When a lot of people think of math, they are reminded of dreaded geometry tests and endless high school homework assignments. Sadly, mathematics is something that many of us stop thinking about as soon as we’re not academically required to. We let go of things like the quadratic equation and prime factorization and reach for our iPhones whenever we need to add or multiply numbers. As the old saying goes, if you don’t use it, you lose it, and this applies especially to math.

But whether it’s been a few years or a few decades since your last math class, it’s never too late to polish up your number skills. Besides the mental workout that running through a good math problem can provide, knowing a few simple tricks for how to manipulate values in different wants can help make everyday tasks quicker and easier. Spend a little time reading over our list and practicing the techniques (practice makes perfect!) we highlighted so you can bypass the calculator the next time you need to pull some numbers together.

Math!

Multiply any number by 11

This trick is great because it doesn’t require any multiplication—with just a few simple additions, you can calculate the product of any number and 11. Grab a piece of paper and a pencil and run through this process a few times with some numbers until you have it down.

- Step one, write down the problem. Let’s do this one with 11 x 81,775.

“11 x 81,775″

- Start by writing down the last number in the larger number.

“5″

- Now add the last two numbers in the larger number. Write the sum down next to the previously written number.

“7+5 = 12″

- Since there the answer is two digit, we’ll carry the one over to the next summation. Write the “2″ from the “12″ down next to the “5″ you just wrote down.

1             <- “1″ carried over from the “12″
“25″

- Now add the next pair to the left in the larger number. In 81,775, that’s “77″.

“7 + 7 = 14″

Add the 1 carried over from the previous summation.

“14 + 1 = 15″

- Once again, write the “5″ from the “15″ down next to the previously written down “25″ and carry the “1″.

1             <- “1″ carried over from the “15″
“525″

- Keep repeating this process until you get to the first two digits in the larger number.

- The next pair of numbers in “81,775″ after “77″ is “17″.

“1 + 7 = 8″

Add the 1 carried over from the previous summation.

“8 + 1 = 9″

Write the “9″ down next to the previously written “525″.

“9525″

- The next pair of numbers in “81,775″ after “17″ is “81″.

“8 + 1 = 9″

Write the “9″ down next to the previously written “9525″.

“99525″

- Once you hit the last pair to the right, in this case, “81″, you just need to add the first digit of the large number (“8″ in the case of “81,775″) onto the previously written down “99525″ for your final answer.

“899,525″

81,775 * 11 = 899,525

Problems to try yourself:

• 11 x 2,394

• 11 x 847,332

• 11 x 1,295,372,983

 

Square a two digit number ending in 5

Multiplying a two digit number by itself is super easy when it ends in 5.

- Start by writing down the number you want to square.

“35″

- Take the digit in the tens column, in the case of “35″ it’s “3″, and add 1 to it.

“3 + 1 = 4″

- Multiply the sum you get by the digit in the tens place (“3″).

“4 x 3 = 12″

- Write down “25″ after the product you just got and you are done!

“1225″

“35 x 35 = 1225″

 

Problems to try yourself:

• 25 x 25

• 95 x 95

• 75 x 75

 

Multiply large numbers together (up to 20 x 20)

This is a great trick that you can do in your head by keeping track of just a few numbers and running some easy single digit multiplications. If you want to multiply any two two-digit numbers together, just follow these steps.

- Start by writing down the problem you want to do. We’ll go with “14 x 19″ in this example. Always frame the problem with the larger of the two numbers being multiplied together on top of the smaller number.

19
x 14

-  Highlight the top two digits on the number on top and the ones digit on the number on bottom.

19
x 14

to get “19″ and “4″. Add those numbers together.

“19 + 4 = 23″

- Add a zero to that sum.

“23, add a 0 = 230″

- Multiply the two digits in the singles spaces together. From “84″ we get “4″ and from “23″ we get “3.

“4×9 = 36″

- Add the sum you get to the “870″ from above for your final answer!

“36 + 230 = 266″

“14 x 19 = 266.”

 

Problems to try yourself:

• 16 x 12 =

• 18 x 19 =

• 14 x 16 =

Multiply any number by 9

9 is my favorite number and you can do some really fun things when you multiply it by other numbers. Here is a quick and easy way to multiply any single digit number by 9 (in case you don’t have it memorized, which you should).

- We’ll go with “9 x 7″ for this example. Start by subtracting 1 from the number you are multiplying by 9.

7 – 1 = 6.

- Write that down as the tens digit for your answer. To get the ones digit, just subtract the digit in the tens place from 9.

“9 – 6 = 3″

- Write down the answer in the ones spot and you’re done!

“9 x 7 = 63″

 

Problems to try yourself:

• 9 x 9 =

• 9 x 8 =

• 9 x 4 =

 

Another cool property of a summation of any number by nine is that the digits of the answer, when summed up themselves down to a single digit, will be either 3, 6, or 9. For example,

9 x 4,934 = 44,406.

44,406—>  4 + 4 + 4 + 0 + 6 = 18 (Note, 18 is divisible by 9)

18—> 1 + 8 = 9

Let’s do another.

9 x 238,763,895,675 = 2,148,875,061,075

2,148,875,061,075 —> 2 + 1 + 4 + 8 + 8 + 7 + 5 + 0 + 6 + 1 + 0 + 7 + 5 = 54

54 —> 5 + 4 = 9

Multiply any number by 5

5 is half of 10, which gives it some interesting properties that can be used to multiply any number against it. We’re going to show two examples—the first with an even number, the second with an odd number. Our first example is “244 x 5″.

- Start by dividing the number you’re dividing by 5 in half.

Half of 244 is 122.

- Add a zero on the end of the number and you have your answer.

122, add a 0 —> 1220

“244 x 5 = 1220″

- If you’re multiplying an odd number by 5, you just need to make one simple change to the process. Let’s multiply 489 x 5. Start by subtracting 1 from the number you are multiplying by 5.

“489 – 1 = 488″

- Now that you are dealing with an even number, you just need to repeat the process from above. Take half of 488 and add a zero.

“Half of 488 is 244. Add a zero to get 2,440.”

- To get the final answer, just add a five to that number (to compensate for the 1 in the first step “489 – 1 = 488.

“2,440 + 5 = 2,445″

488 x 5 = 2,445

 

Problems to try yourself:

• 96 x 5 =

• 248,469 x 5 =

• 997 x 5 =

Test whether a number is not prime

A prime number is one that only has itself and 1 as positive divisor (it can only be cleanly divided by 1 and itself). Composite numbers, in addition to being divisible by 1 and itself, can be divided by other prime numbers. 7 is prime (7 can only be divided by 7 and 1), 9 is composite (9 can be divided by 1, 9, and 3).

23, prime (23 can only be divided by 1 and 23).

65, composite (65 can be divided by 5 and 13

37, prime (37 can only be divided by 1 and 37).

120, composite (120 can be divided by 1, 120, 2, 5, and 3)

There is no quick and easy way to test if a number is a prime number, but there are a few ways that you can test whether any given number is not a prime.

This trick doesn’t really come up much in everyday life, but it still stands as a cool thing to know.

The first easy way to test if a number is not prime is whether it ends in an even number (meaning it can be divided by 2), a 5 (it can be divided by 5), or a 0 (it can be divided by 2 and 5). If your number ends in one of those numbers, you know it’s not a prime number.

If you have a number that ends any other number, you can apply this quick test to learn if your number could be a prime number or that it definitely is not.

- Is your number in the form of 6k plus or minus 1, where k = any positive whole number? If it’s not, it is not a prime. Every prime number greater than 3 is in the form 6k+1. If the number you are testing can’t be expressed in as 6k+1, then it is not a prime. It’s important to note that while every prime number is in the form 6k+1, not every number that is in the form 6k+1 is prime. For example—23 is prime and as such, can be expressed as 6k+1 (k = 4: 23 =  6 x (4) – 1). But 25, which can be expressed as 6k+1 (k = 4: 25 =  6 x (4) + 1) is not prime.

So by testing a number to see if it can be expressed as 6k+1, you can tell if a number is definitely not a prime or whether it is possibly a prime.

Problems to try yourself:

• Could 96 be prime?

• Could 631 be prime?

• Could 7,001 be prime?

Main image credit: Teo Romera/Flickr; 11 image credit: Clive Darr/Flickr; 5 image credit: Jules Antonio/Flickr; large numbers image credit: Rich Bowen/Flickr; 9 image credit: yoppy/Flickr; multiply by 5 image credit: Silke Blaschek/Flickr; prime image credit: Tom Purves/Flickr