© t madas. fact © t madas to convert any fraction into decimal form, carry out the division: to...
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© T Madas
© T Madas
Fact
© T Madas
To convert any fraction into decimal form,carry out the division:716 7 16= ¸ 0.4375=
To convert any decimal into a fraction,write it as a fraction out of 10, 100, 100 etc: 7
100.7=
38100
0.38 =
4061000
0.406 =
31022.3=
51
5=
4641
464 =
2310=
Note that recurring decimals need some algebraic manipulation before converting
© T Madas
The rule for Addition & Subtraction of fractions is:
a bc c± a b
c±=
For example:4 27 7
+ 67
=
5 16 6
- 23
=46
=
When the denominators of the fractions are different we must find a common denominator before adding or subtracting them.
© T Madas
The rule for Addition & Subtraction of fractions is:
a bc c± a b
c±=
For example:4 27 7
+ 67
=
5 16 6
- 23
=46
=
2 75 15
+ =15 15
+ =6 7 1315
3 58 12
+ =24 24
+ =9 10 1924
© T Madas
Multiplication of fractions follows the rule:
a cb d
´ = acbd
=a c´b d´
For example:4 25 3
´ 815
=
5 24 9
´ 518
=1036
=
3 25
´ 21
´35
= 65
=
What is the physical meaning of fraction multiplication?
© T Madas
Find of 23
15
2 153
´
Find of 15
23
1 25 3
´
215
=
215
=
This is in analogy of multiplication of decimals:
0.7 x 0.8 finds 0.7 of 0.8or 0.8 of 0.7
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Two fractions such that one is obtained by turning the other “upside down”
Reciprocals
Reciprocals are said to be inverses of each other with respect to the operation of multiplication
The reciprocal of is because:
23
32
32 13 2
´ =
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Two fractions such that one is obtained by turning the other “upside down”
Reciprocals
Reciprocals are said to be inverses of each other with respect to the operation of multiplication
The reciprocal of is because:
58
85
5 8 158
´ =
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Two fractions such that one is obtained by turning the other “upside down”
Reciprocals
Reciprocals are said to be inverses of each other with respect to the operation of multiplication
The reciprocal of is 3 because:
13
1 3 13
´ =
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Two fractions such that one is obtained by turning the other “upside down”
Reciprocals
Reciprocals are said to be inverses of each other with respect to the operation of multiplication
The reciprocal of 7 is because:
17
17 17
´ =
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Two fractions such that one is obtained by turning the other “upside down”
Reciprocals
Reciprocals are said to be inverses of each other with respect to the operation of multiplication
The reciprocal of 2.33 is because:
12.33
12.33 12.33
´ =
© T Madas
Division of fractions follows the rule:
a cb d
¸ ab
= adbc
=dc
´
Examples of fraction division:4 25 3
¸ 45
= 32
´ 1210
= 65
=
3 24
¸ 34
= 12
´ 38
=
© T Madas
© T Madas
Three adverts appear on a page of a newspaper.
The 1st advert covers 1/4 of the page.
The 2nd avert covers 1/8 of the page.
The 3rd advert covers 3/16 of the page.
What fraction of the page is not covered by adverts?14
18+ +
316 =
x 2
x 2
x 4
x 4
416
216+ +
316= 9
16
If is covered by adverts
then is not covered by adverts.
916
716
© T Madas
© T Madas
1. How many quarters in 2 ?
2. How many quarters in 3 ?
3. How many tenths in 2 ?
4. How many tenths in 1 ?
5. How many twelfths in 1 ?
12
34
31035
13
342 =11
4
© T Madas
1. How many quarters in 2 ?
2. How many quarters in 3 ?
3. How many tenths in 2 ?
4. How many tenths in 1 ?
5. How many twelfths in 1 ?
12
34
31035
13
342 =11
4123 = 7
2 =144
© T Madas
1. How many quarters in 2 ?
2. How many quarters in 3 ?
3. How many tenths in 2 ?
4. How many tenths in 1 ?
5. How many twelfths in 1 ?
12
34
31035
13
342 =11
4123 = 7
2 =144
3102 =23
10
© T Madas
1. How many quarters in 2 ?
2. How many quarters in 3 ?
3. How many tenths in 2 ?
4. How many tenths in 1 ?
5. How many twelfths in 1 ?
12
34
31035
13
342 =11
4123 = 7
2 =144
3102 =23
10351 = 8
5 =1610
© T Madas
1. How many quarters in 2 ?
2. How many quarters in 3 ?
3. How many tenths in 2 ?
4. How many tenths in 1 ?
5. How many twelfths in 1 ?
12
34
31035
13
342 =11
4123 = 7
2 =144
3102 =23
10351 = 8
5 =1610
131 = 4
3 =1612
© T Madas
© T Madas
A rectangle is 6⅝ cm long by 3½ cm wide.1. Calculate it perimeter.2. Calculate its area.
6⅝ cm
3½
cm to find the
perimeter:586 1
23+ 586 1
23++ =
Method 1
5819+ 5
8+ =
10819+ =5419+ =
÷ 2
÷ 2
1419+ =1
1420 cm
© T Madas
A rectangle is 6⅝ cm long by 3½ cm wide.1. Calculate it perimeter.2. Calculate its area.
6⅝ cm
3½
cm to find the
perimeter:586 1
23+ 586 1
23++ =
Method 2
538
72+ 53
872++ =
1068
142+
x 4
x 4=
1068
568+ =
1628 =
2820
1420 cm
=
© T Madas
A rectangle is 6⅝ cm long by 3½ cm wide.1. Calculate it perimeter.2. Calculate its area.
6⅝ cm
3½
cm
to find the area:5
86 123x =
538
72x =
37116
31623 cm2
= 37 116
2 3
5 3
© T Madas
© T Madas
Roulla used half of her exercise book in the autumn term.So far this term she has used a further one sixth of it.
1. What fraction of her exercise book has she used so far?2. How many pages does her exercise book have if she has 30 pages left?
12
16+
x 3
x 3= 3
616+ = 4
6 = 23
÷ 2
÷ 2
If she has used of her exercise book
she must have of it left.
If of her exercise book is 30 pages
then the entire exercise book must have 90 pages
23
13
13
© T Madas
© T Madas
Johnny spent his monthly allowance as follows:
of it on lunch and food snacks
of it on two music CDs
of it on a new book
1. What fraction of his monthly allowance has he got left?2. If he is left with £6 what is his monthly allowance?
251316
25
13+ +
16 =
x 10
x 10
x 6
x 6
x 5
x 5
1230
1030+ +
530= 27
30 = 910
÷ 3
÷ 3
Johnny has spent of his monthly allowance
so he must have of his monthly allowance left.
If of his monthly allowance is £6
then his monthly allowance must be £60
910
110
110
© T Madas
© T Madas
Edmonton is 3⅝ miles away from Southgate.Barnet is 2¾ miles away from Southgate.How much further from Southgate is Edmonton than Barnet?
583 3
42– = 298
114– = 29
8228– = 7
8
x 2
x 2
Edmonton is ⅞ of a mile further from Southgate than Barnet is.
© T Madas
© T Madas
Ethan works day and night shifts in alternating weeks.He works:5 days for 7¾ hours per day during his “day-shift” week.5 nights for 6½ hours per night in his “night-shift” week.Calculate how many hours he works a fortnight.
Week 1:5 x 3
4 =7 5 x314 = 155
4 = 3438
Week 2:5 x 1
2 =6 5 x132 = 65
2 = 1232
Adding the two figures:3
438 1232+ =70 1
41+ = 1471
Ethan works 71¼ hours every fortnight
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© T Madas
[You may shade the shapes below to help you with your answer]
Calculate4 12÷3
4
© T Madas
[You may shade the shapes below to help you with your answer]
Calculate4 12÷3
4
124 3
4÷ = 92
34÷ = 9
243x = 36
6 = 6
© T Madas
© T Madas
Bethany uses ⅝ metres of ribbon to wrap up a gift box.How many identical gift boxes can she wrap using a 7½ metre roll of ribbon?
127 5
8÷ = 152
58÷ = 15
285x = 120
10 = 12
Bethany can wrap up 12 such boxes
© T Madas
© T Madas
There is of the original amount left
1. What fraction of the original amount of juice remains in the carton?
2. Who drunk the most juice? [you must show full workings]
Tony drank of a full carton of orange juice.
His sister Alice drank of what was left.
13
34
If Tony drank of a full carton there is of a full carton left.
Therefore Alice drank of of a full carton
The operation that finds “something” of “something” is:multiplication
13
34
23
23
34
23x = 6
1212= Alice drunk half the carton
13
12+
x 2
x 2= 2
636+ = 5
6
x 3
x 3
16
[who drank the most?]
© T Madas
Let us solve the problem pictorially
Tony drunk of a full carton
Alice drunk of what was left
We are left with of a full carton
Tony drunk of a full carton
Alice drunk of a full carton
Which is the same as
1334
16
1336
12
1. What fraction of the original amount of juice remains in the carton?
2. Who drunk the most juice? [you must show full workings]
Tony drank of a full carton of orange juice.
His sister Alice drank of what was left.
13
34
© T Madas
© T Madas
13.548
6.7524
The school day in Northgate School starts at 08:45 and finishes at 15:30.What fraction of a 24 hour day does the school day take up? [Give your answer in its simplest form.]
08:45
09:00
15:00
to
to
to
09:00
15:00
15:30
15 minutes
6 hours
30 minutes
6 hours, 45 minutes6¾ hours6.75 hours
=x 2
x 2= 27
96932=
x 2
x 2
÷ 3
÷ 3
6752400
6.7524 =
x 100
x 100= 27
96932=
÷ 25
÷ 25
÷ 3
÷ 3
© T Madas
© T Madas
To make a litre of a certain fruit punch, fruit juices are mixed in the following proportions:
1. What fraction of a litre corresponds to kiwi fruit juice?
2. What is the ratio of these juices as apple : cranberry : kiwi ?
3. What fraction of a litre from each fruit juice is contained in 2½ litres of this fruit punch?
total: 1 litre
of a litrekiwi
of a litrecranberry
of a litreapple
amounttype of juice
5124
15
1960
512
415+ =
x 4
x 4
x 5
x 5
2560
1660+ = 41
60
1 4160– =60
604160– = 19
60
© T Madas
1. What fraction of a litre corresponds to kiwi fruit juice?
2. What is the ratio of these juices as apple : cranberry : kiwi ?
3. What fraction of a litre from each fruit juice is contained in 2½ litres of this fruit punch?
To make a litre of a certain fruit punch, fruit juices are mixed in the following proportions:
total: 1 litre
of a litrekiwi
of a litrecranberry
of a litreapple
amounttype of juice
5124
15
1960
512
415: :
x 4
x 4
x 5
x 5
1960
2560
1660: : 19
60
x 60 x 60 x 60
25 : 16 : 19
© T Madas
1. What fraction of a litre corresponds to kiwi fruit juice?
2. What is the ratio of these juices as apple : cranberry : kiwi ?
3. What fraction of a litre from each fruit juice is contained in 2½ litres of this fruit punch?
To make a litre of a certain fruit punch, fruit juices are mixed in the following proportions:
total: 1 litre
of a litrekiwi
of a litrecranberry
of a litreapple
amounttype of juice
5124
15
1960
=
=
=
=
of a litrex
of a litrex
of a litrex
of a litrex5124
15
1960
5252
52
52
2524
2030
23
95120
1924
52
=
=
© T Madas
Exam Question
© T Madas
´ 358
34
1
58
2
272
Calculate the area of the following trapezium:
=34
1 74
=272 16
7
=58
2 218
( )´12
74 + 21
8=A ´ 16
7
( )= ´12
148
+ 218
´ 167
= 12
´ 167
5= 25 cm
© T Madas
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