Learning a few simple tricks can make math easier and more enjoyable. From calculating a restaurant tip to saving a few seconds on an exam, tallying totals in your head can give you a head start on almost any problem. It won't always work out and you should have a failsafe, such as a calculator or an app on your phone, if you are uncertain about the outcome. As in most mathematical endeavors, practice really does make perfect.
As an amateur mathematician, you should learn your limits. If you can perform advanced multiplication and division in your head, you probably don't need to review these simple shortcuts. But if you have problems adding, dividing, multiplying, or subtracting multiple-digit numbers visually, you should learn a few simple tricks that will help you save time on tests.
1. Multiplication tables
Learning your times tables make it much easier to multiply and divide at the drop of a hat. These tables are really nothing more than patterns that can be mastered with a bit of practice. Repeat them backwards and forwards, at random, until you know them like the back of your hand. You should be able to see each table in your head by the time you have master the material.
2. Visualization is important
You don't have to be Good Will Hunting or Little Man Tate to actually see
mathematical problems and make them move in your head. Yes, you can always write the sum out. But visualizing it will help you save time on easy answers. Of course, you shouldn't attempt this shortcut unless you can get the right answers every time. If you have any issue calculating numbers in your head, without a pad and pencil in reach, don't do it. The ten or twenty seconds you might save are not worth an incorrect answer.
3. Practice, practice, practice
The most important word of advice your math teachers will give you is to practice your multiplication tables regularly. Yes, they should come quite easily after a month or two, but that doesn't mean they'll be there forever. Many high school students benefit greatly from reviewing these tables before they take their SATs. Always remember, the more you practice, the more numbers you can divide or multiply in no time. Yes, most of us can breeze through single digit numbers, but how about double, even triple-digit ones? You might thing those kinds of numbers are reserved for the Rain Men of this world, but that simply isn't true. With a little bit of practice, nearly anyone can multiply and divide large numbers.
4. Don't give up
Even if you have a head for numbers, it will take you time to get good enough at calculations to use these visualization methods on a test. If you have any question about their effectiveness, never utilize them on an exam in place of a pad and pencil. Ideally, you should be able to get the same results in a fraction of the time in your mind each time out.
5. Challenge yourself
When you can do the basics with your eyes closed, try to press yourself with problems that have more than one or two numbers. Practice often enough to complete these calculations more quickly than you could with a calculator. After all, that's the point. You want to train your mind to take shortcuts and save you time on important tests and exams.
6. If necessary, use a calculator
There are very few test and exams that ban calculators completely. Even on the SAT and AP exams, students are allowed to use calculators on math-related subjects and sections. As we mentioned, doing simple problems in your mind can help your save time. But if you cannot complete these calculations accurately and consistently, you should never be embarrassed or ashamed to reach for a calculator. At the very least, you can use them to check your answers.
7. Math is fun
Okay, it may not be a blast. Obviously, we all have a different interpretation of what a good time may be. Some of us can take shortcuts and solve problems in our heads. That is not only rewarding, it also gives us a temporal advantage on tests and exams. For most of us, however, we must rely on the things we can see and touch, like our fingers. Memorizing math tables on our fingers is a lot easier on our first five digits than it is on our second. The reason can probably be attributed to miscounting, but really...who knows?
8. Squaring
There are countless math tricks and shortcuts that can help a person of any ability level arrive at the right answer a bit faster. Squaring is one of the rare talents that only a few folks can complete competently in their heads. However, if you know this simple trick, you too can pretend to be a math whiz, even if you aren't one. How it works?
If, for example, you need to square a two-digit number that ends in 5, simply multiply the first number by itself, plus one, and add 25 to the end. For example, if you are squaring 25, simply multiple the first number by itself plus one, i.e., 2+1=3, and square it, which equals 6. Next, put the 25 on the end, which makes it 625.
9. Real knowledge rules
These little tricks and stratagems are all well and good, but they are no substitute for practice. The easiest and most effective way to save time on important
math tests and exams is to learn your multiplication tables backwards and forwards. Tricks are really no substitute for real knowledge. You should have a firm grasp on your tables so that you can save time on simple answers during important evaluations.
In conclusion, it is important to reiterate that a calculator can be a useful tool, especially if you are unsure about your multiplication tables. Even if you use it simply to check your work, make sure you bring one along, if they are allowed.