The meaning of an expression such as is not immediately obvious, but a comparison with a more familiar expression, say may help. asks us to work out how many twos there are in 6 (the answer is 3). In exactly the same way, asks how many halves there are in 4. Figure 3.2 illustrates this in terms of circles. Each circle contains two half-circles, and 4 circles therefore contain 8 half-circles. So
Figure 3.2 Four circles each containing two half-circles.
This can be extended into a general rule:
To divide by a fraction, turn it upside down and multiply.
So
And
Finally, remembering that 3 can be written as
Question 3.7
Work out the following, leaving each answer as the simplest possible fraction:
