Calculate: 3 5 + 4 7 5 6 − 2 7 1) 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

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

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

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

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

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

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

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?

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?

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?

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

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

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

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

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

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)

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

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

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)