# add math in head by jiajunhit · Pull Request #57 · muan/scribble · GitHub ## Calculate percentages backward

X% of Y = Y% of X. You can always swap those percentages if doing the maths is easier the other way around. So 68% of 25 = 25% of 68 = 68/4 = 17.

That makes a lot of calculations easy, once you’ve memorized the percentages that equal basic fractions:

• 10% = 1/10

• 12.5% = 1/8

• 16.666…% = 1/6

• 20% = 1/5

• 25% = 1/4

• 33.333…% = 1/3

• 50% = 1/2

• 66.666…% = 2/3

• 75% = 3/4

## Mental Multiplication Using Factors

Like rounding up, one of the multiplication tricks is to factor the number before multiplying it. Let us look at how to do that by trying to multiply 45 x 22.

1. Factor the number

2. Multiply the number with the first factor (left to right)

4. Multiply the product with the second factor (left to right)

In the multiplication tricks we saw earlier, you will have to remember the product of the first digit to add/subtract with the product of the second digit. However, in mental multiplication using factors you just multiply the second factor with the first product, so you don’t have to remember so many numbers as you calculate.

Now you try multiplying 21 x 63 using the factor method. The procedure is the same as before and you can find it below:

## 3. Types of Calculations in Consulting Math

Basic Operations Add, subtract, multiply, divide – those four basic operations form the majority of calculations done by consultants. Simple, isn’t it? You do need to keep in mind however, that consultants usually deal with large numbers and a multitude of items in their calculations; that means you must be extra careful  – forgotten zeroes aren’t good for either business or case interviews.

Simple Equations Equations in management consulting context are mostly used to determine the conditions required for specific outcomes (e.g.: revenue to break even). These equations usually contain one or two variables and no power – only one step away from the most basic calculations.

Percentage Percentages are really useful to put things in perspective; effectively a fraction with a denominator of 100, percentages are often more intuitive and accurate than normal fractions (e.g.: 23% vs 3/13) The widespread use of percentages is a distinctive feature of business language: we usually say “revenue has increased by 50%” or “we need to cut costs by 20%”; we don’t usually say 1/2 or 1/5 in those contexts.

## Tips

• Be patient. It will take your child a while to learn some concepts. If you’re both getting frustrated, take a break and try again later.

• The first and most important number to teach a little child is zero. Kids learn numbers 1 through 4 by counting their fingers. Starting at 0 when teaching math can make grasping concepts easier in the future.[citation needed] ## 15 Math Tricks for kids

### 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.

 3.14159

### 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

## Find more shortcuts

Listverse has some easy mental maths shortcuts. Wikipedia has many advanced shortcuts that cover arithmetic, squares and cubes, roots, and logarithms. And Better Explained lists some common unit conversions.