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Math Tricks can be used to solve mathematical calculations easily and quickly by using shortcuts. These Tricks help us simplify various mathematical operations for exams or everyday use.
Let's discuss the most essential tricks in Maths with solved examples.
Some of the basic math tricks are:
Let's discuss these tricks in detail.
Tricks to add number can be written in following steps:
- Step 1: Identify the nearest 10s multiple.
- Step 2: Combine the multiples of 10s.
- Step 3: Adjust the deficiency by Adding/Subtracting.
Now take an example to understand this approach,
Add 48+77.
As per 1st step, The closest to the 10s multiple for 48 is 50
The closest to the 10s multiple for 77 is 80.
Then add these new number 50+80= 130.
The deficiency of number 48 is 2
The deficiency of number 77 is 3
So, 130 – (2 + 3) = 130 – 5
= 125.
Steps to add large numbers quickly are discussed below:
The best trick of Subtraction is rounding the number to be subtracted such that its unit place or above is zero.
Let's take an Example of subtracting 1847 from 1900.
- Step 1: Add 3 in 1847 to obtain 1850.
- Step 2: Next, subtract 1850 from 1900.
- Step 3: Add 3 to the result, It will become 50+3 = 53.
Subtract each digit except the last from 9 and subtract the final digit from 10 when subtracting from 1,000.
For example: 1,000 – 773
The answer is 227.
This section delves into various multiplication tricks, including the use of finger math, breaking down complex numbers, etc.
Crisscross System Of Multiplication
Case 1: Multiplying a 2-digit number by a 2-digit number
Example: 43 × 12
- Step 1: We multiply the digits in one’s place, that is, 3 × 2 = 6. We write 6 in the ones place of the answer.
- Step 2: Now, we cross multiply and add the products, that is, (4 × 2) + (3 × 1) = 11. We write the 1 in the tens place of the answer and carry forward 1 to left side multiplication for add.
- Step 3: Now we multiply the ones digits, that is, 4 × 1 = 4 and add 1
- Now complete multiplication is: 4|11|6
- So, the answer is 516.
Case 2: Multiplying a three-digit number by another three-digit number
Example: 121 × 302
- Step 1: Multiply 1 by 2 to get the product 2.
- Step 2: Cross-multiply by taking the product of (2 × 2) and adding it to (1 × 0), resulting in the final answer of 4.
- Step 3: Multiply (1 × 2), (2 × 0), and (3 × 1), and then add the three products to obtain the final answer of 5.
- Step 4: Multiply (1 × 0) and (3 × 2) to get the final answer of 6.
- Step 5: Multiply the leftmost digits, which is (1 × 3), and get the answer of 3.
- Therefore, the ultimate result is 36542.
We are going to discuss a useful trick in math for quick division.
Suppose we are Dividing a Large number by 5,
For example: 3456 / 5 = ?
- Step 1: Multiply the number by 2.
3456x2 = 6912
- Step 2: Move one decimal place.
That would be, 691.2
So, the answer is 3456 / 5 = 691.2
Read More,
Some easy calculations shortcuts are:
Let's discuss these tricks in detail.
Let's learn a shortcut to quickly find out the square of a number.
For example: Let's find the square of 213.
213 - 3 = 210
213 + 3 = 216
210 x 216 = 45,360
Since 32 = 9, we add 45,360 + 9 = 45,369.
| Concept | Steps or Explanation |
|---|---|
| Finding Squares Ending in 5 | |
| Example | Square of 65. |
| Step 1 | Square the last two digits: 5² = 25. |
| Step 2 | Multiply the tens digit (6) by the next consecutive number (7): 6 × 7 = 42. |
| Step 3 | Combine the result (42) with 25: 4225. |
| Result | 65² = 4225. |
| Squaring a Two-digit Number | |
| Example | Square of 47. |
| Step 1 | Add the tens and units digits: 7 + 47 = 54. |
| Step 2 | Multiply this sum by the tens digit: 54 × 4 = 216. |
| Step 3 | Square the units digit: 7² = 49. |
| Step 4 | Combine the results: 2160 + 49 = 2209. |
| Result | 47² = 2209. |
In this section, we are going to discover a trick to easily calculate the square root of a number.
For example, let us find the square root of 4489.
Therefore, √4489 = 67
The tricks mentioned in this section will help you make faster calculation of percentages.
p % of y = y % of p
Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
Calculation of Percentages | |||
1/2 | 50% | 1/50 | 2% |
1/3 | 33.3% | 1/25 | 4% |
1/4 | 25% | 1/20 | 5% |
1/5 | 20% | 1/12 | 8.33% |
1/6 | 16(2/3)% | 3/8 | 37.5% |
1/7 | 14(2/7)% | 2/5 | 40% |
1/8 | 12(1/2)% = 12.5% | 3/5 | 60% |
1/9 | 11(1/9)% | 3/4 | 75% |
1/10 | 10% | 5/4 | 125% |
Some other percentage related tricks are:
- Percent to Decimal: Move the decimal point two places to the left. For example, 165% = 165/100 = 1.65.
- Percent to Fraction: Place the percent number in the numerator and 100 in the denominator, then simplify in smaller fraction simplify. For example, 52% = 52/100 = 26/50 = 13/25.
- Decimal to Percent: Move decimal point two places to the right, For example, 1.6 = 160%.
Read More,
Most common tricks for fractions and decimals are:
Let's discuss these tricks in detail.
| Concept | Steps or Explanation |
|---|---|
| Simplifying Fractions | |
| Step 1 | Write the factors of the numbers in the numerator and denominator. |
| Step 2 | Find the Greatest Common Factor (GCF). |
| Step 3 | Divide the numerator and denominator by the GCF until no common factor remains. |
| Example | Simplify 18/40: GCF is 2, so 18/40 becomes 9/20 after division. |
| Converting Fraction to Decimal | |
| Example | Convert 7/8 to a decimal. |
| Step 1 | Choose a Multiplying Factor that makes the denominator a power of 10. |
| Step 2 | Identify the denominator (8) and multiply by 125 to get 1000. |
| Step 3 | Multiply both numerator and denominator by 125. |
| Step 4 | Calculate the new numerator (7 × 125 = 875). |
| Step 5 | Express the fraction with the denominator as a power of 10 (875/1000). |
| Step 6 | Convert to decimal: 875/1000 = 0.875. |
| Decimal Approximation | |
| Rule | Round up if the tenth digit is 5 or greater; round down if less than 5. |
| Example 1 | 24.738 ≈ 24.74 (8 is greater than 5, so round up). |
| Example 2 | 23.2341 ≈ 23.23 (4 is less than 5, so round down). |
Read More:
These are some handy shortcuts related to algebraic expression:
Let's discuss them in detail.
| Concept | Steps or Explanation |
|---|---|
| Factoring Trick | |
| Example Equation | x² + 5x + 6 = 0 |
| Step 1 | Check the sign of the second term (+5). |
| Step 2 | Multiply the numerical values of the first and third terms (1 × 6 = 6). |
| Step 3 | Break this number into factors whose sum equals the numerical value of the second term (3, 2). |
| Step 4 | Change the sign of these factors: -3, -2. |
| Combining Like Terms | |
| Step 1 | Identify like terms (terms with the same variable and exponent). |
| Example | In 3x + 2y − 5x + 4y, like terms are 3x and −5x (both have x). |
| Step 2 | Group like terms together. |
| Step 3 | Combine coefficients of like terms, keeping the variable part unchanged. |
| Example Calculation | 3x − 5x = −2x and 2y + 4y = 6y. |
Read More,
Trigonometric ratios can be learnt using the SOH-CAH-TOA trick:
Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Reciprocal Trignometric ratios are: cosecθ= 1/sinθ, secθ = 1/cosθ and cotθ = 1/tanθ.
Some other math tricks with relevant examples are discussed below:
| Arithmetic Shortcut | Steps or Explanation |
|---|---|
| Addition of Ten Digits Numbers | |
| Example | Add 54 and 33. |
| Step 1 | Break down the second number into tens and units: 33 = 30 + 3. |
| Step 2 | Add the tens places first: 54 + 30 = 84. |
| Step 3 | Add the unit place: 84 + 3 = 87. |
| Multiplication Shortcut for 15 | |
| Example | Multiply 43 by 15. |
| Step 1 | Add zero to the end of the first number: 430. |
| Step 2 | Divide this number by 2: 430/2 = 215. |
| Step 3 | Add the result to the original number with zero: 430 + 215 = 645. |
| Quick Multiplication by Breaking Down Numbers | |
| Example | Multiply 27 by 12. |
| Step 1 | Split the first number into two parts: 27 = 20 + 7. |
| Step 2 | Multiply the second number by the sum of the split numbers: 12 × (20 + 7). |
| Step 3 | Calculate the result: 240 + 84 = 324. |
| Multiplication of Two-Digit Numbers | |
| Example | Multiply 14 by 27. |
| Step 1 | Halve the even number: 14/2 = 7. |
| Step 2 | Double the other number: 27 × 2 = 54. |
| Step 3 | Multiply the halved and doubled numbers: 54 × 7 = 378. |
| Divisibility Rule | Description |
|---|---|
| By 2 | A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8 (even number). |
| By 3 | A number is divisible by 3 if the sum of its digits is divisible by 3. |
| By 4 | A number is divisible by 4 if its last two digits form a number divisible by 4. |
| By 5 | A number is divisible by 5 if its last digit is 0 or 5. |
| By 6 | A number is divisible by 6 if it is divisible by both 2 and 3. |
| By 8 | A number is divisible by 8 if its last three digits are divisible by 8. |
| By 9 | A number is divisible by 9 if the sum of its digits is divisible by 9. |
| By 10 | A number is divisible by 10 if its last digit is 0. |
Read More On:
| Trick Name | Steps or Explanation |
|---|---|
| Same Three-Digit Number | |
| Step 1 | Think of any three-digit number where each digit is the same (e.g., 111, 222, 333). |
| Step 2 | Add up the digits (e.g., 3, 8, 9). |
| Step 3 | Divide the three-digit number by the sum from Step 2 (e.g., 111/3 = 37). |
| Result | The answer is always 37. |
| Three Digits become Six | |
| Example | Multiply 371 by 7, 11, and 13. |
| Result | 371 × 7 × 11 × 13 = 371371. |
| Multiplication by 5 | |
| Rule | Multiplying any number by 5 ends in 0 or 5. |
| Examples | 33 × 5 = 165, 12 × 5 = 60. |
| Multiplication by 10 | |
| Rule | Multiplying any number by 10 ends in 0. |
| Examples | 5 × 10 = 50, 10 × 10 = 100. |
| Multiplying Two-Digit Integers by 11 | |
| Step 1 | Add the two digits of the number. |
| Step 2 | Insert the sum in between the two digits. |
| Example | 71 × 11: 7 + 1 = 8, so the answer is 781. |
| Close Together Method for Multiplication | |
| Formula | (n + a)(n + b) = n(n + a + b) + ab |
| Example | Multiply 34 by 36. |
| Calculation | 34×36 = (30 + 4)(30 + 6) = 30(40) + 24 = 1200 + 24 = 1224. |
| Result | 34×36 = 1224. |
Easily memorize the table of 9 by observing the pattern
09, 18, 27, 36, 45, 54, 63, 72, 81, 90
We can see the numbers at the ten’s place are increasing by 1, and the numbers at the unit place are decreasing by 1.
To memorize the value of pi,
Count the letters in each word of the phrase "How I wish I could calculate pi" to learn the first seven digits of pi: 3.141592.
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For example, find the cube root of 15625 by dividing the number into parts.
Let's try to understand this with the help of the following steps:
- Take the three rightmost digits (625) and recognize the digit which is cube of 625. (5)3 = 625.
- Consider the remaining digits (15) and find the cube of a number smaller than 15, 23 = 8, 33 = 27).
- The cube root of 15625 is 25.
Here are some exercise questions on math shortcuts for you to solve:
Q1. Solve 34 × 5 × 5.
Q2. Solve 1321 × 11.
Q3. Find Square root of number 7744.
Q4. Solve 18 × 67.
Q5. Find cube root of number 19683.
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