The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

This is one of the most popular questions on the website, and also one of the most poorly answered.

I have found that the concept of simplifying fractions is one that many students pick up on quickly, but if they are not careful, and if the examples they are given are not chosen carefully enough, they can get into the habit of simplifying looking to half the numerator and denominator until they can't do it any more.

Another issue we have to content with as teachers is students' poor knowledge of their times-tables. The 7s in particularly tend to be poor known, and this question certainly tests that.

Here is what you might learn from students who give the different responses:

Answer a)
might suggest students think they can simply cancel the 1 on the top with the 1 on the bottom. An interesting question to ask higher achieving students is when does cancelling a number from the top and bottom actually lead to the correct answer

Answer b)
implies students have not found the factor of 7

Answer c)
may tell you that students only look to halve the top and bottom

Answer d)
is correct

I believe this question is a really good one to ask to assess students' misconceptions with simplifying fractions

And if you have used the question, or have any thoughts or comments about it – perhaps you would include a different incorrect answer – then please share your comments below. And please consider creating a question yourself on the website! :-)