How to Divide Numbers in Your Head on the SAT
A good way to think of division is the opposite of multiplication. For instance, if you know that 7 x 4 = 28 than it should be easy to figure out what 28/4 is. Just as we did with multiplication, we want to break down larger numbers into smaller bits. 280/7 is the same 28/7 but with a zero at the end of it. One way to think of this is to split up 280 into 28 x 10. Dividing it by 4, we get: 28/4 x 10 = 70.
Of course, not all numbers end in ‘0’. What if we have 175/5? Well, we can break 175 into 150 + 25 (notice how this doesn’t have a multiplication sign in the middle the way that 28 x 10). So when we divide by 5, we are dividing both of those numbers: 150/5 + 25/5 = 30 + 5 = 35.
This tactic works when the number you are dividing by (in this case ‘5’) divides evenly into both numbers. Say, for instance, that you have 216 and you are dividing it by ‘4’. It helps to notice that 16 is divisible by 4. In fact, a rule of dividing by 4 is that if the last two digits of the number are divisible by 4, the entire number is divisible by 4. So I can break up 216 into 200 and 16, giving me 200/4 and 16/4, which equals 50 + 4 = 54.
One final note, before a couple of practice questions: throughout this post, when I’m showing you these tactics, they are for mental math (meaning: no pencil and paper). So don’t write down 200/4 + 16/4. The reason I show you this is it is not too difficult to do those steps in your head. Try it below!