Transcript fraction-revision1

Fraction Revision
Finding Fractions of Amounts
If you are asked for
3
5
of an amount
1
3
5 by dividing by 5 and then find 5 by
Find
multiplying by 3.
3
5
To find of 60:
60 ÷ 5 = 12
12 x 3 = 36
3 of 60 is 36
5
Finding Fractions of Amounts
If you are asked for
2
7
of an amount
1
2
7 by dividing by 7 and then find 7 by
Find
multiplying by 2.
2
7
To find of 35:
35 ÷ 7 = 5
5 x 2 = 10
2 of 35 is 10
7
Finding Fractions of Amounts
If you are asked for
5
9
of an amount
1
5
9 by dividing by 9 and then find 9 by
Find
multiplying by 5.
5
9
To find of 63:
63 ÷ 9 = 7
5 x 7 = 35
5 of 63 is 35
9
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
What is..
1 of 60
2
A)
15
B)
6
C)
30
D)
40
What is..
1 of 60
4
A)
20
B)
15
C)
4
D)
12
What is..
1 of 36
3
A)
6
B)
9
C)
8
D)
12
What is..
1 of 56
4
A)
14
B)
16
C)
12
D)
18
What is..
3 of 66kg
6
A)
13kg
B)
11kg
C)
21kg
D)
33kg
What is..
3 of 100m
4
A)
66.6666m
B)
75m
C)
80m
D)
25m
What is..
3 of 100ml
5
A)
20ml
B)
60ml
C)
35ml
D)
15ml
What is..
1 of €200
8
A)
€45
B)
€50
C)
€80
D)
€25
What is..
20 Of 280
40
A)
80
B)
100
C)
140
D)
120
What is..
7 of 90
9
A)
70
B)
49
C)
81
D)
74
2/4, ½ and 3/6 look different but these
fractions
are
the
same,
are
Three
They
friends
allall
each
eat
6have
sweets
12they
sweets
Abbie puts hers into 4 piles
EQUIVALENT
Libby puts hers into 2 piles
and eats 2 of them
and eats 1 of them
Abbie has had
2/4
Libby has had
1/2
Chrissy puts hers into 6
piles and eats 3 of them
Chrissy has had
3/6
Are these fractions EQUIVALENT?
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
8
24
12
36
÷8
1
3
÷12 1
3
Are these fractions EQUIVALENT?
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
8
10
12
16
÷2
4
5
÷4
3
4
Are these fractions EQUIVALENT?
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
9
12
21
28
÷3
3
4
÷7
3
4
What number goes here?
15
20
32
40
÷5
3
4
÷8
4
5
What number goes here?
2
3
1
5
X8
8
24
X9
9
45
Equivalent Fractions
10 multiple choice questions.
Work out your answer then
click to see if you were right
Which fraction is equivalent to....
1
2
A)
3
9
C)
4
8
B)
2
8
D)
4
10
Which fraction is equivalent to....
1
3
A)
C)
3
9
4
8
B)
4
12
D)
5
20
Which fraction is equivalent to....
1
4
A)
C)
5
16
3
10
B)
7
21
D)
4
16
Which fraction is equivalent to....
1
10
A)
C)
3
30
4
44
B)
4
44
D)
4
44
Which fraction is equivalent to....
3
4
A)
12
20
C)
16
20
B)
18
20
D)
15
20
Which fraction is equivalent to....
2
5
A)
6
25
C)
8
22
B)
6
15
D)
12
35
Which fraction is equivalent to....
5
6
A)
15
24
C)
35
36
B)
D)
30
36
10
18
Which fraction is equivalent to....
4
9
A)
12
54
C)
8
27
B)
16
81
D)
16
36
Which fraction is equivalent to....
5
7
A)
10
21
C)
30
42
B)
35
35
D)
15
28
Which fraction is equivalent to....
9
11
A)
63
77
C)
63
88
B)
27
22
D)
45
44
Cancelling fractions down
It is often best to have the numbers as small as
possible when we write fractions
Instead of
12
20
we would have
3
5
We have cancelled the fractions down, by dividing top and
bottom numbers by the same number (in this case 4)
15
3
=
35
7
Divide by 5
24 = 2
36
3
Divide by 12
55
5
=
66
6
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
Cancel completely
12
15
A)
3
5
C)
2
5
B)
3
4
D)
4
5
Cancel completely
4
8
A)
1
3
C)
1
2
B)
2
8
D)
1
4
Cancel completely
7
21
A)
3
7
C)
1
8
B)
1
3
D)
1
7
Cancel completely
15
25
A)
C)
3
4
5
6
B)
D)
4
5
3
5
Cancel completely
28
32
A)
C)
7
8
14
16
B)
7
14
D)
4
6
Cancel completely
27
36
A)
5
7
C)
6
8
B)
3
5
D)
3
4
Cancel completely
24
60
A)
3
8
C)
2
7
B)
2
5
D)
1
5
Cancel completely
55
66
A)
8
9
C)
6
7
B)
D)
5
6
4
6
Cancel completely
48
64
A)
C)
3
4
3
5
B)
4
6
D)
2
3
Cancel completely
56
72
A)
1
2
C)
7
9
B)
2
5
D)
6
7
Mixed numbers and improper fractions
When you see a fraction with a large number in front of it,
this is a MIXED NUMBER.
2
2
3
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 an IMPROPER FRACTION
5
3
8
4
9
2
Mixed numbers and improper fractions
You need to be able to:
• turn MIXED NUMBERS into IMPROPER
FRACTIONS
•turn IMPROPER FRACTIONS into MIXED
NUMBERS
Improper fractions to mixed numbers
14
3
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:
14
2
= 43
3
Improper fractions to mixed numbers
19
5
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:
19
4
= 35
5
Improper fractions to mixed numbers
31
10
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:
31
1
= 3 10
10
Mixed Numbers to Improper fractions
To turn the mixed numbers into top heavy fractions:
3
1
10
31
=
10
Multiply these numbers together= 30
Add on the number at the top= 31 (this will be the top number)
The number at the bottom will stay the same
Mixed Numbers to Improper fractions
To turn the mixed numbers into top heavy fractions:
5
3
4
23
=
4
Multiply these numbers together= 20
Add on the number at the top= 23 (this will be the top number)
The number at the bottom will stay the same
Mixed Numbers to Improper fractions
To turn the mixed numbers into top heavy fractions:
6
2
5
32
=
10
Multiply these numbers together= 30
Add on the number at the top= 32 (this will be the top number)
The number at the bottom will stay the same
Improper fractions
10 multiple choice
questions
2
3
2=
A)
22
3
C)
8
3
B)
4
3
D)
7
3
4
5
3=
A)
17
5
C)
34
5
B)
19
5
D)
12
5
1
2
4=
A)
8
2
C)
12
2
B)
4
2
D)
9
2
3
5
10 =
A)
53
5
C)
35
5
B)
13
4
D)
50
5
1
3
6=
A)
18
3
C)
6
3
B)
9
3
D)
19
3
10
3
A)
1
C)
2
=
9
3
B)
3
1
3
D)
9
1
3
1
3
57
8
A)
8
C)
7
=
1
8
B)
6
1
8
D)
9
2
8
3
8
15
4
A)
4
C)
3
=
3
4
B)
3
1
4
3
4
D)
4
1
4
21
10
A)
2
C)
10
1
10
1
2
=
B)
1
11
10
D)
2
11
20
26
5
A)
4
C)
6
=
1
5
B)
1
5
D)
5
6
5
1
5
5
Fractions and Percentages
• Think of percentages as fractions with 100 as
the denominator so,
17 % =
32 % =
88 % =
17
100
32
100
88
100
Fractions and Percentages
• Some fractions can be simplified
25 % =
55 % =
30 % =
25
100
55
100
30
100
=
1
4
11
20
=
3
10
=
Fractions and Percentages
To 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.
12
20
x5
60%
60
100
Fractions and Percentages
To 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.
7
10
x10
70%
70
100
Fractions and Percentages
Sometimes you need to simplify the fraction first.
14 2
=
35 5
x20
40%
40
100
Fractions and Percentages
Sometimes you need to simplify the fraction first.
26 13
=
40 20
x5
65%
65
100
Practise Questions, click to show answers
60%
1
4
70%
33
100
8%
51
100
27%
4
5
80%
1
5
Fractions to Percentages
10 multiple choice questions,
work out your answer then
click to see if you were right
Convert this fraction to a percentage
1
2
A)
20%
B)
100%
C)
50%
D)
40%
Convert this fraction to a percentage
1
4
A)
40%
B)
25%
C)
4%
D)
2%
Convert this fraction to a percentage
1
10
A)
10%
B)
100%
C)
1%
D)
20%
Convert this fraction to a percentage
1
5
A)
2%
B)
15%
C)
5%
D)
20%
Convert this fraction to a percentage
3
4
A)
80%
B)
12%
C)
45%
D)
75%
Convert this fraction to a percentage
21
100
A)
0.21%
B)
2.1%
C)
210%
D)
21%
Convert this fraction to a percentage
4
10
A)
4%
B)
40%
C)
44%
D)
10%
Convert this fraction to a percentage
3
5
A)
6%
B)
15%
C)
60%
D)
80%
Convert this fraction to a percentage
1
100
A)
100%
B)
1%
C)
0.1%
D)
0.110%
Convert this fraction to a percentage
1
3
A)
33.333333.. %
B)
13%
C)
3%
D)
11%
Fractions and Decimals
Thousandths
Hundredths
Tenths
Units
Tens
Hundreds
To turn fractions into decimals and decimals into
fractions we need to remember column names
000.000
Hundredths
Tenths
Decimals to Fractions
Tenths
0.03
is 3 hundredths
0.5
is 5 tenths 5
10
3
100
Hundredths
Tenths
Decimals to Fractions
Hundredths
Tenths
0.12
0.01
is 12 hundredths
is 1 hundredth 1
100
12
100
Thousandths
Hundredths
Tenths
Decimals to Fractions
Thousandths
Hundredths
Tenths
0.032
0.154
Don’t forget you may
have to simplify
is 32 thousandths
32
1000
is 154 thousandths 154
1000
64
= 0.64
100
152 = 0.152
1000
Thousandths
Hundredths
Tenths
Units
7
=
0.7
10
Tens
Hundreds
Fractions to Decimals
000.000
3
= 0.03
100
53 = 0.053
1000
2 = 0.002
1000
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
1
2
1
4
3
5
3
10
11
20
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
1
2
10
20
5
20
1
4
5
20
3
5
15
20
3
10
6
20
11
20
11
20
10
20
11
20
15
20
Now order them
6
20
What denominator do we need now?
1
3
20
60
20
60
4
6
40
60
2
5
24
60
5
12
25
60
5
6
50
60
25
60
40
60
50
60
Now order them
24
60
Ordering Fractions- click for answers
ANSWERS
1. 1/4 3/8
2. 2/5 ½
3. 1/3 5/12
4. 1/4 1/2
5. 1/4 2/5
6. 1/3 4/9
7. 2/6 1/4
8. 2/7 2/4
½ and 4/8
3/5 and 6/10
1/1
4/6
2/3
5/6
1/2
6/10
1/2
2/3
5/12
2/3
5/8
11/14
3/4
2/29
3/4
7/8
3/4
5/6
7/9
3/2
Things you should know
The top number of a fraction is the
NUMERATOR
The bottom number of a fraction is the
DENOMINATOR
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