How to do quick math in your head

10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

644 + 238

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 – 8 = 882

So the answer to 644 +238 is 882.

2. Subtracting from 1,000

Here’s a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 – 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

  • Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
  • Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

5 x 4 = 20

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

  • Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
  • Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

5 x 3 = 15

4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

  • 10 if the number ends in 0
  • 9 when the digits are added together and the total is evenly divisible by 9
  • 8 if the last three digits are evenly divisible by 8 or are 000
  • 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
  • 5 if it ends in a 0 or 5
  • 4 if it ends in 00 or a two digit number that is evenly divisible by 4
  • 3 when the digits are added together and the result is evenly divisible by the number 3
  • 2 if it ends in 0, 2, 4, 6, or 8

5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1: Subtract 1 from the number that is being multiplied by 9.

3 – 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2: Subtract that number from the number 9.

9 – 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

11 x 25

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

2_5

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

2_7_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

8_(8 +8)_8

(8 + 1)_6_8

9_6_8

There is the answer to 11 x 88: 968

7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

  • Step 1: Move the decimal point over by one place, 235 becomes 23.5.
  • Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

  • Step 1: Multiply the first digit by itself plus 1.
  • Step 2: Put a 25 at the end.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

20 x 120

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

Video

Memorizing Pi

To remember the first seven digits of pi, count the number of letters in each word of the sentence:

"How I wish I could calculate pi."

This becomes 3.141592.

Subtract without carrying digits

Mental subtraction is easiest when you can subtract each digit without having to carry any places. If the second number has some bigger digits than the first, it gets more complicated. To avoid carrying places, you want to get rid of those bigger digits. Here’s how:

Say you’re calculating 925-734. That tens place makes things a little complicated. It’d be easier to calculate 925-724, and then subtract that extra 10 separately: 925-724 = 201, and 201-10 = 191. There’s your answer.

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Convert temperatures

To roughly convert from Celsius to Fahrenheit, multiply by 2 and add 30. From Fahrenheit to Celsius, subtract 30 and divide by 2. (To more precisely convert C to F, multiply by 1.8 and add 32.)

The order is important: The addition/subtraction is always closer to the Fahrenheit side of the conversion. If you forget the order, you know that 32° F = 0° C, so you can test your formula against that.

Or just memorise that room temperature is about 20–22 °C or 68–72 °F, and normal body temperature is around 36-37° C or 97-99° F, depending on several factors.

Becoming A Human Calculator

You have learnt the basic multiplication tricks. But We have only scratched the surface and there is so much more to cover. If you really want to become a human calculator and take your mental math skills to the next level, then watch this video. In the video I will share the story of how I actually struggled with math and how I got to where I am today. You will learn the secret that will shorten your learning curve and speed up your journey to mental math mastery. To watch the video click here.

How do you add and subtract fast in your head?

  1. To add 9 to another number, add 10 and then subtract 1: 36 + 9 = 36 + 10 – 1 = 45.
  2. To add 18 to another number, add 20 and then subtract 2: 48 + 18 = 48 + 20 – 2 = 66.
  3. To add 97 to another number, add 100 and then subtract 3: 439 + 97 = 439 + 100 – 3 = 536.

What is a Multiplicand and a Multiplier?

Before we get into multiplication tricks to do mental math, let us quickly define what a multiplicand and a multiplier is. Take for example, the multiplication problem 43 x 23. Here the number 43 is the multiplicand – the number being multiplied. The number 23 is the multiplier – the number which is multiplying the first number.

There are several multiplication tricks for mental math in this post. Each mental multiplication method will have two examples. The first example, visible to everybody, will introduce you to the multiplication trick. The second example, visible only to logged-in users, will have variations not covered in the first example. So log in or sign up for free to access the entire content.

Simplify Before You Solve It

The key is to simplify before you start.  Victor writes:

“Revenue = 2 million buyers x 15% market share x $300 revenue per buyer

Most people gravitate to solving a math problem in exactly the form  in which it is presented, but it’s often easier to simplify the problem into a series of smaller problems.  For example, I notice that the first number ($2 million) and the last number ($300) are easy numbers to multiply, so I would mentally rewrite the equation as follows:

(2 million x $300) x 15%

That works out to $600 million x 15%”

2. LISTENING TO MUSIC // PATTERN THEORY AND SYMMETRY

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The making of music involves many different types of math, from algebra and geometry to group theory and pattern theory and beyond, and a number of mathematicians (including Pythagoras and Galileo) and musicians have connected the two disciplines (Stravinsky claimed that music is "something like mathematical thinking").

But simply listening to music can make you think mathematically too. When you recognize a piece of music, you are identifying a pattern of sound. Patterns are a fundamental part of math; the branch known as pattern theory is applied to everything from statistics to machine learning.

Danielson, who teaches kids about patterns in his math classes, says figuring out the structure of a pattern is vital for understanding math at higher levels, so music is a great gateway: "If you're thinking about how two songs have similar beats, or time signatures, or you're creating harmonies, you're working on the structure of a pattern and doing some really important mathematical thinking along the way."

So maybe you weren't doing math on paper if you were debating with your friends about whether Tom Petty was right to sue Sam Smith in 2015 over "Stay With Me" sounding a lot like "I Won't Back Down," but you were still thinking mathematically when you compared the songs. And that earworm you can't get out of your head? It follows a pattern: intro, verse, chorus, bridge, end.

When you recognize these kinds of patterns, you're also recognizing symmetry (which in a pop song tends to involve the chorus and the hook, because both repeat). Symmetry [PDF] is the focus of group theory, but it's also key to geometry, algebra, and many other maths.

Six Digits Become Three

  1. Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552.
  2. Divide the number by 7.
  3. Divide it by 11.
  4. Divide it by 13.

The order in which you do the division is unimportant!

The answer is the three-digit number.

Examples: 371371 gives you 371 or 552552 gives you 552.

  1. A related trick is to take any three-digit number.
  2. Multiply it by 7, 11, and 13.

The result will be a six-digit number that repeats the three-digit number.

Example: 456 becomes 456456.

How do I get good at maths fast?

  1. Practice. As with any subject or discipline, the best way to get better is to practice.
  2. Understand Mistakes. Math is one of the subjects where your work really matters to get to the solution.
  3. Grasp Concepts.
  4. Get Help When Needed.

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