FRACTIONS

• Equivalence

• Simplifying

• Ordering

• Arithmetic

• Fraction of

Equivalent Fractions

• Fractions are made up of two parts

• A top number and a bottom number

• Although fractions may look different they can have the same value

Equivalent Fractions

• If we multiply the top number and the bottom number by the same amount the value of the fractions does not change

Simplifying or Cancelling Down

• If we divide top and bottom numbers by the same amount we do not change the value of the fraction

• Dividing to create fractions with smaller number makes the fraction simpler

20

12

40

245

3

40

2410

6

40

24

or

or

Ordering Fractions

• As with all number we need to be able to order and compare fractions

• We can do this using equivalent fractions

• If fractions have the same bottom number then the fraction with larger top number is bigger 7

2

7

4

Comparing Fractions

• Fractions with different bottom numbers• Find the LCM of both bottom numbers• Find the equivalent fraction with the LCM

as bottom number3

2

4

3andCompare

12

8

43

42

x

x12

9

34

33

x

x

3

2

4

3

12

8

12

9 so

Top Heavy Fractions

• Some fractions are larger than 1

• This occurs when the top number is bigger than the bottom number

• We sometimes need to change to a mixed fraction

• DIVIDE OUT and place REMAINDER over BOTTOM NUMBER

7

23

7

23

237

23

7237

23

remainder

dividedby

Top Heavy Fractions

• We can also change mixed fractions into top heavy fractions

11

58

11

3)115(

11

35

x

Adding/Subtracting Fractions

• Adding or subtracting fractions with the same bottom number

• Just add / subtract the top numbers 9

1

9

4

9

57

5

7

2

7

3

Adding / Subtracting fractions

• Adding or Subtracting fractions with different bottom numbers

• We need to change to equivalent fractions and then add / subtract

• Some are straight forward

4

1

4

1

2

14

3

4

1

2

14

2

2

1

and

Adding / Subtracting Fractions

• UPSIDE DOWN IRONING BOARD

5

2

7

3

Adding / Subtracting fractions

• Use the bottom number of one fraction to change the other fraction

5

2

7

3

75

7253

x

xx

35

1415

35

29

Multiplying Fractions

• Multiplying is easier• Multiply the top numbers and multiply the

bottom numbers• Simplify if necessary

35

6

75

32

7

3

5

2

x

xx

Dividing Fractions

• Dividing by a fraction• Step 1 Flip the second fraction i.e the

fraction you are dividing by• Step 2 Multiply

8

11

8

9

24

33

2

3

4

3

3

2

4

3

x

xx

Mixed fractions arithmetic

• There are many ways to attempt this

• The method that always works is to change the fractions into top heavy fractions

• Proceed as for ‘normal’ fractions

560

209

28

11

20

19

11

28

20

1911

28)

54

49511(

11

28)5

9

4

11(

11

62)

5

41

4

32(

x

x

xx

Finding Unitary Fractions of

• Unitary fractions are fractions with one as the top number

• To find a unitary fraction of an amount just divide by the bottom number

976

1

5

1or

70£5350£

350£5

1

of

Finding Fractions of

• We want to find two fifths of £350• Method 1

• We want to find two fifths of £350• Method 2

140£5

700£5

350£2

350£5

2

x

x

140£270£

70£5350£

:350£5

2

x

of

Divide by the bottom numberMultiply by the top

The order is up to you

• http://www.slideshare.net/sbishop2/4-rules-of-fractions