

5outof20

4 Francescafired27arrowsatatargetandhitthebullseye6times.Whatfractionofarrows missedthebullseye?

5 Abiscuitrecipecontained500 gofflour,175 gofsugarand125 gofbutter.Whatfractionoftherecipeisbutter?

e f

g h

e f

g h

16outof22

35marksoutofapossible40 2hoursof1 day(1day= 24hours)

5minutesofhalf-an-hour(1hour= 60minutes) 25centsoutof$2 ($1 = 100cents)

300secondsof1hour(1hour= 3600seconds) 23daysofMarch(31),April(30)andMay(31)

..../...../20... TWO AMOUNTS AS A FRA

CTION TWO AM

OUNTS AS A FRACTION

5HSERIES TOPIC

35Fractions


What else can you do? Fractions

Word problems with fractions

(i) In a group of eighteen friends, one third are girls and one sixth of these girls have blonde hair. How many blonde girls are in the group?

Here are some other word problem examples

`

While on a shopping trip, Xieng spent two fifths of her money on clothes and one third on cosmetics. What fraction of her money did Xieng have left?

` Xieng still has 154 of her money after shopping

52

31

156 5

1511

1515

1511

154

+ =

= +

=

- =

Add the numerators together

(ii) During one night, possums ate two fifths of the fifty five fruits on a tree. If one eleventh of the eaten fruit grew back, how many fruits are now on the tree?

fraction of Xieng’s money spent on shopping

Fraction of money Xieng has leftFraction spentFraction for all of Xieng’s money

` There is 1 blonde girl in the group of friends.

61

31 18

61

31

118

1818

1

# #

=

=

=

=

number of blonde girls in the group

55

22

2

55 22 2

52

5110

22

111

1122

35

#

#

=

=

=

=

=

=

= - +

=

Number of fruits eaten

Number of fruits that grew back

` Number of fruits now on the tree

pieces of fruit

` of of

36 Fractions


5HSERIES TOPIC



1 Atarecenttrivianight,onetableofcompetitorsansweredfiveeighthsofthefiftysixquestionscorrectly.Howmanyquestionsdidtheygetincorrect?

2 CoTinusuallytakesapproximatelysixtyandonequarterstepseveryminutewhenwalking.Howmanystepsdoesheexpecttotakewhenheexercisesbywalkingforoneandtwothirdhourseachday?

3 Avegetablegardenhasonethirdcarrots,onesixthpumpkins,onequarterherbs,andtherestarepotatoplants.Howmanypotatoplantsareinthisgardenofeightyplants?

4 Aclassoftwentyfourstudentscomparedeyecoloursonachart.Twothirdsoftheclasshadbrowneyes,andthreeeighthsofthosebrown-eyedstudentswereboys.Howmanygirlshadbrowneyes?

..../...../20...

WORD PROBLEMS

WITH FRACTIONS

WORD PROBLEMS

WITH FRACTIONS

5HSERIES TOPIC

37Fractions




5 Foroneparticularschool: Thereare256 studentsinYear7. TheYear8, 9and10groupsallhavehalfthenumberofstudentsthantheyearjustbelowthem. HowmanystudentsarethereatthisschoolinYears7to10?

6 Fivestudentsinaclasshaveacombinedtotalofninetyprofilesaddedasfriendsonaweb-basedsocialnetworksite. Threefifthsoftheninetyprofilesaresharedbyallfiveofthestudents.Thesesharedprofilesrepresent onesixthofthetotalnumberofdifferentprofilesaddedasfriendsbyallthestudentsintheclass. Howmanydifferentprofilesarelinkedtostudentsfromthisclass?

7 FiveseventhsofthefiftysiximagesusedasbackgroundsonMeagan’stouchpadwerephotosshetookherself.Aftermovingfiveeighthsofthesephotostoanothercomputer,whatfractionofthebackgroundimagesnowarenotphotostakenbyher?

Remember me?

..../...../20...

WORD PROBLEMS

WITH FRACTIONS

WORD PROBLEMS

WITH FRACTIONS

38 Fractions


5HSERIES TOPIC


Reflection Time

Reflectingontheworkcoveredwithinthisbooklet:

Whatusefulskillshaveyougainedbylearningaboutfractions?

2 Writeaboutonewayyouthinkyoucouldapplyfractionstoareallifesituations.

3 Ifyoudiscoveredorlearntaboutanyshortcutstohelpwithfractionsorsomeothercoolfacts, jotthemdownhere:

1

5HSERIES TOPIC

39Fractions


Cheat Sheet FractionsCheat Sheet Fractions

Here is a summary of the things you need to remember for fractions

Proper fractionsRepresent parts of a whole number or object. The numerator is smaller than or equal to the denominator. numerator number of equal parts you have denominator total number of equal parts

Equivalent proper fractionsThese are fractions with different numbers that represent the same amount.


Improper fractions Mixed numbers

numerator > denominator A ‘mix’ of whole numbers and proper fractions.

Fractions on the number line number of equal steps taken between 0 and 1 total number of equal steps between 0 and 1

number of equal steps towards the next whole number total number of equal steps between start and next whole number

Reciprocal fractions Original fraction Reciprocal fraction

Mixed number Reciprocal fraction

Comparing fractionsWrite equivalent fractions by changing the denominators to their LCM, then compare the numerators

Adding and subtracting fractionsIf the denominators (bottom) are the same, then simply add or subtract the numerators (tops).If the denominators are the different, change to equivalent fractions with the same denominators using the LCM. Then add or subtract the numerators of the new fractions.

Multiplying and dividing fractionsTo multiply fractions, just remember: Multiply the numerators (top) and the denominators (bottom).To divide an amount by a fraction, just remember: flip the second fraction (reciprocal) then multiply.

Fractions of an amount ‘of’ means ‘# ’ ` Find 52 of 2 means calculate

52 # 20

Two amounts as a fraction 2 out of 5 as a fraction is

52 . If the two amounts are in different units, change the larger amount into

the smaller units. Eg, 200 g out of 2 kg becomes 200 g out of 2000 g.

21

84

42

21` = = = Equivalent fractions

23

45 1

21 1

41

21

321

Start

52

25

321

27

72

27

21

33

#

#

31

22

#

#

63

62

2

10

43

40 Fractions


5HSERIES TOPIC

Fractions Notes


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Fractions

Documents

Fractionsnavigatemath.weebly.com/uploads/7/9/7/7/7977444/g7_fractions.pdf · Proper fractions Proper fractions represent parts of a whole number or object. (ii) Shade these to match