Derry says"I am thinking of a fraction. My fraction is bigger than 1/2 but smaller than 2/3. The numerator and the denominator of my fraction are both single digit numbers." What fraction could Derry be thinking of? Show your working out (3)

How about we put the fractions into decimals?

1/2 is 0.5

2/3 is 0.66666 (6)

So we need to find something that is between them.

the denominator can't be 2, because bigger than 1/2 is 2/2, which is 1 and is bigger than 0.6

it also can't be 3, because smaller than 2/3 is 1/2, which is 0.333 ... and is smaller than 0.5.

Can it be 4? we can't have 2/4 (it's the same as 1/2), or 3/4, it's 0.75, and it's bigger than 0.666 ...

how about 5?

2/5=0.4, no, too small

3/5=0.6 - perfect! that's the answer!