Starter Name at least 3 equivalent fractions each 2 5 9 17 4 13 6 20 4 10 3 23

Multiplying and Dividing Fractions Wednesday, 29 May 2019 Multiplying and Dividing Fractions Objectives : To be able to multiply and divide a fraction by a fraction To be able to multiply and divide mixed numbers

= 3 10 = 6 20 Multiplying and Dividing Fractions Let’s look at two fractions from the starter. 2 5 × 3 4 How can we multiply these? = 3 10 = 6 20

Multiplying and Dividing Fractions Me lazy. Me don’t want to draw out a bit table. There must be a quicker way of doing this! Ug. 2 5 × 3 4 2×3 5×4 6 20 3 10

Multiplying and Dividing Fractions But what about mixed numbers? Ug. 2 2 5 ×5 3 4 If the question is given as a mixed number, the answer should be too. 12 5 × 23 4 276 20 Questioning: Why does 2 2/5 go to 12/5? How do we change an improper fraction into a mixed number? How can we work out 12*23? We could use grid. Emphasise that the multiplication of a mixed number question may lead you into a difficult multiplication 138 5 27 3 5

I’ve had a go at this question. Have I done it right? Multiplying and Dividing Fractions I’ve had a go at this question. Have I done it right? Questions: this doesn’t work. Why not? This is like doing 34x21 by doing 3x2 and 4x1. We’re missing lots of information out.

I’ve had a go at this question. Have I done it right? Multiplying and Dividing Fractions I’ve had a go at this question. Have I done it right? x 3 4 5 2 6 1 3 4 15 Questions: this doesn’t work. Why not? This is like doing 34x21 by doing 3x2 and 4x1. We’re missing lots of information out.

Multiplying and Dividing Fractions Ex1. Pick 12 2 3 4 5 × Q1 2 5 3 × Q2 4 7 3 5 × Q3 5 6 1 4 × Q4 3 8 5 7 × Q5 3 4 7 8 × Q6 6 11 4 7 × Q7 5 9 2 7 × Q8 7 12 5 11 × Q9 3 4 8 15 × Q10 9 4 8 5 × Q11 14 8 6 5 × Q12 8 9 1 4 × 1 Q13 1 4 2 3 × Q14 2 2 9 3 4 × Q15 2 4 5 6 × 2 Q16 1 5 4 × 3 Q17 1 1 4 2 3 × 2 Q18 1 1 5 2 3 × 2 Q19 1 1 5 3 4 × 3 Q20 1 2 7 5 8 × 2 Q21 3 1 9 7 × 2 Q22 3 4 7 5 6 × 3 Q23 2 2 3 × 3 Q24 3

Multiplying and Dividing Fractions 8 15 4 15 12 35 5 24 15 56 21 32 24 77 10 63 35 132 6 15 18 5 =3 3 5 21 10 =2 1 10 10 9 =1 1 9 3 2 =1 1 2 5 3 =1 2 3 32 15 =2 2 15 39 10 =3 9 10 10 3 =3 1 3 16 5 =3 1 5 9 2 =4 1 2 69 8 =8 5 8 49 6 =8 1 6 69 7 =9 6 7 121 9 =13 4 9

Multiplying and Dividing Fractions One place we multiply fractions is in probability. Two bags with discs in. The chance of getting an orange disc in the first bag = 4 11 The chance of getting an orange disc in the first bag = 2 13 The chance of getting an orange disc in both bags = 4 11 × 2 13 = 8 143

Multiplying and Dividing Fractions What is the chance… (a) I pick out two blue discs (b) I pick out two purple discs (c) I pick out a blue from bag one and a purple from bag two? (d) I pick out a blue from bag one and a green from bag two? (e) I pick out an orange from bag one and a green from bag two?

Multiplying and Dividing Fractions What is the chance… (a) I pick out two blue discs 4 11 × 4 13 = 16 143 (b) I pick out two purple discs 3 11 × 3 13 = 9 143 (c) I pick out a blue from bag one and a purple from bag two? 4 11 × 3 13 = 12 143 (d) I pick out a blue from bag one and a green from bag two? 4 11 × 4 13 = 16 143 (e) I pick out an orange from bag one and a green from bag two? 4 11 × 4 13 = 16 143

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

Equivalent Fractions Question 1 1 2 × 1 4 Timer

Multiplying and Dividing Fractions Question 2 6 7 × 2 5 Timer

Multiplying and Dividing Fractions Question 3 3 7 × 1 9 Timer

Multiplying and Dividing Fractions Question 4 1 1 2 × 4 9 Timer

Multiplying and Dividing Fractions Question 5 1 5 9 ×3 4 5 Timer

Multiplying and Dividing Fractions Your answers: 1 8 12 35 1 27 2 3 5 41 45

Multiplying and Dividing Fractions Let’s look at dividing fractions 1 2 ÷ 1 8 We can think of this question as how many eights go into one half. It’s clear to see that 4 eights would go into one half. So 1 2 ÷ 1 8 =4

Multiplying and Dividing Fractions Let’s look at a harder question 3 5 ÷ 3 4 This is harder to understand. Clearly less than one lot of 3 4 goes into 3 5 , but we can’t tell the exact amount from the diagram. We need a numerical method.

Multiplying and Dividing Fractions 3 5 ÷ 3 4 We could find common denominators and then divide. 12 20 ÷ 15 20 12 20 ÷ 15 20 = 12÷15 20÷20 = 4 5 1 𝑜𝑟 4 5 This is a pretty horrible and complex method, though. If we’re clever we can calculate fractional division nicely.

Multiplying and Dividing Fractions 3 5 ÷ 3 4 Instead of dividing, we could do the inverse to the inverse. This line of thinking of is similar to the idea that a subtraction of a negative is the same as an addition. What is the inverse of dividing? Multiplying What is the inverse of 3 4 ? 4 3 3 5 ÷ 3 4 = 3 5 × 4 3 = 12 15 = 4 5

Multiplying and Dividing Fractions Another example using the inverse method. 3 7 ÷ 2 9 3 7 × 9 2 3×9 7×2 27 14 1 13 14

Multiplying and Dividing Fractions And with mixed numbers… 1 3 7 ÷3 2 9 10 7 ÷ 29 9 10 7 × 9 27 10×9 7×27 10 21 90 189

Equivalent Fractions Ex3. Pick 12 ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ 1 ÷ ÷ ÷ 1 5 7 ÷ Q1 3 4 2 5 ÷ Q2 4 5 1 3 ÷ Q3 2 7 3 8 ÷ Q4 5 6 1 2 ÷ Q5 4 7 3 ÷ Q6 5 6 2 ÷ Q7 3 4 2 9 ÷ Q8 4 7 5 8 ÷ Q9 2 9 7 10 ÷ Q10 2 3 5 9 ÷ Q11 4 7 8 11 ÷ Q12 3 4 6 7 ÷ 1 Q13 5 9 2 3 ÷ Q14 2 5 8 13 16 ÷ Q15 2 6 7 9 10 ÷ 1 Q16 3 5 4 ÷ 1 Q17 2 2 8 5 6 ÷ 2 Q18 1 6 7 5 8 ÷ 1 Q19 2 2 5 3 4 ÷ 2 Q20 1 2 3 1 4 ÷ 2 Q21 1 1 6 2 7 ÷ 2 Q22 2 4 7 2 3 ÷ 3 Q23 2 1 4 2 3 ÷ 2 Q24 3

Multiplying and Dividing Fractions 14 15 15 8 =1 7 8 12 5 =2 2 5 16 21 10 6 =1 2 3 25 12 =2 1 12 27 8 =3 3 8 32 35 20 63 18 15 =1 1 5 44 56 21 52 3 5 6 3 3 13 60 133 1 4 9 15 34 1 69 91 28 55 20 27 91 96 54 77 1 7 32

Multiplying and Dividing 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 simplify?

Multiplying and Dividing Fractions Question 1 1 4 ÷ 1 12 Timer

Multiplying and Dividing Fractions Question 2 1 2 ÷ 1 3 Timer

Multiplying and Dividing Fractions Question 3 5 9 ÷ 7 11 Timer

Multiplying and Dividing Fractions Question 4 2 9 ÷ 7 18 Timer

Multiplying and Dividing Fractions Question 5 2 2 3 ÷1 3 4 Timer

Multiplying and Dividing Fractions Your answers: 3 1 1 2 55 63 36 63 = 4 7 32 21 =1 11 21

Problem Solving 1 2 3 Place some numbers in the boxes to make this true.