This document explains fractions including:
- The numerator and denominator define a fraction, with the denominator indicating the number of equal parts in the whole and the numerator indicating how many parts are selected.
- Fractions can be proper, improper, mixed numbers, or equivalent. Equivalent fractions have the same value when simplified to their lowest terms.
- To order fractions, find a common denominator by finding the lowest common multiple of the denominators, then compare the numerators.
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http://sandymillin.wordpress.com/iateflwebinar2024
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This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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18. Simplifying Fractions
To simplify a fraction, we find an
equivalent fraction which uses
the smallest numbers
possible.
We do this by
dividing.
We need to know our tables
for this!
Ask yourself, what can I
divide both 24 and 40 by?
8 is the biggest number we
can divide both by and 3/5
uses the smallest possible
numbers as we cannot
divide them by anything
else.
19. Look at this one
28
56
The first thing I notice is
that 28 and 56 are both in
the 7 times table. So I’m
going to divide both
numbers by 7.
28
56
÷
÷
4
7=
7= 8
Is this simplified? NO!
4
8
I can still divide
both numbers
by 4.
÷
÷
4=
4=
1
8
26. We can see that 2/8 is the same length as 1/4
So 2/8 = 1/4
They are equivalent fractions
1 whole
1/2
1/2
1/4
1/4
1/4
1/4
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
31. We can see that ½ is
the same as 2/4, 3/6,
4/8 and 5/10.
These are
EQUIVALENT
FRACTIONS.
32. How do we know that two fractions are
the same?
We cannot tell whether two fractions are the same
until we simplify them to their lowest terms.
A fraction is in its lowest terms (simplified) if we cannot find a
whole number (other than 1) that can divide into both its
numerator and denominator (A common factor).
Examples:
is not reduced because 2 can divide into
both 6 and 10.
is not reduced because 5 divides into
both 35 and 40.
10
6
40
35
33. How do we know if two fractions are the same?
More examples:
is not reduced because 10 can divide
into both 110 and 260.
is reduced.
is reduced
260
110
15
8
23
11
To find out whether two fraction are equal, we
need to reduce them to their lowest terms.
34. How do we know that two fractions are the same?
Examples:
Are
21
14 and
45
30 equal?
21
14 reduce
3
2
7
21
7
14
45
30 reduce
9
6
5
45
5
30
reduce
3
2
3
9
3
6
Now we know that these two fractions are
actually the same!
35. Another way to find equivalent
fractions…
LOOK FOR A PATTERN
1 2 3 4 5
2 4 6 8 10
36. How do we know that two fractions are the same?
Another example:
Are and equal?
reduce
reduce
This shows that these two fractions are not
the same!
40
24
42
30
42
30
40
24
20
12
2
40
2
24
reduce
5
3
4
20
4
12
7
5
6
42
6
30
41. Improper Fractions and Mixed Numbers
An improper fraction can be converted to a
mixed number and vice versa.
3
5
An improper fraction is a
fraction with the numerator larger
than or equal to the
denominator.
A mixed number is a whole
number and a fraction
together
7
3
2
Any whole number can be
transformed into an improper
fraction.
,
1
4
4
7
7
1
42. Improper Fractions and Mixed Numbers
3
2
1
3
5
Converting improper fractions
into mixed numbers:
- divide the numerator by the
denominator
- the quotient is the leading number,
- the remainder as the new numerator.
7
17
7
3
7
2
7
3
2
Converting mixed
numbers into improper
fractions.
,
4
3
1
4
7
More examples: 5
1
2
5
11
50. ORDERING FRACTIONS
You will be asked to order fractions from
Greatest to Least and from Least to Greatest
You have three strategies to choose from:
1. Draw a picture
2. Use Bottoms Up
3. Use Fraction Fringe
52. ORDERING FRACTIONS WITH BOTTOMS
UP
1 1 1
3 6 9
1. Compare 1 and 1
3 6
2. Compare 1 and 1
3 9
3. Compare 1 and 1
6 9
1 1
3 6
>
1 1
3 9
>
1 1
6 9
>
Since 1/3 was largest 2 times, it is the largest fraction!
1/6 is next, followed by 1/9. 1 1 1
9 , 6 , 3
53. Ordering fractions
1 2 3 4 7
9 9 9 9 9
(if ordered smallest largest)
If the DENOMINATOR is the same, look at the
NUMERATORS, and put the fractions in order.
54. Ordering fractions
We need to convert our fractions to
EQUIVALENT fractions of the same
DENOMINATOR. We will come back to this
example.
If the DENOMINATOR is different, we have a
problem that must be dealt with differently.
3 7 4 1 2
6 8 4 3 4
55. Ordering fractions
If the DENOMINATOR is the different, we have
a problem that must be dealt with differently.
4 3
6 9
Here’s an easier example, with just 2
fractions to start us off.
56. Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
4 3
6 9
This means that we check to see which
numbers are in the 6 times table, and the 9
times table. We need a number that appears
in both lists.
57. Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
Multiples of 6 are
6, 12, 18, 24, 30, 36, 42, 48, 54, 60……
Multiples of 9 are
9, 18, 27, 36, 45, 54, 63, 72, 81, 90……
58. Ordering fractions
COMMON MULTIPLES are:
Multiples of 6 are
6, 12, 18, 24, 30, 36, 42, 48, 54, 60……
Multiples of 9 are
9, 18, 27, 36, 45, 54……
59. Ordering fractions
COMMON MULTIPLES are:
18, 36 and 54. There are others that are higher, but we
only look at smaller numbers.
Remember: Smaller numbers are SIMPLER.
18 is the smallest number that is common, so we’ll use
this.
60. Ordering fractions
4
6
We need to convert these fractions so they
have the same denominator.
12
18
x 3
x 3 3
9
6
18
x 2
x 2
62. Ordering fractions
3 4
9 6
And this is the correct order
Because these EQUIVALENT
FRACTIONS are in order
12
18
6
18
63. Ordering fractions
The LOWEST COMMON DENOMINATOR is 24
– check for all the multiples of the
DENOMINATORS. 24 is the first number to
appear in all the lists.
Remember our example
3 7 4 1 2
6 8 4 3 4
64. Ordering fractions
The LOWEST COMMON DENOMINATOR is 24
– check for all the multiples of the
DENOMINATORS. 24 is the first number to
appear in all the lists.
Convert to 24ths
12 21 24 8 12
24 24 24 24 24
65. Ordering fractions
This tells you how large our fractions are.
Check which order they go in.
Convert to 24ths
2nd 4th 5th 1st 3rd
3 7 4 1 2
6 8 4 3 4
