As we all know, a lot of students as well as a lot of parents are intimidated by math problems, specifically if they involve large numbers. Understanding techniques on how to do math quickly can help students improve math skills and develop greater confidence in it.
Here is a great refresher if it is your job to teach math
Tricks for doing fast math
Here are 10 fast math strategies students and also adults can use to do math in their heads. Students should be able to accurately and confidently solve math problems that they once feared solving once these strategies are mastered.
Round to the nearest whole number
Adding large numbers
It can be difficult to add large numbers in your head. This method demonstrates how to facilitate this process by making all the numbers a multiple of 10. Here is a sample:
744 + 338
While these numbers are hard to deal with, rounding them up will make them easier to calculate. So, in this case, 744 becomes 750, and 338 becomes 340.
Add 750 and 340 together. The total is 1090. It must be determined how much we added to the numbers to round them up in order to find the answer to the original equation.
So, 750 – 744 = 6 and 340 – 338 = 2
For a total of 8 add 6 and 2 together
To find the answer to the initial equation, you should subtract 8 must from 1090.
1090 – 8 = 1082
Subsequently, the answer to 744 + 338 is 1082.
Subtracting from 1,000
Here’s a basic rule to subtract a large number from 1,000: Every number should be subtracted except the last from 9 and subtract the final number from 10
For instance:
1,000 – 667
Step #1: Subtract 6 from 9 = 3
Step #2: Subtract 6 from 9 = 3
Step #3: Subtract 7 from 10 = 3
The answer is 333.
Check out our rounding calculator
Multiplying 5 times any number
There is a quick way to find the answer when multiplying the number 5 by an even number:
For instance, 5 x 6 =
Step #1: Take the number being multiplied by 5 and cut it in half, this makes the number 6 become the number 3.
Step #2: Add a zero to the number to get the answer. In this instance, the result is 30.
5 x 6 = 30
The formula is a bit different when multiplying an odd number times 5.
For instance, consider 5 x 7.
Step #1: Subtract one from the number being multiplied by 5, in this instance the number 7 becomes the number 6.
Step #2: Now halve the number 6, which makes it the number 3. Make 5 the last digit and you will get 35, which is the answer.
5 x 7 = 35
Division tricks
Below you will find a quick way to know when a number can be evenly divided by these specific numbers:
- If it ends in 0, 2, 4, 6, or 8, it is 2
- When the digits are added together and the result is evenly divisible by the number 3, it is 3
- If it ends in 00 or a two-digit number that is evenly divisible by 4, it is 4
- If it ends in a 0 or 5, it is 5
- If it is an even number and when the digits are added together the answer is evenly divisible by 3, it is 6
- If the last three digits are evenly divisible by 8 or are 000, it is 8
- When the digits are added together and the total is evenly divisible by 9, it is 9
- If the number ends in 0, it is 10
Multiplying by 9
It is an easy method that is practical for multiplying any number by 9. Here is how it works:
Let’s use the sample of 5 x 9.
Step #1: Subtract 1 from the number (5 in this case) that is being multiplied by 9.
5 – 1 = 4
The number 4 is the first number in the answer to the equation.
Step #2: Subtract that number from the number 9.
9 – 4 = 5
The number 5 is the second number in the answer to the equation.
So, it will be 9 x 5 = 45
10 and 11 times tricks
When multiplying any number by 10 the trick is to add a zero to the end of the number. For instance, 82 x 10 = 820.
There is an easy trick for multiplying any two-digit number by 11 as well. Here it is:
11 x 45
Take the original two-digit number (in this case 45) and put a space between the digits.
4_5
The next step is to add those two numbers together and put the result in the center:
4_(4 + 5)_5
4_9_5
The answer to 11 x 45 is 295.
If the digits in the center add up to a digit with two numbers, insert the second digit and add 1 to the first one. Here is a sample of equation 11 x 99:
9_(9 + 9)_9
(9 + 1)_8_9
10_8_9
There is the answer to 11 x 99: 1089
Percentage
It can be tricky to find a percentage of a number, but it makes it much easier to understand when thinking about it in the right term. For example, to find out what 5% of 235 is, stick to this technique:
Step #1: Move the decimal point over by one place, 335 becomes 33.5.
Step #2: Divide 33.5 by the number 2, the answer is 16.75. That is the answer to the original equation as well.
Swiftly square a two-digit number that ends in 5
Let’s use the number 45 as an example.
Step #1: Multiply the first digit by itself plus 1.
Step #2: Put a 25 at the end.
45 squared = [4 x (4 + 1)] and 25
[4 x (4 + 1)] = 2020 and 25 = 2025
45 squared = 1225
Tough multiplication
If one of the numbers is even while multiplying large numbers, divide the first number in half, and then double the second number. This approach will solve the problem quickly. For example, consider:
40 x 220
Step #1: Divide the 40 by 2, which equals 20. Double 220, which equals 440.
Then multiply your two answers together.
40 x 440 = 8800
The answer to 40 x 220 is 8800.
Multiplying numbers that end in zero
Actually, it is fairly simple to multiply numbers that end in zero. It contains multiplying the other numbers together and then adding the zeros at the end. For example:
300 x 500
Step #1: Multiply the 3 times the 5
3 x 5 = 15
Step #2: Place all 4 of the zeros after the 15
150000
300 x 500= 150,000
Practicing these fast math tricks can help students as well as teachers to improve their math skills and become confident in their understanding of mathematics.