Starter Replace the ? 2 5 = ? 15 9 17 = ? 51 4 13 = ? 26 6 20 = 18 ? 4 10 = ? 70 3 23 = ? 230

Starter Replace the ? 2 5 = 6 15 9 17 = 27 51 4 13 = 8 26 6 20 = 18 60 4 10 = 28 70 3 23 = 30 230

Adding and Subtracting Fractions Saturday, 04 May 2019 Adding and Subtracting Fractions Objectives : To be able to add and subtract fractions with different denominators To be able to subtract mixed numbers

Adding and Subtracting Fractions Let’s look at two fractions. 2 5 1 4 How can we add these? At the moment we’re stuck, because the fractions have different denominators. We can’t add fifths to quarters. They’re different things. We need to find equivalent fractions with the same denominators.

Adding and Subtracting Fractions 2 5 1 4 I need to think of a number in both the 5 and 4 multiplication tables. I know. 20 is in both the 5 and 4 multiplication tables. This means I can write equivalent fractions with 20 as the denominator. Ug. 8 20 5 20 13 20 + =

5 7 + 9 11 55 77 + 63 77 = 118 77 Adding and Subtracting Fractions Another (harder) example 5 7 + 9 11 We need to find a number in both the 7 and 11 multiplication tables, so that when we find equivalent fractions, they both have the same denominator. 55 77 + 63 77 = 118 77

118 77 1 41 77 Adding and Subtracting Fractions This answer isn’t the best it could be. We don’t like having improper fractions. Let’s convert it to a mixed number. 1 41 77 77 divides into 118 once, with a remainder of 41

The Golden Rule Adding and Subtracting Fractions You can only add fractions with the same denominators. If the denominators are different you need to find equivalent fractions.

Adding and Subtracting Fractions Ex1. Let’s do some practice. Simplify where possible. 1 4 2 8 + 2 10 5 + 3 21 2 7 + 1 6 4 12 + 6 8 4 16 - 5 6 18 1 - 6 11 4 22 - 7 5 7 2 14 - 8 2 12 3 + 9 3 4 2 16 - 10 3 5 15 + 11 7 8 2 24 - 12 1 3 2 5 + 13 2 5 4 + 14 2 7 3 5 + 15 4 6 1 + 16 3 8 2 7 - 17 3 4 5 8 - 18 7 11 4 - 19 5 9 2 7 - 20 7 8 5 9 + 21 3 4 8 15 - 22 9 4 8 5 + 23 14 8 6 5 - 24

Adding and Subtracting Fractions Ex1. Let’s do some practice. 4 8 1 2 6 10 3 5 = 9 21 3 7 6 12 1 2 = 1 = 2 3 = 4 8 16 1 2 = 3 18 1 6 = 8 22 4 11 = 8 14 4 7 = 5 6 7 8 10 12 5 6 = 10 16 5 8 = 14 15 19 24 9 10 11 12 11 15 18 20 9 10 = 14 31 35 22 24 11 12 = 16 13 15 5 56 1 8 5 77 17 63 17 18 19 20 103 72 = 72 31 1 13 60 77 20 = 20 17 3 22 40 11 20 = 24 21 22 23

Adding and Subtracting Fractions Ex2. Spot the odd one out. In each row there’s an answer that’s different. Spot it. 1 3 + 1 6 1 5 + 1 9 3 8 − 1 4 6 11 + 4 8 6 10 + 1 5 6 7 − 5 11 4 8 + 4 9 2 3 + 2 9 3 4 + 2 11 6 7 + 4 8 5 6 + 3 9 4 5 + 3 7 5 6 − 1 3 3 9 + 1 6 5 8 − 5 9 2 3 − 2 5 2 5 + 1 3 2 3 − 1 5 4 5 − 1 7

Not a 15 on the denominator Adding and Subtracting Fractions Ex2. Answers 1 2 14 45 1 8 1 22 Not a unit fraction 4 5 31 77 17 18 8 9 Not 𝑛 𝑛+1 41 44 1 5 14 1 1 6 1 8 35 Not a mixed number 5 72 Not a half 4 15 11 15 7 15 23 35 Not a 15 on the denominator

Adding and Subtracting Fractions 5 QUICK QUESTIONS CHECK Now it’s time to check your learning. You’ll see five questions. They all have a 30 second timer. How many can you get right?

Adding and Subtracting Fractions Question 1 1 2 + 3 8 Timer

Adding and Subtracting Fractions Question 2 3 7 − 5 14 Timer

Adding and Subtracting Fractions Question 3 3 7 + 1 5 Timer

Adding and Subtracting Fractions Question 4 1 4 − 1 5 Timer

Adding and Subtracting Fractions Question 5 5 7 + 3 5 Timer

Adding and Subtracting Fractions Your answers: 7 8 1 14 22 35 1 20 1 11 35

Adding and Subtracting Fractions What about if we add mixed numbers? 1 5 7 +2 1 3 We need to convert the mixed numbers to improper fractions before adding. 12 7 + 7 3 = Now let’s find equivalent fractions. 36 21 + 49 21 = 85 21 =4 1 21

Adding and Subtracting Fractions Ex3. Let’s do some practice. Simplify where possible. 2 4 1 + 1 2 3 1 - 2 2 4 9 3 - 3 2 2 6 + 2 4 1 5 2 10 + 3 5 1 5 8 1 4 - 1 6 2 1 5 2 15 + 2 7 1 2 3 12 - 2 8 4 2 7 5 8 + 2 9 3 1 9 7 - 2 10 4 4 7 5 6 + 3 11 2 2 3 - 3 12 3 BrainBox Extension: 4 7 13 −4 1 6 −3 2 9

Adding and Subtracting Fractions Ex3. Answers 3 4 1 3 1 9 4 6 2 3 = 2 1 1 2 2 3 2 4 2 4 10 2 5 = 4 5 4 3 8 5 15 1 3 = 3 7 3 5 12 6 1 8 2 51 56 61 63 17 42 9 5 10 1 11 6 12 0 BrainBox Extension: −2 199 234

I need the biggest value key! Which colour should I use? Adding and Subtracting Fractions 1 7 10 +1 7 12 2 2 3 −1 1 9 2 3 4 +1 2 3 1 1 2 +2 5 13 2 1 3 −2 1 6 I need the biggest value key! Which colour should I use?

1 5 9 3 17 60 4 5 12 3 23 26 1 6 Adding and Subtracting Fractions I need the blue key! 1 6

Adding and Subtracting Fractions 5 QUICK QUESTIONS CHECK Now it’s time to check your learning. You’ll see five questions. They all have a 60 second timer. How many can you simplify?

Adding and Subtracting Fractions Question 1 2 8 9 + 4 9 Timer

Adding and Subtracting Fractions Question 2 1 6 7 + 1 5 Timer

Adding and Subtracting Fractions Question 3 1 5 9 +1 1 8 Timer

Adding and Subtracting Fractions Question 4 3−2 2 5 Timer

Adding and Subtracting Fractions Question 5 3 1 2 −1 1 12 Timer

Adding and Subtracting Fractions Your answers: 3 1 3 2 2 35 2 49 72 3 5 2 5 12

Problem Solving Three candidates were running for office. One of them got half the vote.   Another got two fifths of the vote.   What fraction did the third get?

Problem Solving 1 10