Below is a sample question for a Grade 8 student. The question is for a student of typical ability for this grade.

What is a number greater than 9/10 but smaller than 10/11?

This question requires the student to think logically and rule out possible answers.

The student needs to break down what the question says into parts which they can manage and think about separately.

The student’s first instinct should be to think that they cannot compare the fractions if they have different denominators. Thus, they should first change both fractions so that they have a common denominator.

The least common multiple of 10 and 11 is 121. So, to get a common denominator, the student should cross multiply 9/10 by 11/11 and 10/11 by 10/10 like so:

Now the student can compare the two fractions easily. Now that they have common denominators, the student can pick any fraction that has a numerator between 99 and 100 with a denominator of 110.

For example, 99.5/110 would be a sufficient answer. However, they should simplify the fraction by multiplying it by 2/2 like so:

This logical reasoning is the basis behind all mathematics and here at Forbest Academy we encourage and nurture students’ logical thinking skills.