Fraction Revision. Things you need to know about fractions... Finding Fractions of Amounts Equivalent Fractions and cancelling down Top Heavy Fractions

$Page 1: Fraction Revision. Things you need to know about fractions... Finding Fractions of Amounts Equivalent Fractions and cancelling down Top Heavy Fractions$
Fraction Revision

Things you need to know about fractions...

Finding Fractions of Amounts

Equivalent Fractions and cancelling

down

Top Heavy Fractions and Mixed Numbers

Adding and Subtracting

Fractions

Multiplying Fractions Dividing Fractions

Fractions and Decimals

Fractions and Percentages Ordering Fractions

Click this to get back hereThings you

should know

These are REALLY

important


35

If you are asked for of an amount

Find by dividing by 5 and then find by multiplying by 3.

To find of 60:60 ÷ 5 = 1212 x 3 = 36

15

35

35

35

of 60 is 36


27



To find of 35:35 ÷ 7 = 55 x 2 = 10

17

27

27

27

of 35 is 10


59



To find of 63:63 ÷ 9 = 75 x 7 = 35

19

59

59

59

of 63 is 35


A quick way to remember what to do is:

“Divide by the bottom, times by the top”

Fractions of Amounts

10 multiple choice questions, work out your

answer then click to see if you were right

30

15

40

6

What is..

12

of 60

A) B)

C) D)

1520

124

What is..

14

of 60

A) B)

C) D)

12

6 9

8

What is..

13

of 36

A) B)

C) D)

14 16

1812

What is..

14

of 56

A) B)

C) D)

33

13 11

21

What is..

36

of 66

A) B)

C) D)

7566.6666

2580

What is..

34

of 100

A) B)

C) D)

6020

1535

What is..

35

of 100

A) B)

C) D)

25

45 50

80

What is..

18

of 200

A) B)

C) D)

140

80

120

100

What is..

2040

Of 280

A) B)

C) D)

70 49

7481

What is..

79

of 90

A) B)

C) D)


Multiplying FractionsTo multiply simply times the numbers at the top, then times the numbers at the bottom, you may have to simplify

34

58

x = 1532

27

56

x = 1042

35

79

x = 2145

=

= 715

521

Simplify before multiplying67

56

x = 1x57x1

1

1

=57

45

38

x = 1x35x2

1

2

=310

49

67

x = 4x23x73

2

=821

This will help with division

too, do it after the

keep, change flip

bit


Dividing FractionsTo divide remember KEEP, CHANGE, FLIP-KEEP the first fraction-CHANGE the multiply sign to divide-FLIP the second fraction

34

58

÷ = 2420

34

x 85

= =1 420 or 1

15

12

78

÷ = 814

12

x 87

= = 47

47

34

÷ = 1621

47

x 43

=


Equivalent Fractions

Three friends each have 12 sweetsAbbie puts hers into 4 piles

and eats 2 of them

Abbie has had 2/4

Libby puts hers into 2 piles and eats 1 of them

Libby has had 1/2

Chrissy puts hers into 6 piles and eats 3 of them

Chrissy has had 3/6

They all eat 6 sweets2/4, ½ and 3/6 look different but these

fractions are all the same, they are EQUIVALENT

Are these fractions EQUIVALENT?

8241236

1313

÷8

÷12

Simplify the fractions

Look for the biggest number that goes into the top and bottom of the fractions

Divide by the number

These fractions are equivalent


8101216

4534

÷2

÷4




These fractions are NOT equivalent


9122128

3434

÷3

÷7




These fractions are equivalent

What number goes here?

15203240

3445

÷5

÷8

What number goes here?

2315

824945

X8

X9

Equivalent Fractions

10 multiple choice questions. Work out your answer then click to see if

you were right

A) B)

C) D)

12

28

39

48

4 10

Which fraction is equivalent to....

A) B)

C) D)

13

4 12

39

48

5 20


A) B)

C) D)

14

7 21

5 16

3 10

4 16


A) B)

C) D)

1 10

4 44

3 30


4 44

4 44

A) B)

C) D)

34

15 20


18 20

12 20

16 20

A) B)

C) D)

25

6 15


6 25

8 22

12 35

A) B)

C) D)

56

30 36


15 24

35 36

10 18

A) B)

C) D)

49

1636


12 54

16 81

8 27

A) B)

C) D)

57

3042


10 21

35 35

15 28

A) B)

C) D)

9 11

6377


27 22

63 88

45 44

Cancelling fractions down

It is often best to have the numbers possible when we write fractions

Instead of we would have

We have cancelled the fractions down, by dividing top and bottom numbers by the same number (in this case 4)

12 20

3 5

15 35

24 36

55 66

=

=

=

3 7

2 3

5 6

Divide by 5

Divide by 12

Divide by 11

Cancelling fractions down

If we pick the biggest number possible to divide by we only have to cancel down once.

We must always check that there are no more numbers which go into the top and bottom number

When there are no more numbers which go into the top and bottom of the fraction, the fraction is FULLY SIMPLIFIED or CANCELLED DOWN FULLY

Cancelling Fractions

10 multiple choice questions

A) B)

C) D)

1215

45

3 5

3 4

2 5

Cancel completely

A) B)

C) D)

48

28

13

12

1 4

Cancel completely

A) B)

C) D)

7 21

1 3

37

18

1 7

Cancel completely

A) B)

C) D)

1525

4 5

3 4

5 6

3 5

Cancel completely

A) B)

C) D)

28 32

7 14

7 8

4 6

14 16

Cancel completely

A) B)

C) D)

2736

3 4

3 5

5 7

6 8

Cancel completely

A) B)

C) D)

2460

2 5

3 8

2 7

1 5

Cancel completely

A) B)

C) D)

5566

5 6

8 9

6 7

4 6

Cancel completely

A) B)

C) D)

48 64

34

4 6

3 5

2 3

Cancel completely

A) B)

C) D)

5672

79

1 2

2 5

6 7

Cancel completely


Mixed numbers and top heavy fractions

When you see a fraction with a large number in front of it, this is a MIXED NUMBER.

223 This mean, 2 and 2 thirds

When we have a fraction where the number at the top (NUMERATOR) is bigger than the number at the bottom (DENOMINATOR) we have a TOP HEAVY FRACTION

53

84

92

Mixed numbers and top heavy fractions

You need to be able to:

• turn MIXED NUMBERS into TOP HEAVY FRACTIONS

•turn TOP HEAVY FRACTIONS into MIXED NUMBERS

Top heavy fractions to mixed numbers

143

How many 3’s go into 14? 4

What is the remainder? 2

So we can make 4 wholes and we have 2 thirds left over:

423

143

=


195



So we can make 3 wholes and we have 4 fifths left over:

345

195

=


3110



So we can make 3 wholes and we have 1 tenth left over:

3110

3110

=

Mixed Numbers to Top heavy fractions

To turn the mixed numbers into top heavy fractions:

3 110

3110

=

Multiply these numbers together=

Add on the number at the top=

30

31 (this will be the top number)

The number at the bottom will stay the same



5 34

234

=



20





6 25

3210

=



30



Top heavy fractions

10 multiple choice questions

83

223

73

43

A) B)

C) D)

223 =

195

175

125

345

A) B)

C) D)

345 =

92

82

42

122

A) B)

C) D)

412 =

535

134

505

355

A) B)

C) D)

1035 =

193

183

93

63

A) B)

C) D)

613 =

31

9 2

A) B)

C) D)

103 =

13

13

13

93

7

8

9

6A) B)

C) D)

578 =

18

28

38

18

3

4

4

3A) B)

C) D)

154 =

34

14

14

34

2 1

2 10

A) B)

C) D)

2110 =

12

1110

1120

110

5

4 5

6

A) B)

C) D)

265 =

15

65

15

15


Fractions and Percentages

• Think of percentages as fractions with 100 as the denominator so,

17 % =

32 % =

88 % =

1710032

100

88100

Fractions and Percentages• Some fractions can be simplified

25 % =

55 % =

30 % =

2510055

100

30100

14

1120

310

=

=

=

Fractions and PercentagesTo turn a fraction into a percentage you need to use what you know about equivalent fractions. Turn your fraction into an equivalent fraction over 100.

1220

60100

x5

60%

Fractions and PercentagesTo turn a fraction into a percentage you need to use what you know about equivalent fractions. Turn your fraction into an equivalent fraction over 100.

710

70100

x10

70%

Fractions and PercentagesSometimes you need to simplify the fraction first.

1435

40100

x20

40%

25=

Fractions and PercentagesSometimes you need to simplify the fraction first.

2640

65100

x5

65%

1320=

60% 70% 8% 27% 80%

14

33100

51100

45

15

Practise Questions, click to show answers

Fractions to Percentages

10 multiple choice questions, work out your

answer then click to see if you were right

50%

20%

40%

100%A) B)

C) D)

Convert this fraction to a percentage

12

25%40%

2%4%

A) B)

C) D)


14

10% 100%

20%1%

A) B)

C) D)


1 10

20%

2% 15%

5%

A) B)

C) D)


15

75%

80% 12%

45%

A) B)

C) D)


34

21%

0.21% 2.1%

210%

A) B)

C) D)


21 100

40%4%

10%44%

A) B)

C) D)


4 10

60%

6%

80%

15%A) B)

C) D)


35

1%100%

0.110%0.1%

A) B)

C) D)


1 100

33.333333.. % 13%

11%3%

A) B)

C) D)


13


Adding and Subtracting Fractions

Two rulers add three rulers is:

Four pens add five pens is:

9 pens

5 rulers

Two pens add Five rulers is:

We can’t so this until we have a name that describes both groups

7 Pieces of equipment

When we add fractions we need them to have the same name


27

37

57+ =

29

49

69+ =

111

311

411+ =


27

37

57+ =

29

49

69+ =

511

311

211- =


We need to make sure the denominator of both fractions is the same before we add or subtract

25

310

710

+ =

103

10+ =

4

We need a number in the 5 and 10 times table to use as our bottom number- 10?



13

512

912

+ =

125

12+ =

4




25

36

2730

+ =

30 30+ =

12


15



78

23

524

- =

24 24

- =21


16

Adding and Subtracting Fractionsa) 7/8b) 8/12c) 7/9d) 7/10e) 2/3

a) 11/12b) 7/10c) 8/15d) 16/12 or 1 ¼e) 11/24

a) 1 7/12b) 1 5/56c) 29/30d) 29/52e) 1 1/10

a) 5/8b) 5/12c) 1/3d) 2/5e) 1/2

a) 7/20 b) 8/21c) 23/36d) 9/22e) 71/126

Click for answers


Fractions and DecimalsTo turn fractions into decimals and decimals into fractions we need to remember column names

000.000

Hun

dred

s

Tens

Uni

ts

Tent

hs

Hun

dred

ths

Thou

sand

ths

Decimals to Fractions

0.03 is 3 hundredths 3100

Tent

hs

Hun

dred

ths

0.5 is 5 tenths 510

Tent

hs


0.12 is 12 hundredths 12100

Tent

hs

Hun

dred

ths

0.01 is 1 hundredth 1100

Tent

hs

Hun

dred

ths


0.032 is 32 thousandths 321000

Tent

hs

Hun

dred

ths

Thou

sand

ths

0.154 is 154 thousandths 1541000

Tent

hs

Hun

dred

ths

Thou

sand

ths

Don’t forget you may have to simplify

Fractions to Decimals

710

64100

1521000

=

=

=

0.7

0.64

0.152

3100= 0.03

531000

=0.053 21000

=0.002

000.000

Hun

dred

s

Tens

Uni

ts

Tent

hs

Hun

dred

ths

Thou

sand

ths

Fractions to Decimals

You can also turn fractions into decimals by dividing the top number by the bottom number either with a calculator or any other method you

may know


Ordering Fractions

To order fractions you need to know all about equivalent

fractions

It’s difficult to order fractions when they have different

denominators

12

14

35

310

1120

What number is in the 2,4,5,10 and 20 times table, we need a

common multiple

20?

Make all fractions have 20 as a denominator

12

14

35

310

1120

Now order them

1020

520

1520

620

1120

520

620

1020

1120

1520

What denominator do we need now?

13

46

25

512

56

Now order them

2060

4060

2460

2560

5060

2060

2460

2560

4060

5060

Ordering Fractions- click for answersANSWERS1. 1/4 3/8 ½ and 4/8

3/42. 2/5 ½ 3/5 and 6/10

2/293. 1/3 5/12 1/1 4/6

3/44. 1/4 1/2 2/3 5/6

7/85. 1/4 2/5 1/2 6/10

3/46. 1/3 4/9 1/2 2/3

5/67. 2/6 1/4 5/12 2/3

7/98. 2/7 2/4 5/8 11/14

3/2


Fraction Percentage Decimal

1/2 50% 0.5

1/4 25% 0.25

3/4 75% 0.75

1/5 20% 0.2

1/10 10% 0.1

1/100 1% 0.01

Things you should know

The top number of a fraction is the NUMERATORThe bottom number of a fraction is the DENOMINATOR

Documents

Fraction Revision. Things you need to know about fractions... Finding Fractions of Amounts Equivalent Fractions and cancelling down Top Heavy Fractions