Below is a question a typical grade 4 student would receive on a math exam. The question is for students of an average ability level.
Which missing value makes these fractions equal?
To answer this question, students must be aware of what each part of the fraction means. The numerator determines the number of parts and the denominator displays the total number of parts.
With fractions questions visualization is very beneficial to students.
Here is a grid broken into 16 parts where 4 are highlighted.
Now we take the same grid however we only split it into 8 parts.
From here we can tell, if we want to keep the same amount of area shaded as the original, we only need to color 2 blocks.
Once students are aware of this, they find it easier to see why we use division and multiplication to find equivalent fractions, and it becomes much easier to teach them to perform the same operation on the top and bottom of a fraction to keep the fraction in the same proportion.