1. Adding, Subtracting, Multiplying and Dividing Fractions

2. EXAMPLES
1) Find the Lowest Common Multiple (LCM) of the following pairs of numbers:
3 and 7
(b)
6 and 9
Write out the multiples of 3 and 7 and circle the lowest common one
Write out the multiples of 6 and 9 and circle the lowest common one
3 →
6 →
3, 6, 9, 12, 15, 18, 21, 24 …
6, 12, 18,
7 →
9 →
7, 14, 21, 28 …
9, 18, 27, 36 …
LCM = 21
LCM = 18

3. Warm up What is the lowest common multiple of: 2 6 = 3 and 4 12 15 5
Find a the missing numbers
What is the lowest common multiple of: 2 6 =
3 and 4 12 15 5
5 and 6 30 3 15 = 8
4 and 6 12 40
3 and 8 24 25 5 = 6
5 and 10 10 30

4. Take out your homework

5. Take out your homework

6. Adding, Subtracting, Multiplying and Dividing Fractions
21/05/14
Learning Objective:
To be able to add, subtract, multiple and divide fractions
Learning outcome:
To be able to add, subtract, multiply and divide the following fractions

7. Adding Fractions There are 3 Simple Steps to add fractions:
Step 1: Make sure the bottom numbers (the denominators) are the same.
Step 2: Add the top numbers (the numerators), put the answer over the denominator.
Step 3: Simplify the fraction (if needed).

8. Examples = 5 7 2 7 + 3 7 = 6 9 2 9 + 4 9 = 4 11 1 11 + 3 11

9. What if the denominators were different? Any idea?
We need to make sure the denominator of both fractions is the same before we add. = + = 2 5 + 3 10 4 10 3 10 7 10
We need a number in the 3 and 12 times table to use as our bottom number + 1 3 = = 9 12 + 5 12 4 12 5 12

10. We need a number in the 5 and 6 times table to use as our bottom number= 2 5 + 3 6 = 27 30 12 30 + 15 30

11. On your own

12. Subtracting Fractions= 3 5 4 5 - 1 5 = 7 14 11 14 - 4 14 = 2 11 9 11 - 7 11

13. We need to make sure the denominator of both fractions is the same before we add or subtract= 4 5 - 3 15 = - 12 15 3 15 9 15 = - = 4 12 3 4 3 4 - - 5 12 9 12 5 12

14. - = 7 8 2 3 - = 21 24 16 24 5 24

16. Multiplying Fractions3 4 5 8 15 32 x = 1 2 7 5 6 10 42 5 21 2 7 5 6 5 21 x x = = = 3 3 5 7 9 21 45 7 15 x = =

17. Dividing Fractions 4 7 3 4 4 7 4 3 16 21 ÷ = x = 4 1 2 7 8 1 2 8 7 814 4 7 4 7 1 2 8 7 ÷ = x = = x = 1 2 3 4 5 8 3 4 8 5 24 20 6 5 3 4 8 5 6 5 ÷ x = = x = = 1

19. 3 32 5 48 1 1 9 1 1 4 25 5 1 7 16 2 65 18 3 11 18 = 2 1 11 1 11 = 1 1 4 2 8 1 8 = 1 1 1 1 1 1 3 = 2 1 1 2 1 1 2 1 2 4 1

20. Mixed numbers and top heavy fractions
When you see a fraction with a large number in front of it, this is a MIXED NUMBER. 2 2 3
This means, 2 and 2 thirds
When we have a fraction where the number at the top (NUMERATOR) is bigger than the number at the bottom (DENOMINATOR) we have a TOP HEAVY FRACTION 5 3 8 4 9 2

21. Mixed numbers and top heavy fractions
You need to be able to:
turn MIXED NUMBERS into TOP HEAVY FRACTIONS
turn TOP HEAVY FRACTIONS into MIXED NUMBERS

22. Top heavy fractions to mixed numbers14 3
How many 3’s go into 14? 4
What is the remainder? 2
So we can make 4 wholes and we have 2 thirds left over: 14 3 = 4 2 3

23. Top heavy fractions to mixed numbers19 5
How many 5’s go into 19? 3
What is the remainder? 4
So we can make 3 wholes and we have 4 fifths left over: 19 5 = 3 4 5

24. Top heavy fractions to mixed numbers31 10
How many 10’s go into 31? 3
What is the remainder? 1
So we can make 3 wholes and we have 1 tenth left over: 31 10 = 3 1 10

25. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions: 3 1 10 31 10 =
Multiply these numbers together= 30
Add on the number at the top=
31 (this will be the top number)
The number at the bottom will stay the same

26. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions: 5 3 4 23 4 =
Multiply these numbers together= 20
Add on the number at the top=
23 (this will be the top number)
The number at the bottom will stay the same

27. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions: 6 2 5 32 5 =
Multiply these numbers together= 30
Add on the number at the top=
32 (this will be the top number)
The number at the bottom will stay the same

28. 3 1 10 5 3 4 x = 31 10 23 4 = x 5 3 4 6 2 5 x = 23 4 32 5 x =

29. 3 1 10 6 2 5 ÷ = 31 10 32 5 31 10 5 32 ÷ = = x 6 1 4 6 2 5 = ÷ 25 4 32 5 25 4 5 32 = x = ÷