Sixer Guide to:

Equivalent Fractions

You have exactly 30 seconds to do the following:

1) Open you math Keytab to a new page2) Write today’s date on the left with you

name on the right3) Underline today’s title which will be

“Equivalent fractions”.

Equivalent fractionsA fraction can have many different appearances, these are called equivalent fractionsIn 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

21 =

42

Or we can cut the original cake into 6 equal pieces,

Equivalent fractionsA fraction can have many different appearances, these are called equivalent fractionsNow we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same.

Therefore,

21 =

42 =

63

If you don’t like this, we can cut the original cake into 8 equal pieces,

Equivalent fractionsA fraction can have many different appearances, they are called equivalent fractionsThen we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same.

21 =

42 =

63 =

84

We can generalize this to

21

= nn

21 whenever n is not 0

Therefore,Wow, that’s confusing!

Equivalent Fractions

One Whole

1

Cut them in half

Equivalent Fractions

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 againI still show

1 2

Equivalent Fractions

But I also show

2 4

Equivalent Fractions

One half is EQUIVALENT TO2 quarters

12

24

Equivalent Fractions

12

24

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

160200

1620

45

÷ 10

÷ 10

÷ 4

÷ 4

Equivalent Fractions

1545

6080

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

1545

÷ 3

÷ 3

6080

÷ 10

÷ 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

1545

515

÷ 3

÷ 3

6080

68

÷ 10

÷ 10

Equivalent Fractions

1545

515

÷ 3

÷ 3

÷ 5

÷ 5

6080

68

÷ 10

÷ 10

÷ 2

÷ 2

Equivalent Fractions

1545

515

13

÷ 3

÷ 3

÷ 5

÷ 5

6080

68

34

÷ 10

÷ 10

÷ 2

÷ 2

Equivalent Fractions

1545

13

6080

34

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

1545

13

6080

34

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:

is not reduced because 10 can divide into both 110 and 260.

is reduced.

is reduced

260110

158

2311

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:

Are2114 and

4530 equal?

2114 reduce

32

721714

4530 reduce

96

545530

reduce

32

3936

Now we know that these two fractions are actually the same!

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!

4024

4230

4230

4024

2012

240224

reduce

53

420412

75

642630