Introduction To Simplifying Fractions

Equivalent FractionsEquivalent Fractions

One WholeOne Whole

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Shown is Shown is one half one half on the lefton the left and and one half on the one half on the rightright..

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NUMERATORNUMERATORHow many pieces we How many pieces we have!have!

DENOMINATORDENOMINATORHow many pieces the How many pieces the whole one is split whole one is split into!into!

Equivalent FractionsEquivalent FractionsI cut my shape I cut my shape againagain

I still haveI still have

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22On the leftOn the left and and one half on the one half on the rightright, but each , but each half is in two half is in two pieces now pieces now (quarters).(quarters).


So we have also So we have also split each half split each half into…into…

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44So we can see how So we can see how 2 quarters is 2 quarters is equal - or equal - or equivalent toequivalent to 1 1 half.half.


One half is One half is EQUIVALENT TOEQUIVALENT TO

2 quarters 2 quarters

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This symbol looks like an equals sign This symbol looks like an equals sign with a third line. It is the with a third line. It is the mathematical sign for EQUIVALENT TO - mathematical sign for EQUIVALENT TO - which means “is worth the same as”.which means “is worth the same as”.


We can find equivalent fractions to We can find equivalent fractions to make our numbers easier to handle by make our numbers easier to handle by finding the lowest equivalent finding the lowest equivalent fraction possible. To do this, we fraction possible. To do this, we just have to divide the numerator just have to divide the numerator and denominator by a number that and denominator by a number that both can be divided by with no both can be divided by with no remainder.remainder.160160

200200

1616

2020

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÷ 10÷ 10

÷ 10÷ 10

÷ 4÷ 4

÷ 4÷ 4

A number that you can divide both the numerator and A number that you can divide both the numerator and the denominator by with no remainder is called a the denominator by with no remainder is called a

COMMON FACTORCOMMON FACTOR


This fraction is This fraction is as simple as we as simple as we can make it, can make it, because there is because there is nothing that we nothing that we can divide both can divide both the numerator and the numerator and denominator by denominator by without a without a remainder! remainder!

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200200

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We can use different language We can use different language for making the fraction as for making the fraction as small as possible. small as possible.

Watch out for this language in Watch out for this language in the future. Finding smaller the future. Finding smaller fractions is often called fractions is often called “simplifying” or “cancelling “simplifying” or “cancelling down” or sometimes even down” or sometimes even “expressing a fraction in its “expressing a fraction in its lowest terms.” lowest terms.”

Lowest termsLowest terms

SimplifiedSimplified

Cancelled Cancelled downdown


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The trick is to look The trick is to look for numbers that for numbers that both the NUMERATOR both the NUMERATOR and the DENOMINATOR and the DENOMINATOR can be divided by.can be divided by.

We want numbers We want numbers bigger than 1, since bigger than 1, since any number divided any number divided by 1 gives you the by 1 gives you the same answer!same answer!We call these We call these COMMON FACTORSCOMMON FACTORS


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÷ 3÷ 3

÷ 3÷ 3

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8080

÷ 10÷ 10

÷ 10÷ 10

These numbers These numbers have 3 as a have 3 as a common factor.common factor.

This means they This means they can both be can both be divided by 3 with divided by 3 with no remainder.no remainder.

A common factor A common factor in this example in this example is 10, because is 10, because both 60 and 80 both 60 and 80 can be divided can be divided by 10 exactly!by 10 exactly!


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1515

÷ 3÷ 3

÷ 3÷ 3

6060

8080

66

88

÷ 10÷ 10

÷ 10÷ 10


1515

4545

55

1515

÷ 3÷ 3

÷ 3÷ 3

÷ 5÷ 5

÷ 5÷ 5

6060

8080

66

88

÷ 10÷ 10

÷ 10÷ 10

÷ 2÷ 2

÷ 2÷ 2


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4545

55

1515

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÷ 3÷ 3

÷ 3÷ 3

÷ 5÷ 5

÷ 5÷ 5

6060

8080

66

88

33

44

÷ 10÷ 10

÷ 10÷ 10

÷ 2÷ 2

÷ 2÷ 2


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4545

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33

6060

8080

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If the top If the top number is a 1, number is a 1, we know we can we know we can stop!stop!

If the top If the top and bottom and bottom number are number are not not DIVISIBLE by DIVISIBLE by the same the same number, we number, we stop.stop.


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They have no They have no FACTORS in FACTORS in common other common other than 1than 1

They have no They have no FACTORS in FACTORS in common other common other than 1than 1

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Introduction To Simplifying Fractions