Transcript Fractions and decimals

KS3 Mathematics
N5 Using Fractions
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Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions
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Quarter or not?
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Quarters
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Dividing shapes into given fractions
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Fractions of shapes
Remember, one quarter is written:
one thing
1
divided into
four equal parts
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4
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Fractions of shapes
What fraction of this diagram is shaded?
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Fractions of shapes
Two fifths is written as:
two parts
2
numerator
5
denominator
out of
five parts altogether
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Fractions of shapes activity
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Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions
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Equivalent fractions
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Equivalent fractions
What does
equivalent
mean?
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Equivalent fractions
Look at this diagram:
×2
3
4
=
×2
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×3
6
8
=
18
24
×3
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Equivalent fractions
Look at this diagram:
×3
2
3
=
×3
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×4
6
9
=
24
36
×4
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Equivalent fractions
Look at this diagram:
÷3
18
30
=
÷3
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÷2
6
10
=
3
5
÷2
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Equivalent fractions
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Cancelling fractions to their lowest terms
A fraction is said to be expressed in its lowest terms if the
numerator and the denominator have no common factors.
Which of these fractions are expressed in their lowest terms?
14
16
7
8
20
27
3
13
15
21
5
7
14
35
2
5
32
15
Fractions which are not shown in their lowest terms can be
simplified by cancelling.
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Drag and drop equivalent fractions
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Mixed numbers and improper fractions
When the numerator of a fraction is larger than the
denominator it is called an improper fraction.
For example,
15
is an improper fraction.
4
We can write improper fractions as mixed numbers.
15
4
can be shown as
15
=
4
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3
3
4
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Improper fraction to mixed numbers
37
Convert
to a mixed number.
8
37
8
8
8
8
+
+
+
=
8
8
8
8
8
+
1+1+1+1+
5
= 4
8
=
37 ÷ 8 = 4 remainder 5
5
8
5
8
37
=
8
This number is the remainder.
4
5
8
This is the number of times 8 divides into 37.
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Mixed numbers to improper fractions
2
to a mixed number.
7
3
2
37 =1 + 1 + 1 +
Convert
2
7
7
7
7
2
=
+
+
+
7
7
7
7
23
=
7
To do this in one step,
… and add this number …
3
2
23
=
7
7
… to get the numerator.
Multiply these numbers together …
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Find the missing number
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Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions
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Writing one amount as a fraction of another
Sometimes we need to know one amount as a fraction of
another.
What fraction of one week is three days?
Monday
Tuesday
Wednesday
3
Thursday
Friday
Saturday
Sunday
three days
out of
7
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seven days altogether
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Writing a number as a fraction of another
We can describe one number as a fraction of another.
What fraction of 72 is 45?
÷9
45
5
We write
=
72
8
÷9
We can say 45 is 5/8 of 72.
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Writing a number as a fraction of another
What fraction of 2.5 metres is 75 centimetres?
First, convert 2.5 metres to 250 centimetres.
÷25
75
3
We write
=
250
10
÷25
We can say 75 centimetres is 3/10 of 5 metres.
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Writing a number as a fraction of another
We can also write a larger number as a fraction of a smaller one.
What fraction of 25 is 35?
÷5
35
7
We write
=
25
5
÷5
We can say 35 is 7/5 of 25 or 12/5 of 25.
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Writing one amount as a fraction of another
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Fractions of distances
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Fractions on a clock face
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Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions
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Pelmanism – Fractions and decimals
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Comparing decimals and fractions
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Converting decimals to fractions
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Using equivalent fractions over 10, 100, or 1000
We can convert some fractions to decimals by converting
them to an equivalent fraction over 10, 100 or 1000.
For example,
×5
13
65
=
20
100
×5
65
= 0.65
100
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Converting fractions to decimals
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Fractions and division
A fraction can be thought of as the result of dividing one
whole number by another.
For example,
30
30 ÷ 8 =
=
8
3
6
=
8
3
3
4
We can also write this answer as a decimal:
3
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3
=
4
3.75
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Converting fractions to decimals
There are many ways to convert a fraction to a decimal.
The quickest way is to use a calculator.
For example,
5
= 5 ÷ 16 = 0.3125
16
This is a terminating decimal.
6 = 6 ÷ 11 = 0.545454… This is a recurring decimal.
11
All recurring and terminating decimals can be written as
exact fractions.
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Recurring decimals
.
1
= 1 ÷ 3 = 0.33333… = 0.3
3
.
1
= 1 ÷ 6 = 0.16666… = 0.16
6
..
2
= 2 ÷ 11 = 0.18181… = 1.18
11
.
.
3
= 3 ÷ 7 = 0.42857142857142… = 0.428571
7
3
We can also write
= 0.43 (to 2 decimal places).
7
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Using short division
We can also convert fractions to decimals using short division.
For example,
5
=5÷7
7
0 .7 1 4 2 8 5 7 . . .
5
1
3
2
6
4
5
7 5.0 0 0 0 0 0 0
.
.
5
= 0.714285
7
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Contents
N5 Using fractions
N5.1 Fractions of shapes
N5.2 Equivalent fractions
N5.3 One number as a fraction of another
N5.4 Fractions and decimals
N5.5 Ordering fractions
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Using diagrams to compare fractions
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Using decimals to compare fractions
3
7
Which is bigger
or
?
8
20
We can compare two fractions by converting them to
decimals.
3
8
= 3 ÷ 8 = 0.375
7 = 7 ÷ 20 = 0.35
20
0.375 > 0.35
so
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3
8
>
7
20
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Using equivalent fractions
3
5
Which is bigger
or
?
8
12
Another way to compare two fractions is to convert them to
equivalent fractions.
First we need to find the lowest common multiple of 8 and 12.
The lowest common multiple of 8 and 12 is 24.
3
5
Now, write
and
as equivalent fractions over 24.
8
12
×3
3
8
9
=
24
×3
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×2
and
5
10
=
12
24
so,
3
8
<
5
12
×2
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Using a graph to compare fractions
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Ordering fractions
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Fractions on a number line
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Mid-points
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Connect three fractions
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