1. Calculate:
5 6 − 2 7 1) 2)

2. What steps did you take when adding or subtracting the fractions?
Discuss
To add or subtract fractions we first must have a common denominator
We were looking for the lowest common multiple of the 2 denominators in order to find it

3. Sometimes it is easy to find the common denominator.
Can you think of an example when the common denominator it is easy to find?
How do we find the common denominator if the numbers are harder?
We can use a venn diagram

4. How can we use a Venn diagram to find the LCM of 28 and 48 First of all, think back to Year 8 and how we found the Product of Prime Factors 28 48
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3

5. How can we use a Venn diagram to find the LCM of 28 and 48
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3

6. Use a Venn diagram to find the LCM of 42 and 36
In pairs …
Use a Venn diagram to find the LCM of 42 and 36
42 = 2 x 3 x 7
36 = 2 x 2 x 3 x 3

7. Use a Venn diagram to find the LCM of 24 and 32
In pairs …
Use a Venn diagram to find the LCM of 24 and 32
24 = 2 x 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2

8. Use a Venn diagram to find the LCM of 45 and 30
In pairs …
Use a Venn diagram to find the LCM of 45 and 30
45 = 3 x 3 x 5
30 = 2 x 3 x 5

9. What about when our fractions are algebraic
What about when our fractions are algebraic? Consider finding the common denominator of x and 3x What could my calculation look like?

10. What about when our fractions are algebraic
What about when our fractions are algebraic? Consider finding the common denominator of 4x and 3x What could my calculation look like?

11. What about when our fractions are algebraic
What about when our fractions are algebraic? Consider finding the common denominator of 5x and 3x What could my calculation look like?

12. How can we use a Venn diagram to find the LCM of x and 3x ?
𝑥 = 𝑥
3𝑥 = 3 x 𝑥

13. How can we use a Venn diagram to find the LCM of 2x and 3x ?
In pairs …
How can we use a Venn diagram to find the LCM of 2x and 3x ?
2𝑥 = 2 x 𝑥
3𝑥 = 3 x 𝑥

14. How can we use a Venn diagram to find the LCM of 4x and 6x ?
In pairs …
How can we use a Venn diagram to find the LCM of 4x and 6x ?
4𝑥 = 2 x 2 x 𝑥
6𝑥 = 2 x 3 x 𝑥

15. How can we use a Venn diagram to find the LCM of x2 and x ?
In pairs …
How can we use a Venn diagram to find the LCM of x2 and x ?
𝑥 = 𝑥
𝑥 2 = 𝑥 x 𝑥

16. How can we use a Venn diagram to find the LCM of 4x2 and 3x?
In pairs …
How can we use a Venn diagram to find the LCM of 4x2 and 3x?
4 𝑥 2 = 2×2×𝑥×𝑥
3x = 3 x 𝑥

17. In your books … 4𝑓 4 6ℎ 5 4 𝑠 2 8 𝑠 3 and and 7 𝑑 2 9 6𝑑 6 8 4 𝑢 2
State the lowest common denominator for each of the following pairs of fractions:
4𝑓 4
6ℎ 5
4 𝑠 2
8 𝑠 3 1
and
LCM = 20 6
and
LCM = s3
7 𝑑 2 9
6𝑑 6
8 4 𝑢 2
6 8𝑢 2
and 7
LCM = 18
and
LCM = 8h2
4 3𝑥
6 5𝑥
2 9 ℎ 3
5 6 ℎ 2 3
and
LCM = 15x 8
and
LCM = 18h3
7 2𝑎
5 6𝑎
3 𝑥𝑦
6 𝑦 4
and
LCM = 6a 9
and
LCM = xy
3 4 𝑥 2
5 6𝑥
3 𝑥
6 𝑥+1 5
and
LCM = 12x2 10
and
LCM = x(x + 1)

18. Match the fractions with their common denominators.
In your pairs …
Match the fractions with their common denominators.

19. Can you think of other examples where we multiply the denominators together to find their lowest common multiple?
Can you think of a numerical example where the only way to get a common multiple is if you multiply the two numbers together?
Hopefully pupils will link to prime numbers here too as well as the others in the tarsia
These numbers are coprime. They share no common factors. The only way to get a LCM is to multiply the 2 denominators together

20. Challenge Problem
Can you find the LCM of (x + 2) and (x + 2)2 Can you find the LCM of (x + 2) and (x + 2)(x + 1)