Transcript Equivalent Fractions interactive mathx

Sixer Guide to:
Equivalent Fractions
You have exactly 30 seconds to do the following:
1) Open you math Keytab to a new page
2) Write today’s date on the left with you name
on the right
3) Underline today’s title which will be “Equivalent
fractions”.
Equivalent fractions
A fraction can have many different appearances,
these are called equivalent fractions
In the following picture we have ½ of a cake
because the whole cake is divided into two
equal parts and we have only one of those
parts.
But if we cut the cake into
smaller equal pieces, we can
see that
1
2
= 2
4
Or we can cut the original
cake into 6 equal pieces,
Equivalent fractions
A fraction can have many different appearances,
these are called equivalent fractions
Now we have 3 pieces out of 6 equal pieces,
but the total amount we have is still the same.
Therefore,
1
2
=
2
4
=
3
6
If you don’t like this, we can
cut the original cake into 8
equal pieces,
Equivalent fractions
A fraction can have many different appearances,
they are called equivalent fractions
Then we have 4 pieces out of 8 equal pieces,
but the total amount we have is still the same.
Wow, that’s confusing!
Therefore,
1 = 2 = 3 = 4
2
4
6
8
We can generalize this to
1
1 n
whenever n is not 0
=
2
2 n
Equivalent Fractions
One Whole
1
Equivalent Fractions
Cut them in half
Equivalent Fractions
Shown is one half
1
2
How many
pieces we want
How many
pieces it’s cut
into
Equivalent Fractions
Shown is one half
1
2
NUMERATOR
DENOMINATOR
Equivalent Fractions
I cut my shape again
I still show
1
2
Equivalent Fractions
But I also show
2
4
Equivalent Fractions
One half is
EQUIVALENT TO
2 quarters
1
2
2
4
Equivalent Fractions
1
2
2
4
This symbol looks like an equals sign with a third line.
It is the mathematical sign for EQUIVALENT TO which means “is worth the same as”.
Equivalent Fractions
We can use equivalent fraction to make our
numbers easier to handle.
Smaller numbers are SIMPLE
160
200
÷ 10
÷ 10
16
20
÷4
÷4
4
5
Equivalent Fractions
15
45
60
80
Look for numbers that
both the NUMERATOR
and the DENOMINATOR
can be divided by.
We want numbers bigger
than 1.
We call these
COMMON FACTORS
Equivalent Fractions
15
÷3
45
÷3
60
÷ 10
80
÷ 10
These numbers have
3 as a common factor.
This means they can
both be shared by 3.
A common factor
here is 10
Equivalent Fractions
15
÷3
5
45
÷3
15
60
÷ 10
6
80
÷ 10
8
Equivalent Fractions
15
÷3
5
÷5
45
÷3
15
÷5
60
÷ 10
6
÷2
80
÷ 10
8
÷2
Equivalent Fractions
15
÷3
5
÷5
1
45
÷3
15
÷5
3
60
÷ 10
6
÷2
3
80
÷ 10
8
÷2
4
Equivalent Fractions
15
1
45
3
60
3
80
4
If the top number is
a 1, we know we can
stop.
If the top and
bottom number
are not
DIVISIBLE by
the same
number, we
stop.
Equivalent Fractions
15
1
45
3
60
3
80
4
They have no
FACTORS in
common other
than 1
They have no
FACTORS in
common other
than 1
You now have exactly 30 seconds to
do the following:
Open you math text to page 164
How do we know that two fractions are the same?
More examples:
110
260
is not reduced because 10 can divide
into both 110 and 260.
8
15
is reduced.
11
23
is reduced
To find out whether two fraction are equal, we
need to reduce them to their lowest terms.
How do we know that two fractions are the same?
Examples:
Are 14
21
and 30
45
equal?
14
21
reduce
14  7 2

21  7 3
30
45
reduce
30  5 6

45  5 9
reduce
63 2

93 3
Now we know that these two fractions are
actually the same!
How do we know that two fractions are the same?
Another example:
24
Are
40
and
24
40
reduce
30
42
reduce
30
42
equal?
24  2 12

40  2 20
reduce
12  4 3

20  4 5
30  6 5

42  6 7
This shows that these two fractions are not
the same!