one way to deal with divisions like the one you presented is to reduce both the numbers in the division by a factor of 10.
In your specific case, if you divide by 10 both, you get 37.5/12.5. You can probably easily figure out the first number of the result should be around 3. You can then multiply 12.5 times 3 and verify it is indeed 37.5.
In terms of general math tips, this is what I would recommend:
- Use correctly 10^ powers in your math computation. For example 3.2B/723M can be transformed in 3200*10^6/732*10^6, which makes it easier to deal with math
- Ask if it is fine to approximate. When you have to deal with math in market sizing, and sometimes even in business cases, you are allowed to approximate math to simplify the computation. In the previous example, for instance, you could transform the computation in 320*10^7/73*10^7, making the overall computation faster.
- Keep good notes. One of the reasons people do mistakes with big numbers is that they don't keep their notes in order, thus forget/misreport numbers
- Divide complex math in smaller logical steps. This is something you can use for big numbers after the application of the 10^ power mentioned above. If you have to compute (96*39)*10^6, you can divide the first element in 96*40 - 96*1 = 100*40 - 4*40 - 96*1 = 4000 – 160 – 100 + 4 = 3744*10^6
- Use shortcuts for fractions. You can learn by heart fractions and thus speed up/simplify the computation - the most useful to know are 1/6, 1/7, 1/8, 1/9.
Finally, in terms of practice before the interview I would recommend to practice math under pressure - not just math. Many candidates are totally fine with calculating 67% of 67 in a quiet environment, but freeze if you ask this suddenly in a case interview.
To practice for this, try always to use a timer with a strict time constraint when you practice math – this will create pressure and help to replicate the actual environment of the interview.
Hope this helps,