Basic Math Rules, Roman Numbers, Math Tricks that will Blow your Mind, 15 math tricks for fast calculation
15 Math Tricks for Fast Calculation
1. Multiplying by 6
If you multiply 6 by an even number, the answer will end with the same digit. The number in the ten's place will be half of the number in the one's place.This ploy works effortlessly and students can add it to their collection of maths magic tricks!
| Example |
6 x 4 = 24
| 24 |
2. The Answer Is 2
Think of a number.
Multiply it by 3.
Add 6.
Divide this number by 3.
Subtract the number from Step 1 from the answer in Step 4.
The answer is 2.
| 2 |
3. Same Three-Digit Number
Think of any three-digit number in which each of the digits is the same. Examples include 333, 666, 777, and 999.
Add up the digits.
Divide the three-digit number by the answer in Step 2.
The answer is 37.
| 37 |
4. Six Digits Become Three
Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552.
Divide the number by 7.
Divide it by 11.
Divide it by 13.
The order in which you do the division is unimportant!
The answer is the three-digit number.
| Example |
371371 gives you 371 or 552552 gives you 552.
A related trick is to take any three-digit number.
Multiply it by 7, 11, and 13.
The result will be a six-digit number that repeats the three-digit number.
| 456 becomes 456456 |
5. The 11 Rule
The 11 rule is one of those magic tricks and methods that can be used to quickly multiply two-digit numbers by 11 in your head.
Separate the two digits in your mind.
Add the two digits together.
Place the number from Step 2 between the two digits. If the number from Step 2 is greater than 9, put the one's digit in the space and carry the ten's digit.
| Example |
72 x 11 = 792.
57 x 11 = 5 _ 7, but 5 + 7 = 12, so put 2 in the space and add the 1 to the 5 to get 627
6. Memorizing Pi
This is probably the most fun tricks in maths -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.
| 3.141592 |
7. Contains the Digits 1, 2, 4, 5, 7, 8
Select a number from 1 to 6.
Multiply the number by 9.
Multiply it by 111.
Multiply it by 1001.
Divide the answer by 7.
The number will contain the digits 1, 2, 4, 5, 7, and 8.
| Example |
The number 6 yields the answer 714285.
| 714285 |
8. Multiply Large Numbers in Your Head
Another math magic tricks and methods to apply to easily multiply two double-digit numbers, is to use their distance from 100 to simplify the math:
Subtract each number from 100.
Add these values together.
100 minus this number is the first part of the answer.
Multiply the digits from Step 1 to get the second part of the answer.
9. Super Simple Divisibility Rules
You've got 210 pieces of pizza and want to know whether or not you can split them evenly within your group. Rather than taking out the calculator, use these simple shortcuts to do the math in your head:
Divisible by 2 if the last digit is a multiple of 2 (210).
Divisible by 3 if the sum of the digits is divisible by 3 (522 because the digits add up to 9, which is divisible by 3).
Divisible by 4 if the last two digits are divisible by 4 (2540 because 40 is divisible by 4).
Divisible by 5 if the last digit is 0 or 5 (9905).
Divisible by 6 if it passes the rules for both 2 and 3 (408).
Divisible by 9 if the sum of the digits is divisible by 9 (6390 since 6 + 3 + 9 + 0 = 18, which is divisible by 9).
Divisible by 10 if the number ends in a 0 (8910).
Divisible by 12 if the rules for divisibility by 3 and 4 apply.
| Example |
The 210 slices of pizza may be evenly distributed into groups of 2, 3, 6, 10.
10. Finger Multiplication Tables
Everyone knows you can count on your fingers. Did you realize you can use them for multiplication? A simple maths magic trick to do the "9" multiplication table is to place both hands in front of you with fingers and thumbs extended. To multiply 9 by a number, fold down that number finger, counting from the left.
| Example 1 |
To multiply 9 by 5, fold down the fifth finger from the left. Count fingers on either side of the "fold" to get the answer. In this case, the answer is 45.
| 45 |
| Example 2 |
To multiply 9 times 6, fold down the sixth finger, giving an answer of 54.
| 54 |
11. 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.
| 882 |
12. 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.
| 444 |
13. Multiplying 5 times any number
When multiplying the number 5 by an even number, there is a quick way to find the answer.
| Example 1 |
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
| 20 |
| Example 2 |
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
| 15 |
14. Division tricks
Here’s a quick trick in maths 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
15. 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.
| Example |
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.
| 2400 |
Basic Math Rules, Roman Numbers, Math Tricks that will Blow your Mind, 15 math tricks for fast calculation
Math Tricks that will Blow your Mind
Divisibility Rules
- A number is divisible by 2 if the last digit of the one’s place is divisible by 2.
- A number is divisible by 3 if the sum of the digits is divisible by 3.
- A number is divisible by 4 if the last two digits in the number are divisible by 4.
- A number is divisible by 5 if the last digit is a 0 or 5.
- A number is divisible by 6 if the number is divisible by both 2 and 3.
- A number is divisible by 8 if the sum of the digits is divisible by 9.
Easy Subtraction with No Grouping
Introduce the concept of looking at subtraction as the distance between two numbers.
So, if you look at the numbers 4,000 and 1,394, the distance between those two numbers is the same as the distance between 3,999 and 1,393. Therefore, if you are provided with the problem of 4,000-1,394, you can subtract 1 from each of those numbers and subtract 1,393 from 3,999 to get the same answer.
Obviously, you are not going to always subtract 1 — that’s only if you need to make the top number (or most of the digits in that number) smaller to decrease the amount of ‘borrowing’ and ‘grouping’ you have to do.
Comparing Fractions Math Trick
Teach Starter Teacher Tip: This is also called ‘cross multiplying’ because you create a cross in the middle
The numbers that students get from cross-multiplying fractions become the two numerators they would get if they’d gone through the process of creating two ‘like’ fractions. All they need to do now is determine the bigger number of the two!
Multiplying Double-Digit Numbers by 11
To multiply any two-digit number by 11, simply add the digits of the number together. Put the result of your addition between the two digits of your original number.
For example, to quickly find the answer to 26 x 11, start by adding the two digits of the number 26 together to get 2+6=8.
Next, put this new number between the original two digits to get 286. That’s the answer!
But wait a second. What if the sum of the two digits is greater than 9? In that case, carry the 1 over to the tens digit and add the two numbers. For example: 47 x 11 = 517. When you break it down: 4+7 = 11.
Japanese Multiplication
This trick takes a multiplication problem and turns it into a simple counting problem that can be solved visually. To show this math trick in action, let’s start with a simple multiplication problem. Basically, you are looking at 2 x 3, or 2 groups of 3.
By drawing 2 lines one way and 3 lines the other, you create an intersection of 2 groups of 3. By counting all of the times the lines intersect, you get your answer: 6.
Now, let’s try a trickier multiplication problem.
- Each place value number in both numbers requires a set of lines.
- The 1 line for the number 1 in 12 is representing (1) ten.
- The 2 lines (going the same way) represent (2) ones.
- With the number 23, the 2 lines (going the other way) represent the (2) tens and the 3 lines represent the (3) ones.
- You need to make sure that both numbers you are multiplying crossover like in the image below.
On the left corner, put a curved line through the wide spot with no points, and do the same on the right, separating the intersections into three groups.
Finally, count the three groups of intersections, giving you the answer of 276.
How does Japanese Multiplication work?
Remember, we are looking at the problem 12 x 23.
- Let’s start with the intersections on the far right. There are 6 intersections, which represent 2 ones x 3 ones. So 6 will be in our ones place for the answer.
- On the far left, there are 2 intersections. This set of lines represents the tens in the original numbers used in the problem. So 2 is 20, and 1 is 10, meaning 20 x 10 equals 200. So, our answer will begin with the number 2 in the hundreds place.
- In the top middle section, we have 2 tens x 2 ones which give us 40. Plus, in the bottom middle section, we have 1 ten x 3 ones which give us 30. We have a total of 70 for the tens place.
- All of this gives us a grand total of 276!
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