1. Skills for Life Support Programme T: 0118 902 1920 F: 0845 838 1207 E: sflenquiries@cfbt.com W: www.excellencegateway.org.uk/sflsp The Skills for Life Support Programme is delivered on behalf of the Learning and Skills Improvement Service by CfBT Education Trust and partners CfBT Education Trust 60 Queens Road Reading RG1 4BS 2.8 Approaches to dividing fractions: modelling Teacher training package for preparatory course for numeracy specialists

2. Skills for Life Support Programme Multiplying a fraction by a fraction Approach To multiply a fraction by a fraction you can multiply the denominators together and multiply the numerators together and cancel when necessary. Example

3. Skills for Life Support Programme Model To make this meaningful it is important to relate it to other things. A real-world situation or model to show the application could be: How much is there in half of a quarter of a chocolate bar? 1 whole ½ of ¼ = 1 / 8 ¼

4. Skills for Life Support Programme Dividing a fraction by a fraction How would you approach this example? Attempt the calculation on your own first then discuss with your group. Agree on an approach and write it down. Come up with at least one model for this example. Use pictures to help.

5. Skills for Life Support Programme Approaches to dividing fractions by a fraction:1 Dividing a fraction by a fraction is the same as multiplying by its reciprocal. Change to improper fractions first.

6. Skills for Life Support Programme Approaches to dividing fractions by a fraction:2 Change to decimals

7. Skills for Life Support Programme Approaches to dividing fractions by a fraction: 3 Sometimes division of fractions problems can be solved without using multiplication. This example is one which could be solved using division.

8. Skills for Life Support Programme Approaches to dividing fractions by a fraction: 4 The distributive law could be used instead of changing the mixed number to an improper fraction

9. Skills for Life Support Programme Models for dividing fractions by a fraction: 1 Dividing by a half is like asking How many halves are there in one and three quarters? I have 1 ¾ pizzas. How many ½ s are there? We can see that we have 3 ½ halves

10. Skills for Life Support Programme Model for dividing fractions by a fraction: 2 How many ½s are in 1¾? I have 1 ¾ metres of ribbon. How many ½ m of ribbon can I get from this? We can see that we can get 3 ½ half metres from 1¾ m 1 ¾ m ½ m

11. Skills for Life Support Programme Model for dividing fractions by a fraction: 3 We have two packs of sugar, one brown one white. The brown sugar is 1 ¾ kg and the white sugar is ½ kg. How many times is the weight of the brown sugar that of the white sugar? 3 ½ times the weight ½ x ? = 1¾ brown sugar white sugar

12. Skills for Life Support Programme Understanding the meaning of division by fractions Meaning of multiplication with fractions Meaning of additionConcept of fractionConcept of unit The conception of inverse operation Meaning of division with whole numbers Meaning of multiplication with whole numbers The meaning of division by fractions

13. Skills for Life Support Programme Acknowledgement Ideas and concept adapted from Knowing and Teaching Elementary Mathematics by Liping Ma (1999). Published by Lawrence Erlbaum Associates