As a test prep expert (and math wiz in particular), I meet a lot of students who have a mental block when it comes to division. The minute they see multi-digit numbers, they freak out—“I didn’t learn those!”—and declare defeat before they’ve even begun. That's the kind of auto-panic that can torpedo scores, be it during test prep or on test day itself.
But that’s not going to be YOUR fate! Because you’ve found my blog series on Math Etiquette—the essential math facts and skills that will help you move quickly through the SAT and ACT. And today, we’re tackling division together. The good news is that there are really only a few ways to divide, and they’re all pretty easy. It’s just a question of not jumping to the conclusion that it’s a HUGE DEAL. I promise you—it’s not a huge deal. Allow me to show you why.
ARTICLE CONTENTS
Division Hack #1 for the SAT and ACT
This one is really simple. Remember all those multiplication facts...the ones you already know from somewhere around first grade? Yeah, those multiplication facts.
Well, here’s the nice thing: division just takes those facts and flips them! So, the first step to division is knowing your multiplication facts forward and backwards. A good place to start is with your multiplication tables up to 12.
For example: 8 × 12 = 96—you knew that, right? Sooo...if you see 96 ÷ 12, you should immediately know the answer is 8.
Do you really see what’s going on? If you know your multiplication facts, you start to associate trios of numbers with one other. So if you’ve really got those facts down, then when you see only two of those numbers, your brain will immediately think of the third in the group.
A similar clusters-of-numbers phenomenon happens with addition: you just need to know that two different groups exist, and consciously pick the “multiplication” group. For example, if I think of the numbers 3 and 5, I’ll probably think of two possibilities: 8 (because 3 + 5 = 8) AND 15 (because 3 × 5 = 15). Since my brain recognizes 3-5-8 as a group AND 3-5-15 as another group, I just need to be aware of which one I want.
SAT and ACT Division Trick 2
“But Kristina! The numbers I’M trying to divide are waaaay longer than that easy example you just provided. I swear I don’t know this one!”
I know, the bigger numbers seem daunting at first. But I’ve got (more) good news for you: long numbers are just made up of small numbers…and you already know all the small numbers!
So here's how I do proceed with those long-strings-of-numbers division problems:
Start with the beginning digit or two (the digit or two on the left side of the long number). Do that small division problem.
Then keep moving over another digit to the right, and keep doing the small division problems.
Soon, you’ll have reached the end of the number!
Let's look at an example, one with a really big number: 19,032 ÷ 6 = ?
Take the first digit, the 1—6 doesn’t go into it.
So now take the leftmost two digits, 19—6 fits into 19 3 times, with 1 left over. Write down the 3 and save the 1. So now your solution is looking like this:
19,032 ÷ 6 = 3__
With your “saved” 1, add on the next digit over: 0. That gives us 10. 6 fits into 10 only 1 time, with 4 left over. Save the 4. Where are we now?
19,032 ÷ 6 = 31__
So, do the same thing: take your saved 4 and tack on the next digit: 3. Thus, we’re now dealing with 43. 6 fits inside 43 7 full times, with 1 left over. Write down 7 and save the 1.
19,032 ÷ 6 = 317__
There’s only one digit left! Take your saved 1 and tack on the final digit in the long number: 2. This gives us 12. 6 fits inside 12 evenly 2 times, with nothing left over. Write that 2 down and you’re done!
19,032 ÷ 6 = 3172
Does this process sound vaguely familiar?? It should. It’s JUST LONG DIVISION, which you already learned in second or third grade...but got out of practice because you probably use your smartphone calculator for everything. (Who among us isn’t guilty of that!)
I’m not going to lie to you and pretend this doesn’t take a few extra seconds. It does. Meaning: you may not want to do long division by hand on the ACT Math section or the SAT Calculator section, but the whole point is: you can if you need to.
Division for No-Calculator Math: Skill 3
This one holds a special place in my heart. It’s the most “Math Etiquette” way of dividing. Now, I do have to admit that it’s based on something a lot of you hate: fractions. But wait! Don't throw your laptop across the room just yet. I swear I'm going somewhere more pleasant with this.
You know how when you divide one fraction by another, you’re really just multiplying the first number by the reciprocal of the second?
Well, let’s just take it a step further. If you divide by a number—ANY number, not just a fraction—you’re always multiplying by its reciprocal! Like this:
Thus, if you want to divide by a number, just place it in the denominator! DONE.
In fact, if you are multiplying by several numbers AND dividing by several numbers, it’s MEGA-easy: the first number and all the numbers you’re multiplying by get placed in the numerator, and each of the numbers you’re dividing by get placed in the denominator. Cross out and simplify and you’re done!
Conclusion
I hope these tips help you gain a more instinctive sense of the way division works. That's what math etiquette is all about, after all! The more you have that grasp, the less time you'll have to expend in a high-pressure situation like the No Calculator Math section...or any standardized math test section. It's important to go beyond memorizing the formulaic "tips and tricks" that are so frequently where people stop in their math test prep—at least if you want the highest possible scores!
Still finding yourself with lingering questions? Well, nothing makes me happier than helping my one-on-one clients learn the kind of foundational math knowledge that saves time, effort, and anxiety while maxing out math scores. Or, for a cheaper and DIY option, check out my ACT Math Cram Plan or SAT Math Cram Plan. Until then, happy dividing!
