Fractions - Revision. Fractions are numbers which mostly describe ____________. parts of a whole E.g. colored: _512 of the rectangle not colored:

Fractions - Fractions - RRevisionevision

Fractions are numbers which mostly descFractions are numbers which mostly descrribe ______________.ibe ______________.parts of parts of a wholea whole

E.g.E.g. colored:colored: ______551212

of of the the rectanglerectangle

not colored:not colored: ______77

1212of of the the rectanglerectangle

a)a) colored:colored: ______7733

circlescircles

not colored:not colored: ______22

33of of a a circlecircle

b)b)colored :colored :

not colored:not colored:

____3355

rectanglesrectangles22

______22

55of of a a rectanglerectangle

Fractions can descFractions can descrribe even more than one whole!ibe even more than one whole!

E.g.E.g.

How to color:How to color:

a)a) ______5566

of of a a parallelogramparallelogram??

b)b) ______7744

squaressquares??

c)c) ______1133

rhombusesrhombuses??44

The parts of the fraction:The parts of the fraction:

____aa

bb

?? numeratornumerator

?? denominatordenominator

?? fraction linefraction line (or (or vinculum)vinculum)

Denominator Denominator tells ustells usinintoto how many how many equalequal parts parts the wholethe whole

Numerator Numerator tells tells usus

how many how many of those of those parts should be colored.parts should be colored.

Fraction line always meansFraction line always meansdivision.division.

E.g.E.g. ____88

44== 8 : 4 =8 : 4 = 22

We used these properties of numerator and We used these properties of numerator and denominator in thedenominator in the previous examples.previous examples.

==

should beshould be divided divided..

ProperProper fractions are fractions with fractions are fractions withthe the numerator less thannumerator less than

ImproperImproper fractions are fractions with fractions are fractions withtthe he numerator greaternumerator greater

than than or or equal to equal to the the denominator.denominator.

E.g. E.g. , , ______1144

, , ______2299

______991010

... are _____ fractions. ... are _____ fractions.

They are ______ than 1.They are ______ than 1.lessless

<<

properproper

the the denominator.denominator.

improperimproper

They are __________________ 1.They are __________________ 1.greater than or equal togreater than or equal to

E.g. E.g. , , ______9944

, , ______5533

______4444

... are ________ fractions. ... are ________ fractions. , , ______6622

≥≥

Which of Which of the the fractions above are equal to 1?fractions above are equal to 1?

How can we recognize fractions which are equal to 1?How can we recognize fractions which are equal to 1?

TheThe numerator numerator is is equal to equal to the the denominator!!denominator!!

ProperProper fractions are fractions with fractions are fractions withthe the numerator less thannumerator less than

ImproperImproper fractions are fractions with fractions are fractions withthe the numerator greaternumerator greater

than or than or equal to the denominator.equal to the denominator.

the the denominator.denominator.

≥≥

Which of Which of the the fractions above are greater than 1?fractions above are greater than 1?

How can we recognize fractions which are greater than 1?How can we recognize fractions which are greater than 1?

The numerator The numerator is is greater than greater than the the denominator!!denominator!!


than or than or equal to equal to the the denominator.denominator.

improperimproperE.g. E.g. , , ______9944

, , ______5533

______4444



≥≥

Any Any improperimproper fraction can be changed into fraction can be changed intoa mixed fraction a mixed fraction orora a natural number.natural number.




, , ______5533

______4444



≥≥

Which of Which of these these fractions can be changed into fractions can be changed into mixed fractions mixed fractions ??

Change them (look at the picture)!Change them (look at the picture)!

______9944

== 22 ______1144

______5533

== 11 ______2233




, , ______5533

______4444


≥≥

Which of Which of these these fractions can be changed into fractions can be changed into natural numbers natural numbers ??

______4444

== 11 ______6622

== 33

ImproperImproper fractions are fractions with fractions are fractions withthe the numerator greater numerator greater



, , ______5533

______4444


Change them (look at the picture)!Change them (look at the picture)!

Now, let's revise how to Now, let's revise how to calculatecalculate it (without it (without a a picture)!picture)!

1.) Change into 1.) Change into a a mixed mixed numbernumber or or aa natural number natural number (do what is possible)(do what is possible)::

______191988

==a)a) 3388

______22

Explanation:Explanation:19:8 equals 19:8 equals 22 and remainder and remainder 33

Rewrite denominator!Rewrite denominator!

==



______191988

==a)a) 3388

______22

______686899

==b)b) 5599

______77

______424277

==c)c) 66

Explanation:Explanation:42:7 equals 42:7 equals 66 (no remainder) (no remainder)

==



______191988

==a)a) 3388

______22

______686899

==b)b) 5599

______77

______424277

==c)c) 66

______363644

==d)d)

______2299

==e)e) This is This is properproper fraction fraction(numerator is less than denominator),(numerator is less than denominator),so we so we can'tcan't change it into change it into a a mixed mixed fraction or into natural number!fraction or into natural number!

99

How did we calculate How did we calculate in all these tasks?in all these tasks?

We divided We divided the the numeratornumeratorby by the the denominator.denominator.

Why?Why?

Because the fraction lineBecause the fraction linealwaysalways means division!means division!

Now let's change a fraction Now let's change a fraction into a into a decimaldecimal number! number!

How to do it?How to do it?

We should divide again,We should divide again,but now but now in writingin writing......

Let's revise it...Let's revise it...

Let's change the number at task "a)" into a Let's change the number at task "a)" into a decimaldecimal number... number...How to do it?How to do it?

______191988

== 19 : 8 =19 : 8 = 22

3300..33

6600

77

4400

55

00

So, we changed the same fractionSo, we changed the same fractioninto both - mixed fraction andinto both - mixed fraction and

decimal number.decimal number.

Remember:Remember:

When we change fractionWhen we change fractioninto any another form,into any another form,

we we always dividealways divide(because the fraction line(because the fraction line

means division)!means division)!

Only when we change into Only when we change into decimaldecimal number, number,

then we then we use use long divisionlong division..

______191988

==a)a) ______223388



Now conversely! Let's revise how to change numbers Now conversely! Let's revise how to change numbers from other forms into fractions...from other forms into fractions...

2.) Change into fraction:2.) Change into fraction:

885555____________77

88==a)a) 66

6 6 ·· 8 + 7 8 + 7

RewriteRewritedenominator!denominator!

==



885555____________77

88==a)a) 66

776969____________66

77==b)b) 99

c) 8 =c) 8 =1188______ ==

1616______22

==2424______33

= ...= ...

(When we divide numerator by denominator, the result must be (When we divide numerator by denominator, the result must be 88 !) !)

== == == == == == = ...= ...



885555____________77

88==a)a) 66

776969____________66

77==b)b) 99

c) 8 =c) 8 =1188______ ==

1616______22

==2424______33

= ...= ...

d) 2.41 =d) 2.41 =100100241241________ Rewrite the given number, but without decimal Rewrite the given number, but without decimal pointpoint......

Write the digit 1 and as many zeros as we have Write the digit 1 and as many zeros as we have decimal digits in the given number...decimal digits in the given number...2 decimal digits2 decimal digits

2 zeros2 zeros

Explanation:Explanation:

==



885555____________77

88==a)a) 66

776969____________66

77==b)b) 99

c) 8 =c) 8 =1188______ ==

1616______22

==2424______33

= ...= ...

d) 2.41 =d) 2.41 =100100241241________

e) 30.9 =e) 30.9 =1010309309________

f) 0.019 =f) 0.019 =100010001919________

773131____________33

77==h)h) 44

g) 27 =g) 27 =112727______ ==

5454______22

= ...= ...

i) 28.93 =i) 28.93 =10010028932893________

Some decimal numbers can be changed into mixed fractions.Some decimal numbers can be changed into mixed fractions.Let's revise it...Let's revise it...

3.) Change into mixed number:3.) Change into mixed number:

a) 2.41 =a) 2.41 =1001004141________22

100100

241241______

Recall:Recall:2.41 can be changed not only into 2.41 can be changed not only into a a mixed fraction, but intomixed fraction, but into an an improper improper fraction as well.fraction as well.Say that improper fraction...Say that improper fraction...

2 decimal digits2 decimal digits2 zeros2 zeros

==

Some decimal numbers can be changed into mixed fractions.Some decimal numbers can be changed into mixed fractions.Let's revise it...Let's revise it...

3.) Change into mixed number:3.) Change into mixed number:

a) 2.41 =a) 2.41 =1001004141________22

b) 30.9 =b) 30.9 =101099________3030

c) 15.007 =c) 15.007 =10001000

77________1515

d) 0.045 =d) 0.045 =This decimal numberThis decimal numbercan'tcan't be changed into be changed into a a mixed fractionmixed fractionbecause it has got because it has got zero wholeszero wholes..We can We can only only change it into change it into a a fraction.fraction.

If we should change it into fraction,If we should change it into fraction,

the solution would be the solution would be 100010004545________ ..

What does it mean - "to reduce aWhat does it mean - "to reduce a fraction" ?fraction" ?

To reduce aTo reduce a fraction means to divide both fraction means to divide both the the numerator and numerator and ddenominator of the fraction by the enominator of the fraction by the samesame number.number.

When we reduce a fraction, does When we reduce a fraction, does the the reduced fraction represent a reduced fraction represent a bigger or a smaller part than the bigger or a smaller part than the originaloriginal fraction? fraction?

They represent equal parts!!They represent equal parts!!

4.) Reduce these fractions to non-reducible fractions:4.) Reduce these fractions to non-reducible fractions:

______10101212

==a)a) We can reduce it by __.22

55

66

______5566

==

When we reduce a fraction to the non-reducible fraction, When we reduce a fraction to the non-reducible fraction, then we get this fraction in the then we get this fraction in the lowest possible termslowest possible terms..

So, we divide both the numerator and denominator by 2 and write the results…


To reduce aTo reduce a fraction means to divide both the numerator and fraction means to divide both the numerator and ddenominator of the fraction by the enominator of the fraction by the samesame number.number.



______24243030

==b)b) We can reduce it by __.66

44

55

______4455

==




To reduce aTo reduce a fraction means to divide both fraction means to divide both the the numerator and numerator and ddenominator of the fraction by the enominator of the fraction by the samesame number.number.



______42426363

==c)c) We can reduce it by __.77

66

99

______6699

Now we can reduce again, by __.33

22

33

______2233

==

== ==



Now let's revise other properties of fractions...Now let's revise other properties of fractions...

a) One whole a) One whole equalsequals ____ fourths. ____ fourths.fourfour 1 =1 = ______4444

==

b) One whole b) One whole equalsequals _____ twelfths. _____ twelfths.twelvetwelve 1 =1 = ______12121212

==

c) Two wholes c) Two wholes equalequal ___ thirds. ___ thirds.sixsix 2 =2 = ______6633

==

5.) Complete these sentences:5.) Complete these sentences:

d) 4 days = weekd) 4 days = week______4477


5.) Complete:5.) Complete:

Explanation:Explanation:

First, let's recall that a week has ___ days.First, let's recall that a week has ___ days.77

So we can conclude that each day is of the week.So we can conclude that each day is of the week.____1177

Now, we should think in this way:Now, we should think in this way:

If If 1 day1 day is is of the weekof the week,,____1177

then then 2 days2 days are are of the weekof the week,,____2277

3 days3 days are are of the weekof the week,,____3377

and and 4 days4 days are are of the weekof the week..____4477




We can explain it in another way:We can explain it in another way:

Again, let's recall that a week has ___ days.Again, let's recall that a week has ___ days.77

MondayTuesday

WednesdayThursday

FridaySaturdaySunday

week:week:

So, let's consider it together with the rectangle divided into So, let's consider it together with the rectangle divided into 77 equal parts!equal parts!

rectangle:rectangle:

Left picture:Left picture:We are interested in We are interested in which part of the week consist of which part of the week consist of 4 4 daysdays......

Right picture:Right picture:Which part of the Which part of the rectangle consist of rectangle consist of 4 4 partsparts......

??____4477

of the weekof the week




Shortly:Shortly:

Rewrite the given number into numerator.Rewrite the given number into numerator.

In the denominator write the In the denominator write the total numbertotal number of days in a week ! of days in a week !

As we already know,As we already know,

the the denominatordenominator is the is the total numbertotal number of equal parts, of equal parts,

and the and the numerator numerator describes the number of parts we are describes the number of parts we are interested ininterested in..


e) 20 min. = houre) 20 min. = hour______20206060

= hour= hour______1133

We can reduce it by __.2020

11

33



f) 5 months = yearf) 5 months = year______551212

12

39

6

____1133

min.min.??2020

hourhour??

JanuaryFebruary

MarchAprilMayJuneJuly

year:year:

AugustSeptember

OctobarNovemberDecember

____551212

of the of the yearyear

??

6.) There are 7 tasks in the Ivan's homework.6.) There are 7 tasks in the Ivan's homework.

Ivan solved 2 of them.Ivan solved 2 of them.

What portionWhat portion of the homework did Ivan solve? of the homework did Ivan solve?

Ivan solved of his homework.Ivan solved of his homework.______2277

What portionWhat portion of the homework does he still have to solve? of the homework does he still have to solve?

He should solveHe should solve of his homework yet. of his homework yet.______5577


1st task2nd task3rd task4th task5th task6th task7th task

homework:homework:

??____2277

of the homeworkof the homework

????________5555

7777of the homeworkof the homeworkof the homeworkof the homework


If children ate If children ate (seven tenths) of (seven tenths) of a a cake, whichcake, which

fraction fraction of of the the cake remained?cake remained?

______771010

7.) 7.)

______331010

(three tenths) of (three tenths) of the the cakecake remained remained..

______331010

of the cakeof the cake ______771010

of the cakeof the cake

8.) Climber Dario climbed of his path in one hour,8.) Climber Dario climbed of his path in one hour,______661414

another of the path in the next one hour, another of the path in the next one hour,

and finally of his path in the third hour.and finally of his path in the third hour.

Did he climb his whole path?Did he climb his whole path?

______441414

______331414

______13131414

______441414

______661414

++ ______331414

++ ==

No, he didn't climb his whole path.No, he didn't climb his whole path.

There remained of his path.There remained of his path.______111414


9.) Seven friends gathered some money and bought 3 chocolates9.) Seven friends gathered some money and bought 3 chocolates

ofof equal equal sizesize. They want to divide . They want to divide the the chocolates equally.chocolates equally. How How muchmuch chocolate will each of them get? chocolate will each of them get?

3 : 7 =3 : 7 = ______3377

Each friend will get of Each friend will get of a a chocolate.chocolate.______3377

Explanation with pictures:Explanation with pictures:

When they divide the first chocolate into 7 equal parts,When they divide the first chocolate into 7 equal parts,

each friend will get each friend will get ____11

77of of the the chocolate.chocolate.

When they divide the second chocolate into 7 equal parts,When they divide the second chocolate into 7 equal parts,



When they divide the third chocolate into 7 equal parts,When they divide the third chocolate into 7 equal parts,



So, after all divisions each friend will haveSo, after all divisions each friend will have____33

77of of a a chocolate.chocolate.

10.) a) 12 chocolates should be divided among 5 friends.10.) a) 12 chocolates should be divided among 5 friends. How many chocolates will each of them get?How many chocolates will each of them get?

12 : 5 =12 : 5 = ______121255

==2255

______22

Each friend will get 2 chocolates.Each friend will get 2 chocolates.______2255


Each friend getsEach friend gets____11

55of the 11th chocolate.of the 11th chocolate.

Each friend getsEach friend gets____11

55of the 12th chocolate.of the 12th chocolate.

So, after all divisions each friend will haveSo, after all divisions each friend will have ____22

55chocolates!chocolates!22

10.) b) What about dividing 12 chocolates among 3 friends?10.) b) What about dividing 12 chocolates among 3 friends?

12 : 3 =12 : 3 = 44

Each friend will get 4 chocolates.Each friend will get 4 chocolates.


After division each friend will haveAfter division each friend will have44 chocolates. chocolates.

11.) Little Ana ate strawberries. How many strawberries11.) Little Ana ate strawberries. How many strawberries

did she eat actually?did she eat actually?

______121222

12 : 2 =12 : 2 ===______121222

Little Ana ate 6 strawberries.Little Ana ate 6 strawberries.

66


strawberriesstrawberries______1212

22= 6 strawberries= 6 strawberries

12.) There are 48 apples in the box.12.) There are 48 apples in the box.

______3388

of the box are red apples,of the box are red apples, ______551212

are green applesare green apples

and and the rest of the the rest of the apples are yellow. apples are yellow.

a) How many apples are of which color?a) How many apples are of which color?

______3388

of 48 isof 48 is 1818red:red:

______551212

of 48 isof 48 is 2020green:green:

( we calculated 48:8( we calculated 48:8··3 )3 )

18 + 20 =18 + 20 = 38, 38, yellow:yellow: 48 - 38 =48 - 38 = 10 10

There are 18 red, 20 green and 10 yellow apples in that box.There are 18 red, 20 green and 10 yellow apples in that box.

b) b) What portion What portion of the box do yellow apples form?of the box do yellow apples form?

______10104848

55

2424We can reduce it by __.22== ______55

2424Yellow apples form (five twenty-Yellow apples form (five twenty-fourths) of the box.fourths) of the box.

______552424

13.) Complete these expressions:13.) Complete these expressions:

a) of a) of 15 15 is is ______2255

66

We calculated:We calculated:

1515 : 5: 5 ·· 2 2 == 66

How to explain this calculation?How to explain this calculation?

we divide it into we divide it into 55 equal parts, and then color equal parts, and then color 22 parts. parts.

Recall: If we want to color of some figure, thenRecall: If we want to color of some figure, then______2255

Here we do just about the sameHere we do just about the same thing! thing!

number 15number 15 into into 55 equal parts, and then take equal parts, and then take 22 parts. parts.

of 15 can be calculated so that we divideof 15 can be calculated so that we divide______2255

1515 : 5: 5 ·· 2 2 == 66

a) of a) of 15 15 is is ______2255


66

b) of b) of 72 72 is is ______4499

3232

c) of c) of 10 10 is is ______3344

Here we can't divide 10:4, so we must calculate inHere we can't divide 10:4, so we must calculate insome another way!some another way!

The word The word ofof means meansmultiplication!multiplication!______3344

·· 101055

22


______151522

== 77 ______1122

77 ______1122

a) of a) of 15 15 is is ______2255


Are weAre we allowed to calculate in that way in the allowed to calculate in that way in thea a and and bb tasks? tasks?

Yes, we are!!!Yes, we are!!!

==

E.g.E.g. ______2255

·· 151533

11


______6611

== 66==

Both proceduresBoth proceduresgive equal results!!!give equal results!!!

66

5 61 2 3 4 7 8 9 10

b) of b) of 72 72 is is ______4499

3232

c) of c) of 10 10 is is ______3344

77 ______1122

a) of a) of 15 15 is is ______2255


How How can wecan we imagineimagine the problem the problem in part cin part c??

66

We have 10 pieces of something, e.g. 10 pears...We have 10 pieces of something, e.g. 10 pears...The dThe denominator 4 tells us that we should divide this "bulk" enominator 4 tells us that we should divide this "bulk" into 4 equal parts... into 4 equal parts...

1st1st 2nd2nd 3rd3rd 4th4th

The nThe numerator 3 tells us to take 3 of these 4 parts...umerator 3 tells us to take 3 of these 4 parts...

How manHow manyy pears do we have in these three parts? pears do we have in these three parts? ____112277

We got the same result !!!We got the same result !!!

d) of d) of is is ______12121313

______39394444

______12121313

·· ______39394444

==33

1111


11

33


______991111

______991111

a) of a) of 15 15 is is ______2255


b) of b) of 72 72 is is ______4499

3232

c) of c) of 10 10 is is ______3344

77 ______1122

66


a) is ______ than 1a) is ______ than 1______2255

lessless , by , by ______3355

..


of the rectangleof the rectangle is less than is less than 1 rectangle1 rectangle,,______22

55

<<

by the by the uncoloreduncolored part, and this part is part, and this part is______33

55of the rectangle.of the rectangle.


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515

greatergreater , by, by ______441515

..


rectanglesrectangles is greater than is greater than 1 rectangle1 rectangle,,______1919

1515

>>

by the part determined by by the part determined by secondsecond rectangle, and it is rectangle, and it is

______44

1515of the rectangleof the rectangle..

15.) 15.) In each inequality below, whichIn each inequality below, which number is number is the the greatergreater??

a)a) ______8899

______5599

>>

>>


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515


..


a)a) ______8899

______5599

>>

<<b)b) ______771010

______1155

22 44

<<


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515


..


a)a) ______8899

______5599

>>

<<b)b) ______771010

______1155

22 44

<<c)c) ______331111

44 55

<<


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515


..


a)a) ______8899

______5599

>>

<<b)b) ______771010

______1155

22 44

<<c)c) ______331111

44 55

d)d) ______3355

______1155

66 66>>

e)e) ______8833

______5522

We multiply through diagonals...We multiply through diagonals...

·

1616

·

1515>>

>>

Instead of Instead of cross-cross-multiplying,multiplying,we can find the common denominatorwe can find the common denominatorand then compare numerators...and then compare numerators...

If we would take the common If we would take the common denominator denominator 33··22, that is 6,, that is 6,then we would get numeratorsthen we would get numerators1616 and and 1515. Multiplication through. Multiplication throughdiagonals is shortcut for that.diagonals is shortcut for that.>>


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515


..


a)a) ______8899

______5599

>>

<<b)b) ______771010

______1155

22 44

<<c)c) ______331111

44 55

d)d) ______3355

______1155

66 66>>

e)e) ______8833

______5522>>

>>


a) is ______ than 1a) is ______ than 1______2255


..

b) is _______ than 1b) is _______ than 1______19191515


..


a) If the a) If the numeratornumerator increases, then the fraction _____________. increases, then the fraction _____________.increasesincreases as well as well

E.g.E.g. ______1133

______2233

______3333

______4433

______5533

If we are looking from the left to the right,If we are looking from the left to the right,the numerators ________.the numerators ________.increaseincrease

Colored parts, that is the fractions _____________.Colored parts, that is the fractions _____________.increase as wellincrease as well

b) If the b) If the denominatordenominator increases, then the fraction _________. increases, then the fraction _________.decreasesdecreases

E.g.E.g. ______1111

______1122

______1133

______1144

______1155

If we are looking from the left to the right,If we are looking from the left to the right,the denominators ________.the denominators ________.increaseincrease

Colored parts, that isColored parts, that is,, the fractions the fractions of the whole of the whole _______._______.decreasedecrease


a) If the a) If the numeratornumerator increases, then the fraction _____________. increases, then the fraction _____________.increasesincreases as well as well


a) If the a) If the numeratornumerator increases, then the fraction _____________. increases, then the fraction _____________.

b) If the b) If the denominatordenominator increases, then the fraction _________. increases, then the fraction _________.decreasesdecreases

increasesincreases as well as well

17.) Figure out:17.) Figure out:

______5566

++a)a) ______4499

== ________________15151818

==++ 88 ______2323

1818== 11 ______55

1818

________________272766

==-- 11 ______2626

66==

44 ______2266

______1122

--b)b) ______1166

==44 ______9922

-- ______1166

==

== We can reduce it by __.22

11

33

44 ______1133

==

18.) Try to figure 18.) Try to figure these these out out mentallymentally!!

5533 ______

77++a)a) ______55

77==33



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11

7755 ______

99--c)c) ______22

99==66



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11

7755 ______

99--c)c) ______22

99==66

______1122

++d)d) ==44 5511

99 ______22



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11

7755 ______

99--c)c) ______22

99==66

______1122

++d)d) ==44 5511

99 ______22

______221111

--e)e) ==66 6622______

1111



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11

7755 ______

99--c)c) ______22

99==66

______1122

++d)d) ==44 5511

99 ______22

______221111

--e)e) ==66 6622______

1111

______1133

--f)f) ______1133

==88 88



5533 ______

77++a)a) ______55

77==33

22______55

--b)b) ______3355

==11

7755 ______

99--c)c) ______22

99==66

______1122

++d)d) ==44 5511

99 ______22

______221111

--e)e) ==66 6622______

1111

______1133

--f)f) ______1133

==88 88

--g)g) ______7788

==66 2211

33 ______88



______27274949

··a)a) ______212199

==33

11


77

33


______9977

== 11 ______2277

______2299

··b)b) ______54541919

==44 ______383899

·· ______54541919

==22

11


11

66


______121211

== 1212

··c)c) ______1166

==99 22 ______9911

·· ______131366

33

22


== ______393922

== 1919 ______1122


::a)a) ______121277

==88 ______8811

·· ______771212

22

33


== ______141433

== 44 ______2233

::b)b) ______7788

==33______1188

______1188

:: ______313188

== ______1188

·· ______883131

11

11


== ______113131

Let's recall theLet's recall the “ “number linenumber line””....

00 11 22 33 44

Place the following numbers onto the number line:Place the following numbers onto the number line:

a)a) 22 ______5566

between __ and __between __ and __22 33

00 11 22 33 44

a)a) 22 ______5566

marked part of the number linemarked part of the number lineshould be divided into ____________should be divided into ____________6 equal parts6 equal parts



00 11 22 33 44

a)a) 22 ______5566

we should count __ parts of the whole from the leftwe should count __ parts of the whole from the left55

22 ____55

66



00 11 22 33 44

a)a) 22 ______5566

22 ____55

66

b)b) ______7722

== 33 ______1122

between __ and __between __ and __33 44 , exactly in the ______, exactly in the ______middlemiddle

33 ____11

22

____77

22



00 11 22 33 44

a)a) 22 ______5566

22 ____55

66

b)b) ______7722

== 33 ______1122

33 ____11

22

____77

22

c)c) ______2233

it is not possible to change it into ait is not possible to change it into a mixed number, mixed number, there are no wholes,there are no wholes,so this number lies between __ and __so this number lies between __ and __00 11



00 11 22 33 44

a)a) 22 ______5566

22 ____55

66

b)b) ______7722

== 33 ______1122

33 ____11

22

____77

22

c)c) ______2233 marked part of the number linemarked part of the number line

should be divided into ____________should be divided into ____________3 equal parts3 equal parts



00 11 22 33 44

a)a) 22 ______5566

22 ____55

66

b)b) ______7722

== 33 ______1122

33 ____11

22

____77

22

c)c) ______2233

we count __ parts we count __ parts ofof the whole from the left the whole from the left22

____22

33



We We shallshall continue this revision in writing continue this revision in writing......

Now we should Now we should be able to be able to solve several more complex tasks solve several more complex tasks with more with more ‘fraction ‘fraction calculatcalculation’ion’ operations. operations.

Open your notebooks...Open your notebooks...

Author of presentation:Author of presentation:

Antonija HorvatekAntonija HorvatekCroatiaCroatia , October 2008., October 2008.

With thanks to:With thanks to:

GSCGSCfor support, great for support, great sugsugggestions and estions and

preliminary helppreliminary help with with the the translation translation

ininto Englishto English

andand

Rex BoggsRex Boggsfor support and help for support and help

with with the the translationtranslation into into fluent U.S. idiom fluent U.S. idiom

(a.k.a. ‘American’)(a.k.a. ‘American’)..

You are welcome to use this presentation in your teaching.Additionally, you can change some parts of it if used solely for teaching.

However, if you want to use it in public lectures, workshops, in writing books, articles, on CDs or any public forum or for any commercial purpose, please ask for specific permission from the author.

Antonija Horvatekhttp://public.carnet.hr/[email protected]

http://public.carnet.hr/~ahorvate






mailto:[email protected]





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