# Tricks and Tips for Doing Math in Your Head

You don’t have to be a math teacher to know that a lot of students—and likely a lot of parents (it’s been awhile!)—are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math, improve math skills and understanding, and excel in advanced courses.

If it’s your job to teach those, here’s a great refresher.

**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.

**10. Multiplying numbers that end in zero**

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

200 x 400

Step 1: Multiply the 2 times the 4

2 x 4 = 8

Step 2: Put all four of the zeros after the 8

80,000

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics—and unafraid to work with numbers in the future.

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