{"id":31047,"date":"2023-06-30T14:36:55","date_gmt":"2023-06-30T14:36:55","guid":{"rendered":"https:\/\/moonpreneur.com\/math-corner\/?p=31047"},"modified":"2025-02-25T08:50:08","modified_gmt":"2025-02-25T08:50:08","slug":"yavadunam-sutra","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/yavadunam-sutra\/","title":{"rendered":"Vedic Math Sutra: Sutra-10 Yavadunam"},"content":{"rendered":"\t\t
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Update:<\/strong> This article was last updated on 24th February 2025 to reflect the accuracy and up-to-date information on the page.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Has long multiplication ever stumped you? Now imagine doing it in seconds as well as not using a calculator! Vedic Maths present some techniques-simple but very powerful-and here today we have one of it-Yavadunam.\u00a0<\/span><\/p>

The famous and amazing ancient Indian math tricks are Vedic Mathematics<\/a>, which are very different and productive ways to do all types of mathematics. One of these is Yavadunam sutra, which presents a very novel method of multiplication. The words “saved<\/strong>“, which means “as much as<\/strong>” and “dunam<\/strong>“, which means “the product<\/strong>“, are derived from Sanskrit. This sutra proves to be a very easy way of multiplying numbers very close to a common base.\u00a0<\/span><\/p>

This blog will discuss the Yavadunam sutra and how it can be used to improve multiplication skills in children.\u00a0<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Learn The Yavadunam Sutra<\/span><\/strong><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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“You reduce it further and further as far as inference from the deficiency, and then establish the square of the deficiency in that manner.” Thus is defined the Yavadunam Sutra. It looks complicated but can be actually broken into a very easy staircase kind of approach to multiplying.<\/span><\/p>

Step 1: Identify a suitable base<\/span><\/strong><\/h4>

The number must be a base number close to both multiplicand and multiplier. Because the bases do not differ from the actual values, these steps are made simpler.<\/span><\/p>

Step 2: Find out the deficiencies<\/span><\/strong><\/h4>

Get the deficiencies of the multiplicand and the multiplier w.r.t the chosen base. So the deficiency is the difference of the number and base in numericals.<\/span><\/p>

Step 3: Adjust the numbers<\/span><\/strong><\/h4>

The new numbers are far easier to work with; subtract deficiencies from base, the numbers will adjust.\u00a0<\/span><\/p>

Step 4: Multiply the adjusted numbers<\/span><\/strong><\/h4>

Multiply the final numbers derived from the previous step.<\/span><\/p>

Step 5: Account for the deficiency of the base<\/span><\/strong><\/h4>

Square it for the deficiency of base and subtract it from the product achieved in the earlier step.<\/span><\/p>

Step 6: Determine the final result<\/span><\/strong><\/h4>

This is the product of the original multiplicand and multiplier because the difference square was taken away from it.\u00a0<\/span><\/p>

Let’s now see a few examples:\u00a0<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Example 1<\/span><\/strong><\/h4>

162 = (16+6)\/62 = 22\/36 = 256<\/span><\/p>

So in the above problem, 16 is 6 more than 10(Base 10), So Excess = 6<\/span><\/p>

Increase it still further to that extent, So (16+6) = 22<\/span><\/p>

Square it\u2019s excessive, So 62 = 36<\/span><\/p>

Final Answer: 256<\/span><\/p>

Example 2<\/span><\/strong><\/h4>

922 = (92-8)\/82 = 84\/64 = 8464<\/span><\/p>

So in the above problem, 92 is 8 less than 100(Base 100), So deficiency = 8<\/span><\/p>

Reduce it further to that extent, So (92-8) = 84<\/span><\/p>

Square its deficiency, So 82 = 64<\/span><\/p>

Final Answer: 8464<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Common Mistakes and How to Avoid Them<\/b><\/span><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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While the powerful yet yavadunam sutra for square proves beginner mistakes while applying it, here are some common mistakes and solutions to avoid them:<\/span><\/p>

1. Choosing Wrong Base<\/b><\/span><\/h4>