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Multiplying and Dividing Fractions: Exploring Equivalent Fractions and Mixed Numbers

Learn how to multiply and divide fractions and mixed numbers with ease. This lesson will teach you how to find equivalent fractions, solve word problems, and simplify fractions.

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Multiplying and Dividing Fractions: Exploring Equivalent Fractions and Mixed Numbers

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  1. Starter Name at least 3 equivalent fractions each

  2. Sunday, 8 January 2017 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. Multiplying and Dividing Fractions Let’s look at two fractions from the starter. How can we multiply these?

  4. 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.

  5. Multiplying and Dividing Fractions But what about mixed numbers? Ug. If the question is given as a mixed number, the answer should be too.

  6. Multiplying and Dividing Fractions I’ve had a go at this question. Have I done it right?

  7. Multiplying and Dividing Fractions I’ve had a go at this question. Have I done it right?

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

  9. Multiplying and Dividing Fractions

  10. 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 = The chance of getting an orange disc in the first bag = The chance of getting an orange disc in both bags =

  11. 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?

  12. 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?

  13. 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?

  14. Equivalent Fractions Question 1 Timer

  15. Multiplying and Dividing Fractions Question 2 Timer

  16. Multiplying and Dividing Fractions Question 3 Timer

  17. Multiplying and Dividing Fractions Question 4 Timer

  18. Multiplying and Dividing Fractions Question 5 Timer

  19. Multiplying and Dividing Fractions Your answers:

  20. Multiplying and Dividing Fractions Let’s look at dividing fractions 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

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

  22. Multiplying and Dividing Fractions We could find common denominators and then divide. This is a pretty horrible and complex method, though. If we’re clever we can calculate fractional division nicely.

  23. Multiplying and Dividing Fractions 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 ?

  24. Multiplying and Dividing Fractions Another example using the inverse method.

  25. Multiplying and Dividing Fractions And with mixed numbers…

  26. 3 4 2 2 1 2 6 2 2 3 3 4 5 2 6 4 3 4 5 5 1 5 4 2 9 5 7 2 1 3 2 13 3 4 6 1 3 2 5 2 5 1 2 2 5 8 5 2 ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ Q10 Q4 Q3 Q9 Q1 Q5 Q6 Q2 Q7 Q8 Q12 Q11 7 9 9 5 5 3 7 7 8 4 6 7 4 4 7 5 3 7 6 7 3 4 6 8 3 9 9 11 4 4 7 5 3 3 10 16 5 7 6 5 8 8 3 7 2 8 10 4 Equivalent Fractions Q23 2 Q24 3 Q17 2 Q19 2 Q22 2 Q15 2 Q21 1 Q14 2 Q20 1 Q18 1 ÷1 ÷2 ÷2 ÷1 ÷2 ÷2 ÷2 ÷3 ÷1 ÷1 ÷ ÷ Q16 Q13 Ex3. Pick 12

  27. Multiplying and Dividing Fractions

  28. 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?

  29. Multiplying and Dividing Fractions Question 1 Timer

  30. Multiplying and Dividing Fractions Question 2 Timer

  31. Multiplying and Dividing Fractions Question 3 Timer

  32. Multiplying and Dividing Fractions Question 4 Timer

  33. Multiplying and Dividing Fractions Question 5 Timer

  34. Multiplying and Dividing Fractions • Your answers: • 3

  35. Problem Solving Place some numbers in the boxes to make this true.

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