Equivalent FractionsEquivalent Fractions

One WholeOne Whole

11

Equivalent FractionsEquivalent Fractions

Cut them in halfCut them in half

Equivalent FractionsEquivalent Fractions

Shown is one halfShown is one half

11

22

How many How many pieces we pieces we wantwant

How many How many pieces it’s cut pieces it’s cut intointo

Equivalent FractionsEquivalent Fractions

Shown is one halfShown is one half

11

22

NUMERATORNUMERATOR

DENOMINATORDENOMINATOR

Equivalent FractionsEquivalent Fractions

I cut my shape againI cut my shape again

I still showI still show

11

22

Equivalent FractionsEquivalent Fractions

But I also showBut I also show

22

44

Equivalent FractionsEquivalent Fractions

One half is One half is EQUIVALENT TOEQUIVALENT TO

2 quarters 2 quarters

11

22

22

44

Equivalent FractionsEquivalent Fractions

11

22

22

44

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

Equivalent FractionsEquivalent Fractions

We can use equivalent fraction to make We can use equivalent fraction to make our numbers easier to handle.our numbers easier to handle.

Smaller numbers are SIMPLESmaller numbers are SIMPLE

160160

200200

1166

2200

44

55

÷ 10÷ 10

÷ 10÷ 10

÷ 4÷ 4

÷ 4÷ 4

Equivalent FractionsEquivalent Fractions

This fraction is as simple as we can make itThis fraction is as simple as we can make it

160160

200200

44

55

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

Watch out for this language in the Watch out for this language in the future. It is often used in Key Stage future. It is often used in Key Stage 3.3.

Simplest formSimplest form

Lowest termsLowest terms

SimplifiedSimplified

Cancelled Cancelled downdown

Equivalent FractionsEquivalent Fractions

1515

4545

6060

8080

Look for numbers that Look 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.bigger than 1.

We call these We call these COMMON FACTORSCOMMON FACTORS

Equivalent FractionsEquivalent Fractions

1515

4545

÷ 3÷ 3

÷ 3÷ 3

6060

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 shared can both be shared by 3.by 3.

A common factor A common factor here is 10here is 10

Equivalent FractionsEquivalent Fractions

1515

4545

55

1155

÷ 3÷ 3

÷ 3÷ 3

6060

8080

66

88

÷ 10÷ 10

÷ 10÷ 10

Equivalent FractionsEquivalent Fractions

1515

4545

55

1155

÷ 3÷ 3

÷ 3÷ 3

÷ 5÷ 5

÷ 5÷ 5

6060

8080

66

88

÷ 10÷ 10

÷ 10÷ 10

÷ 2÷ 2

÷ 2÷ 2

Equivalent FractionsEquivalent Fractions

1515

4545

55

1155

11

33

÷ 3÷ 3

÷ 3÷ 3

÷ 5÷ 5

÷ 5÷ 5

6060

8080

66

88

33

44

÷ 10÷ 10

÷ 10÷ 10

÷ 2÷ 2

÷ 2÷ 2

Equivalent FractionsEquivalent Fractions

1515

4545

11

33

6060

8080

33

44

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

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

Equivalent FractionsEquivalent Fractions

1515

4545

11

33

6060

8080

33

44

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