Multiplication Tricks: Fast Methods and Shortcuts

Multiplication Tricks use place value, algebraic identities and number patterns to simplify calculations. This page covers distributive multiplication, base-10 methods, vertical-and-crosswise multiplication, and shortcuts for multiplying by 5, 11, 25, 50 and numbers ending in 5. Each method includes formulas and simple examples for quick mental calculation.

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What Are Multiplication Tricks?

Multiplication tricks are structured methods that break a product into easier parts using place value, algebraic identities or number patterns. They reduce lengthy multiplication while giving the same exact product as the standard method.

For example, 47 × 6 can be written as (40 + 7) × 6 = 40 × 6 + 7 × 6 = 240 + 42 = 282. The method used depends on the form of the numbers, such as closeness to 10, 100 or 1,000, repeated digits, or a convenient factor such as 25 or 50.

Multiplication Tricks Formula & Tricks

Important Formulas

Distributive property
a × (b + c) = a × b + a × c; a × (b − c) = a × b − a × c

Split one factor into convenient parts and multiply each part separately.

Numbers near a base
(B + x)(B + y) = B(B + x + y) + xy

Here B is usually 10, 100 or 1,000, and x and y are signed deviations from the base.

Difference of two squares
(a + b)(a − b) = a² − b²

Use this when two factors have the same middle value and equal opposite deviations.

Vertical-and-crosswise multiplication
For 2-digit numbers, (10a + b)(10c + d) = 100ac + 10(ad + bc) + bd

Multiply units vertically, crosswise terms, and tens vertically, then combine according to place value.

Quick Tricks

Multiply by 5

Multiply the number by 10 and divide the result by 2. For an even number, divide by 2 first and then multiply by 10.

Example: 68 × 5 = 680 ÷ 2 = 340.
Multiply by 25

Multiply by 100 and divide by 4 because 25 = 100 ÷ 4.

Example: 48 × 25 = 4,800 ÷ 4 = 1,200.
Multiply by 50

Multiply by 100 and divide by 2 because 50 = 100 ÷ 2.

Example: 36 × 50 = 3,600 ÷ 2 = 1,800.
Multiply by 11 for a two-digit number

For 10a + b, place a + b between the two digits when a + b is less than 10. If the sum is 10 or more, carry to the tens digit.

Example: 43 × 11 = 4(4 + 3)3 = 473; 78 × 11 = 7(15)8 = 858 after carrying 1.

Multiplication Tricks Concepts

Distributive Multiplication

Distributive multiplication breaks a factor into tens, hundreds or other convenient parts before multiplying.

Use a × (b + c) = ab + ac or a × (b − c) = ab − ac. Choose parts that are easy to multiply mentally. This method works for whole numbers and decimals when place values are handled correctly.

Example: 86 × 7 = (80 + 6) × 7 = 560 + 42 = 602.

Multiplication Near 10, 100 or 1,000

Numbers close to a power of 10 can be multiplied by using their signed deviations from that base.

For (B + x)(B + y), first calculate B(B + x + y), then add xy. A number below the base has a negative deviation. For 98 × 97, B = 100, x = −2 and y = −3, so the product is 100(100 − 2 − 3) + 6 = 9,506.

Example: 103 × 98 = 100(100 + 3 − 2) + (3 × −2) = 10,100 − 6 = 10,094.

Vertical-and-Crosswise Method

For two 2-digit numbers, multiply units, add the two cross-products, and then multiply tens, while carrying according to place value.

For 23 × 14: units are 3 × 4 = 12, cross-products are 2 × 4 + 3 × 1 = 11, and tens are 2 × 1 = 2. Write the place values from right to left: 12 gives 2 with carry 1; 11 + 1 = 12 gives 2 with carry 1; 2 + 1 = 3. The result is 322.

Example: 23 × 14 = 322.

Special Patterns for 5, 11, 25 and Numbers Ending in 5

Certain multipliers can be converted into division or place-value operations, making the product shorter to calculate.

Use ×5 = ×10 ÷2, ×25 = ×100 ÷4, and ×50 = ×100 ÷2. For the square of a number ending in 5, write n5² as n × (n + 1), followed by 25. For example, 35² gives 3 × 4 = 12 followed by 25, so 35² = 1,225.

Example: 72 × 25 = 7,200 ÷ 4 = 1,800; 65² = 6 × 7 followed by 25 = 4,225.

Multiplication Tricks Video Lessons

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Vedic Maths Multiplication Tricks

Learn practical Vedic Maths techniques for simplifying multiplication calculations. This lesson explains efficient methods to multiply numbers more quickly and accurately in quantitative aptitude problems.

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Practice Multiplication Tricks Questions

Practise published questions related to this topic.

125 percent of the cost price of an article is equal to the 10 percent of its selling price. What is the profit percentage?→ 2At what percentage above the cost price of an article is to be marked to gain 20%, after allowing a discount of 25%?→ 3Three machines in a factory make a beep sound after finishing their cycle times. Machine A beeps every 18 seconds, Machine B beeps every 30 seconds, and Machine C beeps every 45 seconds. If they all beep together at 8:00:00 a.m., what will be the next time they all beep together ?→ 4During a sale 50% of the goods are sold at 40% profit, 30% of the remaining goods are sold at 46% profit and the still remaining goods are sold at a loss of 24%. If there is an overall profit of x%, then what is the value of x?→ 5The LCM of the numbers 7, 12.4 and 1 is:→ 6What is the largest 2 digit number which is exactly divisible by both 9 and 3?→ 7A clerk simplifies 12/√3. The rationalised result is:→ 8√((0.064 × 0.256)/(0.004 × 0.16)) = ?→ 9Find the square root of 64009.→ 10Cost price of 30 articles is Rs. 260. Selling price of 40 articles is Rs. 260. What is the profit/loss percentage? (Cost price of all the articles is same. Selling price of all the articles is same.)→

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Quick Revision Notes

Multiplication Tricks Revision Points

Use the number form to select the shortest correct method.

  • Apply the distributive property when one factor can be split into easy parts.
  • For numbers near B, use (B + x)(B + y) = B(B + x + y) + xy with signed deviations.
  • Use (a + b)(a − b) = a² − b² when the factors are equally distant from a common middle value.
  • In vertical-and-crosswise multiplication, process units, cross-products and tens from right to left with carries.
  • Multiply by 5 by multiplying by 10 and dividing by 2.
  • Multiply by 25 by multiplying by 100 and dividing by 4.
  • For a two-digit number 10a + b multiplied by 11, use 100a + 10(a + b) + b, carrying when a + b is 10 or more.
  • The square of a number ending in 5 is found by multiplying its leading part by the next integer and appending 25.

Multiplication Tricks FAQs

How do you multiply two numbers close to 100?

Use (100 + x)(100 + y) = 100(100 + x + y) + xy. Thus, 98 × 97 = 100(95) + 6 = 9,506.

What is the fastest method for multiplying by 25?

Multiply the number by 100 and divide by 4. For example, 64 × 25 = 6,400 ÷ 4 = 1,600.

How do you multiply a two-digit number by 11?

For 43 × 11, add the digits 4 + 3 = 7 and place the sum between them: 473. If the digit sum is 10 or more, carry the extra 1 to the first digit; 78 × 11 = 858.

How does the difference-of-squares trick work?

Use (a + b)(a − b) = a² − b². For example, 52 × 48 = (50 + 2)(50 − 2) = 50² − 2² = 2,496.

How do you square a number ending in 5?

Multiply the part before 5 by the next integer and append 25. Therefore, 85² = 8 × 9 followed by 25 = 7,225.

What is the vertical-and-crosswise result for 32 × 14?

Units: 2 × 4 = 8; cross-products: 3 × 4 + 2 × 1 = 14; tens: 3 × 1 = 3. Combining with the carry gives 32 × 14 = 448.

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