fraction revision. things you need to know about fractions... finding fractions of amounts...
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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
Finding Fractions of Amounts
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
Finding Fractions of Amounts
27
If you are asked for of an amount
Find by dividing by 7 and then find by multiplying by 2.
To find of 35:35 ÷ 7 = 55 x 2 = 10
17
27
27
27
of 35 is 10
Finding Fractions of Amounts
59
If you are asked for of an amount
Find by dividing by 9 and then find by multiplying by 5.
To find of 63:63 ÷ 9 = 75 x 7 = 35
19
59
59
59
of 63 is 35
Finding Fractions of Amounts
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
Are these fractions EQUIVALENT?
8101216
4534
÷2
÷4
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 NOT equivalent
Are these fractions EQUIVALENT?
9122128
3434
÷3
÷7
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
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
Which fraction is equivalent to....
A) B)
C) D)
14
7 21
5 16
3 10
4 16
Which fraction is equivalent to....
A) B)
C) D)
1 10
4 44
3 30
Which fraction is equivalent to....
4 44
4 44
A) B)
C) D)
34
15 20
Which fraction is equivalent to....
18 20
12 20
16 20
A) B)
C) D)
25
6 15
Which fraction is equivalent to....
6 25
8 22
12 35
A) B)
C) D)
56
30 36
Which fraction is equivalent to....
15 24
35 36
10 18
A) B)
C) D)
49
1636
Which fraction is equivalent to....
12 54
16 81
8 27
A) B)
C) D)
57
3042
Which fraction is equivalent to....
10 21
35 35
15 28
A) B)
C) D)
9 11
6377
Which fraction is equivalent to....
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
=
Top heavy fractions to mixed numbers
195
How many 5’s go into 19? 3
What is the remainder? 4
So we can make 3 wholes and we have 4 fifths left over:
345
195
=
Top heavy fractions to mixed numbers
3110
How many 10’s go into 31? 3
What is the remainder? 1
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
Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions:
5 34
234
=
Multiply these numbers together=
Add on the number at the top=
20
23 (this will be the top number)
The number at the bottom will stay the same
Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions:
6 25
3210
=
Multiply these numbers together=
Add on the number at the top=
30
32 (this will be the top number)
The number at the bottom will stay the same
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)
Convert this fraction to a percentage
14
10% 100%
20%1%
A) B)
C) D)
Convert this fraction to a percentage
1 10
20%
2% 15%
5%
A) B)
C) D)
Convert this fraction to a percentage
15
75%
80% 12%
45%
A) B)
C) D)
Convert this fraction to a percentage
34
21%
0.21% 2.1%
210%
A) B)
C) D)
Convert this fraction to a percentage
21 100
40%4%
10%44%
A) B)
C) D)
Convert this fraction to a percentage
4 10
60%
6%
80%
15%A) B)
C) D)
Convert this fraction to a percentage
35
1%100%
0.110%0.1%
A) B)
C) D)
Convert this fraction to a percentage
1 100
33.333333.. % 13%
11%3%
A) B)
C) D)
Convert this fraction to a percentage
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
Adding and Subtracting Fractions
27
37
57+ =
29
49
69+ =
111
311
411+ =
Adding and Subtracting Fractions
27
37
57+ =
29
49
69+ =
511
311
211- =
Adding and Subtracting Fractions
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?
Adding and Subtracting Fractions
We need to make sure the denominator of both fractions is the same before we add or subtract
13
512
912
+ =
125
12+ =
4
We need a number in the 3 and 12 times table to use as our bottom number- 12?
Adding and Subtracting Fractions
We need to make sure the denominator of both fractions is the same before we add or subtract
25
36
2730
+ =
30 30+ =
12
We need a number in the 5 and 6 times table to use as our bottom number- 30?
15
Adding and Subtracting Fractions
We need to make sure the denominator of both fractions is the same before we add or subtract
78
23
524
- =
24 24
- =21
We need a number in the 8 and 3 times table to use as our bottom number- 24?
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
Decimals to Fractions
0.12 is 12 hundredths 12100
Tent
hs
Hun
dred
ths
0.01 is 1 hundredth 1100
Tent
hs
Hun
dred
ths
Decimals to Fractions
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
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