Four rules of fractions

How to do

Addition and Subtraction

The simple bits

5

1

5

1

5

2

1/7

1/7

1/7

1/7 1/7

1/7

1/7

1/7

1/7

1/7

1/7

1/7

7

2

7

6

7

4

1/8

1/8

1/8

1/8

1/8

1/8

1/8

8

3

8

1

2

1

8

4

Why were they so simple?

• Because they all had the same denominator

• They were all from the same families

What if they are of different families?

1/2

1/4

4

1

2

1

4

3 Because we

know that 1/2 = 2/4

1/8

1/8

1/8

1/4

1/8

1/8

1/8

1/8 1/8

8

5

4

1

8

3

Because we know that 1/4 = 2/8

But what about 1/4 + 1/3?

We can’t add, because they have different denominators – not in the

same family.

1/4

1/3

What family can we change them to?

What will be the new denominator?

1/4

1/3

4 and 3 both divide into 12

So we can change them into 12ths

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

1/12

12

3

4

1

12

4

3

1

12

7

3

1

4

1

What about 1/2 – 2/5?

What family can we change them to?

What will be the new denominator?

1/2

1/5

1/5

2 and 5 both divide into 10

So we can change them into 10ths

1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10 1/10

1/10

1/10

1/10

1/10

10

5

2

1

10

4

5

2

We can do this without the pictures:

10

1

10

4

10

55

2

2

1

Make fractions using a set of numbered cards, and try some addition and subtraction yourself.

Check them with a calculator

Share one example from your group with the rest of the class.

Multiplication and Division

Easy one:

3

2

3

12

1/3

1/3

2/3

+ =

3

22

3

1And because of commutivity,

we can also say:

With two fractions:

half of ¾?

8

3

4

3

2

1

8

3

2

1

4

3or

Without the pictures:

10

3

2

1

5

3

21

4

7

2

3

2

2

1

12

6

4

3

3

2

And division?

Unfortunately, there is no easy way to show diagrams for division of fractions.

Nor is there any obvious way of trying to make sense of it.

The best thing is probably just to learn the rule!

To divide by a fraction

• Do not change the first fraction

• Change the division sign into a multiplication sign

• Turn the second fraction upside down

• Multiply the fractions

6

5

12

10

24

20

3

4

8

5

4

3

8

5

For example:

5

11

5

6

1

2

5

3

2

1

5

3

8

5

24

15

8

3

3

5

8

3

3

21

And finally, what to do about mixed numbers:

2

12

2

5

6

15

12

30

3

2

4

15

2

3

4

15

2

11

4

33

Make fractions using a set of numbered cards, and try some multiplication and division yourself.

Check them with a calculator