I worked through it backwards, starting with each boy having 360.

Thanks!

No problem, I really enjoy these problems!

Making it visual...

The average is between the two fractions.

Taking average is 9/20, not the ans for this qn as denominator must b lesser than 20.

It says not greater than 20, doesn't mean less than 20.

20 is not greater than 20.

This question is not about average. It is about equivalent fractions. You want a fraction bigger than 2/5 but smaller than 1/2. But you cannot compare the fractions until the denominators are the same.

Emma has solved it well. Thank you

The average of two numbers is always between them.

Thanks Kai Meng, that is true indeed. What I intended to explain was in the context of a P5 student. And not to layer 2 different concepts together. But it would be good to extend this for pupils who have a good grasp of math.

I'm for integrating concepts, as I find that many students see the topics as separate and that limits their understanding and problem solving skills in some ways. Anyway there are always multiple ways to answer a question.

ok.... got it.... thanks alot

But what if the qn want a denominator lesser than 20?

Then that's impossible because 9/20 is already at its simplest form.

I roughly work out... I thought 3/7 is psb? (if qn wants denominator less than 20)

3/7 can be an answer if "between" doesn't mean right in the middle between those two given fractions.

There would be other options, if the answers could be given as decimals: 0.41, 0.42...0.49

3/7 does answer the original question. It does not say the answer has to be right in the middle. Neither does it say that there is only one answer. How did you find 3/7 and how would you explain that to a child?

Thanks alot for your explanation, appreciate it much :)

Many possible answers: 3/7, 4/9, 5/11, 5/12, 6/13, etc. get students to justify their answers.

Or 5/12

Key question to the child: "Why did you choose this fraction?"