1. Multiplying and dividing fractions
[N2.3 Extension Starter]
1) Try to find some more pairs of numbers like these, where their sum is the same as their product. Don’t forget to check your answers!
2) To find the reciprocal of a number divide 1 by the number:
so the reciprocal of four is one quarter, because
If you divide a number by 2, the result is What is the reciprocal of the original number?
3) Jot down a fraction, write down its reciprocal Multiply these two numbers. What do you notice? Experiment with some other fractions.
4) Test this statement with some numbers of your choice. “Dividing by a number is the same as multiplying by the reciprocal of the same number.”
Preamble
Four straightforward investigations, for pairs or small groups, involving fractions in
preparation for multiplication and division of fractions to follow. With this in mind,
it is important that pupils are confident in the content of these investigations -
discussion of their finding will bring to the fore any serious problems. There are
opportunities to use correct mathematical vocabulary. Some pupils may need
reminding that , for example, 3 can be written as 3/1.
Possible content
Multiplying and dividing whole numbers and fractions.
Resources
None.
Solution/Notes
The sequence carries on (with several quite interesting number patterns evident).
The original number is 3 as the reciprocal of 3 is 1/3.
The answer is always one (pupils chose their own fractions so this should not be too challenging).
Pupils’ own examples.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010