What you need to know: It is required to know how to perform addition, subtraction, multiplication, and division with fractions. First, you understand that if you multiply the numerator (top) and denominator (bottom) of any fraction by the same number, the value of the fraction stays the same.   ADDITION/SUBTRACTION: In order to add (or subtract) two fractions, they must have the same denominator; the number on the bottom. MULTIPLICATION: Multiplication between fractions is the most straightforward operation we can perform on them. DIVISION: In order to divide one fraction by another, you must remember the Keep/Change/Flip rule, which says that if you are dividing one fraction by another, you Keep the first one the same; Change the divide symbol to a multiplication, and Flip the second fraction. At this point, you only need to perform the multiplication as standard.

Starter What is a fraction?

3 4 This is the numerator. This is how many of the equal parts we’re interested in. This is the denominator. This is how many equal parts the shape/quantity is split into.

What is the highest common factor (HCF) of 6 and 8? 12 2 10 4

What is the highest common factor (HCF) of 6 and 8? 12 2 10 4

What is the highest common factor (HCF) of 12 and 16? 48 12 4 24

What is the highest common factor (HCF) of 12 and 16? 48 12 4 24

What is the highest common factor (HCF) of 10 and 25? 50 2.5

What is the highest common factor (HCF) of 10 and 25? 50 2.5

What is the highest common factor (HCF) of 24 and 36? 12 8 24

What is the highest common factor (HCF) of 24 and 36? 12 8 24

How does this help us with fractions? We are going to simplify fractions later on. To do this, we need to divide both the numerator and the denominator by their highest common factor (HCF).

Would you rather have 1 4 2 2 8 4 of a pizza?

Would you rather have 1 4 2 2 8 4 of a pizza?

Would you rather have 1 4 2 2 8 4 of a pizza?

Would you rather have 1 4 2 2 8 4 of a pizza?

Would you rather have 1 4 2 2 8 4 of a pizza?

We call these equivalent fractions. 1 4 2 2 8 4 They’re all the same! We call these equivalent fractions.

Which of these fractions are equivalent Which of these fractions are equivalent? Shade in your circles to help you! 3 6 4 6 1 3 1 2 2 3 2 6 1 4 5 12 4 12 1 12 3 12 1 6

Which of these fractions are equivalent Which of these fractions are equivalent? Shade in your circles to help you! 3 6 4 6 1 3 1 2 2 12 2 6 1 4 5 12 4 12 1 12 3 12 1 6

9 15 4 12 3 9 15 25 10 30 20 32 10 16 18 30 6 10 2 6 15 24 12 20 5 15 25 40 6 18 50 80 1 3 3 5 5 8

Choose your starting point: Find equivalent fractions to these: Red 1/2 Amber 1/3 Green 2/5 Extension 7/12

Find a fraction equivalent to 2/7 that has: A numerator of 10 A denominator of 49 An even denominator

To simplify or cancel down fractions, we need to find an equivalent fraction with the smallest numerator and denominator possible. Do you remember before when we said about dividing by the highest common factor (HCF)?

16 20 4 Simplify: What’s the highest common factor of 16 and 20? So divide both the numerator and denominator by 4

Simplify: ÷ 4 16 20 4 5 ÷ 4

24 56 8 Simplify: What’s the highest common factor of 24 and 56? So divide both the numerator and denominator by 8

Simplify: ÷ 8 24 56 3 7 ÷ 8

Simplifying Fractions Bingo Choose 9 of these numbers to go in your grid (no repeats allowed) 1/5 2/3 ¾ 3/5 3/8 5/7 ¼ 2/9 2/7 5/9 4/7 4/11 6/7 1/6 1/8 6/11

10/14 = ?

30/55 = ?

4/20 = ?

8/64 = ?

9/12 = ?

3/18 = ?

42/49 = ?

20/30 = ?

6/10 = ?

40/70 = ?

8/36 = ?

2/8 = ?

32/88 = ?

12/32 = ?

10/35 = ?

15/27 = ?

Answers 3 12 1 4 3 15 1 5 = = 2 8 1 4 8 16 1 2 = = 15 20 3 4 10 16 5 8 = = 3 9 1 3 20 32 5 8 = =

What is the lowest common multiple (LCM) of 3 and 7? 21 7 14

What is the lowest common multiple (LCM) of 3 and 7? 21 7 14

What is the lowest common multiple (LCM) of 4 and 9? 36 12 4 24

What is the lowest common multiple (LCM) of 4 and 9? 36 12 4 24

What is the lowest common multiple (LCM) of 6 and 8? 12 2 10 24

What is the lowest common multiple (LCM) of 6 and 8? 12 2 10 24

What is the lowest common multiple (LCM) of 10 and 25? 50 2.5

What is the lowest common multiple (LCM) of 10 and 25? 50 2.5

How does this help us with fractions? We are going to look at comparing fractions. To do this, we need to find a common denominator by finding the lowest common multiple (LCM) of the existing denominators.

Would you rather have 2 1 3 5 4 10 of a pizza? Drawing diagrams won’t necessarily be accurate enough to see a true representation. Let’s look at a numerical method instead.

Start by finding the LCM of 5, 4 and 10 Would you rather have 2 1 3 5 4 10 of a pizza? Start by finding the LCM of 5, 4 and 10 __ __ __ 20 20 20

Next, calculate equivalent fractions with this common denominator Would you rather have 2 1 3 5 4 10 of a pizza? Next, calculate equivalent fractions with this common denominator __ __ __ 20 20 20

2 1 3 5 4 10 x 4 x 5 x 2 8 5 6 __ __ __ 20 20 20

I know which I’d rather have! Would you rather have 8 5 6 20 20 20 of a pizza? I know which I’d rather have!

Answers (smallest to largest) Qs 1 - 4 1 3 1 5 3 4 8 2 8 4 2 1 3 7 2 5 2 5 10 2 1 5 1 4 3 3 12 2 6 4 1 2 3 5 7 2 3 4 6 8

Answers (smallest to largest) Qs 5 - 8 1 2 1 6 3 4 5 2 10 4 1 4 1 2 5 3 9 2 3 6 1 2 5 2 7 4 6 12 3 9 2 2 5 11 3 7 4 8 14 2

Copy and complete the pairs of equivalent fractions. Starter Copy and complete the pairs of equivalent fractions. 1 = 4 3 = __ 2 4 20 2 = 6 1 = __ 9 5 35 15 8 7 3

Adding Fractions 3 + 2 8 8 The denominator doesn’t change because we are still talking about eighths. = 5 8

Subtracting Fractions 3 - 1 6 6 = 2 6 = 1 3 The denominator doesn’t change because we are still talking about sixths. Remember to simplify your answer if you can.

2 + 1 = 6 – 3 = 8 - 3 = 4 + 1 = 7 7 8 8 10 10 5 5

3 4 1 3 3 8 4 5 1 4 2 3 5 8 1 5 2 + 1 = 6 – 3 = 8 - 3 = 4 + 1 = 7 7 8 8 10 10 5 5 3 7 3 8 1 2 1 4 5 8 10 4 9 3 10 8 15 4 7

We can’t add these yet because the denominators are different. 2 + 1 5 4

2 + 1 5 4 What common denominator could we use? 2 + 1 5 4 What common denominator could we use? 20 is the lowest common multiple of 5 and 4

What did we multiply 5 by to get 20? 2 + 1 5 4 8 __ + __ 20 20 4! We need to multiply the numerator by the same number to keep the fractions equivalent What did we multiply 5 by to get 20?

What did we multiply 4 by to get 20? 2 + 1 5 4 5! 8 5 __ + __ 20 20 We need to multiply the numerator by the same number to keep the fractions equivalent What did we multiply 4 by to get 20?

2 + 1 5 4 8 5 __ + __ 20 20 13 20 Now we can add the fractions. 2 + 1 5 4 Now we can add the fractions. 8 5 __ + __ 20 20 13 20 We can’t simplify this one.

We can’t add these yet because the denominators are different. 2 - 3 3 8

2 - 3 3 8 What common denominator could we use? 2 - 3 3 8 What common denominator could we use? 24 is the lowest common multiple of 3 and 8

What did we multiply 3 by to get 24? 2 - 3 3 8 16 __ - __ 24 24 8! We need to multiply the numerator by the same number to keep the fractions equivalent What did we multiply 3 by to get 24?

What did we multiply 8 by to get 24? 2 - 3 3 8 3! 16 9 __ - __ 24 24 We need to multiply the numerator by the same number to keep the fractions equivalent What did we multiply 8 by to get 24?

2 - 3 3 8 16 9 __ - __ 24 24 7 24 Now we can subtract the fractions. 2 - 3 3 8 Now we can subtract the fractions. 16 9 __ - __ 24 24 7 24 We can’t simplify this one.

Answers 7 7 10 12 2 11 35 15 2 22 21 45 54 43 55 90 46 19 63 40

What’s the same and what’s different? Starter What’s the same and what’s different? 1 2 4 8 10 20 2 3

Multiplying Fractions means, ‘One half of three quarters’ 3 4 x 1 2 3 4 Here is of a rectangle: Now, let’s halve the coloured part. 3 4 x 1 2 3 8 =

Multiplying Fractions Multiply the numerators and multiply the denominators together 2 x 1 3 4 = 2 x 1 3 x 4 = 2 12 = 1 6 Simplify if possible!

Multiplying Fractions Extension = 𝟑 2 1 7 x 1 2 5

means, ‘How many eighths are there in one half?’ Dividing Fractions means, ‘How many eighths are there in one half?’ 1 8 ÷ 2 1 2 Here is of a rectangle: Now, let’s divide the shape into eighths. 1 8 ÷ 2 = 4

Dividing Fractions 2 ÷ 1 3 4 = 2 x 4 3 1 = 2 x 4 3 x 1 = 8 3 2 ÷ 1 3 4 = 2 x 4 3 1 Flip the second fraction upside-down and multiply the fractions instead. = 2 x 4 3 x 1 = 8 3 Simplify if possible!

Dividing Fractions Extension = 𝟏 𝟗 𝟏𝟎 4 3 4 ÷ 2 1 2

What could the question have been? Plenary The answer is 𝟑𝟐 𝟒𝟓 What could the question have been?

What’s the same and what’s different? Starter What’s the same and what’s different? 16 3 32 6 5 2 6 5 1 3

The denominator stays the same Convert 19 6 to a mixed number. Remember this means 19 ÷ 6 19 ÷ 6 = 3 r 1 = 3 1 6 The denominator stays the same

= 13 5 Convert 2 3 5 to an improper fraction. 2 𝑥 5+3 5 How many 5ths are in one whole? 2 𝑥 5+3 5 = 13 5 The denominator stays the same

Complete the sheet on converting improper fractions to mixed numbers and mixed numbers to improper fractions.

Answers 6 3 4 13 5 9 7 6 1 2 8 3 27 9 5 1 3 26 11 23 8 1 3 7 23 5 23 6 2 2 5 13 9 67 12 2 1 4 31 11 44 9 5 1 4

2 3 2 + 3 5 1 3 3 - 1 4 5 8 3 + 18 5 10 3 - 9 5 x5 x3 x5 x3 _ 15 40 + 54 _ 15 = 94 15 = 2 4 15 50 _ 15 - _ 15 27 = 23 15 = 1 8 15 1 7 2 x 1 2 5 3 4 4 ÷ 2 1 2 15 7 x 7 5 19 4 5 2 = 105 35 = 3 ÷ 19 4 2 5 38 20 = 1 9 10 x =

Mixed Numbers Calculations Don’t forget to change the mixed numbers to improper fractions first then simplify your answers at the end! Add Subtract Multiply Divide Find a common denominator. Find equivalent fractions with that denominator. Add or subtract the numerators and put the answer over the same denominator. Multiply the numerators together, multiply the denominators together. Flip the second fraction upside-down then multiply instead. 3 1 4 + 1 2 3 4 3 4 - 1 1 3 2 1 4 x 1 2 3 4 2 3 ÷ 1 1 4 2 1 5 + 1 3 4 2 4 5 - 1 3 4 3 1 8 x 2 3 5 2 1 6 ÷ 3 2 3 2 7 8 + 2 4 5 3 1 3 - 1 5 8 1 2 5 x 3 1 9 3 4 5 ÷ 1 5 8

Answers 3 1 4 + 1 2 3 = 4 11 12 4 3 4 - 1 1 3 = 3 5 12 2 1 4 x 1 2 3 = 3 3 4 4 2 3 ÷ 1 1 4 = 3 11 15 2 1 5 + 1 3 4 = 3 19 20 2 4 5 - 1 3 4 = 1 1 20 3 1 8 x 2 3 5 = 8 1 8 2 1 6 ÷ 3 2 3 = 13 22 2 7 8 + 2 4 5 = 5 27 40 3 1 3 - 1 5 8 = 1 17 24 1 2 5 x 3 1 9 = 4 16 45 3 4 5 ÷ 1 5 8 = 2 22 65

Starter 54 x 3 32 x 6 71 x 7 26 x 4 = 162 = 192 = 497 = 104

252 ÷ 4 62 64 63 65

252 ÷ 4 62 64 63 65

445 ÷ 5 86 88 87 89

445 ÷ 5 86 88 87 89

81 ÷ 3 27 29 28 30

81 ÷ 3 27 29 28 30

182 ÷ 7 23 25 24 26

182 ÷ 7 23 25 24 26

288 ÷ 9 30 32 31 33

288 ÷ 9 30 32 31 33

3 4 This is the numerator. This is how many of the equal parts we’re interested in. This is the denominator. This is how many equal parts the shape/quantity is split into.

Start by splitting the amount into 5 equal parts. Calculate 2 of 20 5 Start by splitting the amount into 5 equal parts. £4 £4 £4 £4 £4

We are interested in 2 of these parts. Calculate 2 of 20 5 £4 £4 £4 £4 £4 We are interested in 2 of these parts. £8

Calculate 3 of 49 7 Calculate 5 of 108 9 £21 £60 £7 £7 £7 £7 £7 £7 £7 £12 £12 £12 £12 £12 £12 £12 £12 £12 £21 £60

Use any of these numbers in your grid (NO REPEATS) 24 12 25 63 49 48 15 36 21 54 30 16 9 10 55 33

1 of 36 3

1 of 48 2

3 of 12 4

1 of 110 2

4 of 60 5

1 of 64 4

1 of 42 2

1 of 150 5

3 of 84 4

7 of 70 10

1 of 90 6

2 of 35 7

9 of 40 10

6 of 81 9

5 of 30 6

1 of 99 3

12 is the answer. What was the question? Explain to the person next to you HOW to calculate a fraction of an amount

Answers Question Answer   1 9 of 45 5 3 4 of 884 663 1 7 of 147 21 2 7 of 112 32 2 5 of 50 20 5 12 of 144 60 3 5 of 125 75 7 11 of 143 91 7 8 of 448 392 2 3 of 153 102