{"id":625,"date":"2021-07-24T12:11:42","date_gmt":"2021-07-24T06:41:42","guid":{"rendered":"https:\/\/www.saralstudy.com\/blog\/?p=625"},"modified":"2021-07-24T00:51:12","modified_gmt":"2021-07-23T19:21:12","slug":"vedic-maths-tricks","status":"publish","type":"post","link":"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/","title":{"rendered":"Vedic Maths Tricks"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Vedic Maths has gained a lot of popularity in some of the last years because of its fast and accurate calculations. Calculation is a crucial part of every profession nowadays, and people with fast calculation abilities seems to have special skill, as not everybody has this ability to calculate fast and accurate. Everybody wants to have this skill as it makes people look smarter.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Vedic maths as the name suggests is based on the knowledge gained from our Vedas but not everybody was able to gain the knowledge that has been given our prestigious Vedas as the ancient language is not everybody\u2019s cup of tea. So to make it more simple for common people Swami Bharti Krishna Tirtha Ji Maharaj, who is the Shankaracharya of\u00a0 Govardhan Peeth, Puri, has given six sutras over which <a href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths\/\" target=\"_blank\" rel=\"noopener noreferrer\">Vedic maths<\/a> has been set up and it becomes simple for common people to understand it without putting endless efforts.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now when we say that the information has been taken from Vedas, the question here is which Veda? The answer is \u201cthe Atharvaveda\u201d.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Atharvaveda is said to have extreme knowledge of science and mathematics which people are discovering today, but it has been in our Vedas since ancient time. So the Swami Bharti Ji has decoded the information for all of us, compressed it into 16 sutras and presented it for us.<\/span><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#16_Principles_Sutras_of_Vedic_Mathematic_and_Sub-Sutra\" >16 Principles (Sutras) of Vedic Mathematic and Sub-Sutra<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Example_of_Vedic_Maths_Sutras\" >Example of Vedic Maths Sutras<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_1_Ekadhikina_Purvena\" >Sutra 1: Ekadhikina Purvena<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_2_Nikhilam_Navatashcaramam_Dashatah\" >Sutra 2: Nikhilam Navatashcaramam Dashatah<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_3_Urdhva-Tiryagbyham\" >Sutra 3: Urdhva-Tiryagbyham<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_4_Parvaartya_Yojayet\" >Sutra 4: Parvaartya Yojayet<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_5_Shunyam_Saamyasamuuaye\" >Sutra 5: Shunyam Saamyasamuuaye<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_6_Anurupyena-Sunyamanyat\" >Sutra 6 : Anurupyena-Sunyamanyat<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_7_Sankalana-Vayavakalanabyham\" >Sutra 7: Sankalana-Vayavakalanabyham<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_8_Purana_Purana_Byham\" >Sutra 8: Purana Purana Byham<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_9_Chalana_kalanabyham\" >Sutra 9: Chalana kalanabyham<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_10_Yavadunam\" >Sutra 10: Yavadunam<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_11_Vyashtisamanstih\" >Sutra 11: Vyashtisamanstih<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_12_Shesanyankena_charamena\" >Sutra 12: Shesanyankena charamena<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_13_Sopaantyadvayamantyam\" >Sutra 13: Sopaantyadvayamantyam<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_14_Ekanyunena_Purvena\" >Sutra 14: Ekanyunena Purvena<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_15_Gunita_Samuchaya\" >Sutra 15: Gunita Samuchaya<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Sutra_16_Gunakasamuchya\" >Sutra 16: Gunakasamuchya<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/#Frequently_Asked_Questions\" >Frequently Asked Questions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"16_Principles_Sutras_of_Vedic_Mathematic_and_Sub-Sutra\"><\/span><span style=\"font-weight: 400;\">16 Principles (Sutras) of Vedic Mathematic and Sub-Sutra<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The main sutras and sub-sutra of Vedic maths are:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: left;\"><strong>Name \/ Sutra<\/strong><\/td>\n<td style=\"text-align: left;\"><strong>Corollary \/ Sub-Sutra<\/strong><\/td>\n<td style=\"text-align: left;\"><strong>Meaning<\/strong><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Ekadhikena Purvena (\u090f\u0915\u093e\u0927\u093f\u0915\u0947\u0928 \u092a\u0942\u0930\u094d\u0935\u0947\u0923)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Anurupyena<\/span><\/td>\n<td><span style=\"font-weight: 400;\">By one more than the previous one.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Nikhilam Navatashcaraman Dashatah (\u0928\u093f\u0916\u093f\u0932\u0902 \u0928\u0935\u0924\u0936\u094d\u092e\u091a\u0930\u092e\u0902 \u0926\u0936\u0924\u0903)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Sisyata Sesasamjnah<\/span><\/td>\n<td><span style=\"font-weight: 400;\">All from 9<\/span><span style=\"font-weight: 400;\">The last from 10<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Urdhava \u2013 Tiryagbyham (\u090a\u0930\u094d\u0927\u094d\u0935\u0924\u093f\u0930\u094d\u092f\u0917\u094d\u092d\u094d\u092f\u093e\u092e\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Adyamadyenantyamantyena<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Vertically and crosswise.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Paravartaya Yojayet (\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u094d\u092f \u092f\u094b\u091c\u092f\u0947\u0924\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Kevailash Saptakam Gunyat<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Transpose and adjust.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Shunyam Saamyasamuccaye (\u0936\u0942\u0928\u094d\u092f\u0902 \u0938\u093e\u092e\u094d\u092f\u0938\u092e\u0941\u091a\u094d\u091a\u092f\u0947)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Vestanam<\/span><\/td>\n<td><span style=\"font-weight: 400;\">When the sum is the same that sum is zero.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Anurupye Shunyamanyat (\u0906\u0928\u0941\u0930\u0941\u092a\u094d\u092f\u0947 \u0936\u0942\u0928\u094d\u092f\u092e\u0928\u094d\u092f\u0924\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Shunuya Anayat<\/span><\/td>\n<td><span style=\"font-weight: 400;\">If one is the ratio, the other is zero.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Sankalana- Vyavakalanabhyam (\u0938\u0902\u0915\u0932\u0928 \u0935\u094d\u092f\u0935\u0915\u0932\u0928\u093e\u092d\u094d\u092f\u093e\u0902)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Yavadunam Tavadunikritiya Varga Yojayet<\/span><\/td>\n<td><span style=\"font-weight: 400;\">By addition and subtraction.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Purana Puranabyham (\u092a\u0942\u0930\u0923\u093e\u092a\u0942\u0930\u0923\u093e\u092d\u094d\u092f\u093e\u0902)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Antyayordashakepi<\/span><\/td>\n<td><span style=\"font-weight: 400;\">By the completion.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Chalana \u2013 Kalanabyham (\u091a\u0932\u0928\u0915\u0932\u0928\u093e\u092d\u094d\u092f\u093e\u092e\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Antyayoreva<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Similarities and differences.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Yavadunam (\u092f\u093e\u0935\u0926\u0942\u0928\u092e\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Samuccayagunitah<\/span><\/td>\n<td><span style=\"font-weight: 400;\">The extent of its deficiency.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Vyashtisamasthi (\u0935\u094d\u092f\u0937\u094d\u091f\u093f\u0938\u092e\u0937\u094d\u091f\u093f\u0903)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Lopanasthapanabhyam<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Part and whole.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Shesanyankena Charamena (\u0936\u0947\u0937\u093e\u0923\u094d\u092f\u0919\u094d\u0915\u0947\u0928 \u091a\u0930\u092e\u0947\u0923)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Vilokanam<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Remainder by the last digit.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Sopaantyadyamantyam (\u0938\u094b\u092a\u093e\u0928\u094d\u0924\u094d\u092f\u0926\u094d\u0935\u092f\u092e\u0928\u094d\u0924\u094d\u092f\u092e\u094d)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Gunitasamuccayah<\/span><\/td>\n<td><span style=\"font-weight: 400;\">The ultimate and penultimate.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Ekanyunena Purvena (\u090f\u0915\u0928\u094d\u092f\u0942\u0928\u0947\u0928 \u092a\u0942\u0930\u094d\u0935\u0947\u0923)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Dhyajanka<\/span><\/td>\n<td><span style=\"font-weight: 400;\">By one less than the previous one.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Gunitasamuchyah (\u0917\u0941\u0923\u093f\u0924\u0938\u092e\u0941\u091a\u094d\u091a\u092f\u0903)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Dwandwa Yoga<\/span><\/td>\n<td><span style=\"font-weight: 400;\">The product of some is equal to the sum of the product.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Gunakasamuchyah (\u0917\u0941\u0923\u0915\u0938\u092e\u0941\u091a\u094d\u091a\u092f\u0903)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Adyam Antyam Madhyam<\/span><\/td>\n<td><span style=\"font-weight: 400;\">The factors of the sum is equal to the sum of the factors.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"Example_of_Vedic_Maths_Sutras\"><\/span><span style=\"font-weight: 400;\">Example of Vedic Maths Sutras<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Below are the 16 Vedic Maths Sutras example:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_1_Ekadhikina_Purvena\"><\/span><span style=\"font-weight: 400;\">Sutra 1: Ekadhikina Purvena<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(One is more than the previous one)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This Sutra is very useful and helps in finding the products of the numbers, if the unit digit&#8217;s sum of the two numbers totals to 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a024 x 26 =?<br \/>\n<\/span><span style=\"font-weight: 400;\">= (first digit x one more than first digit) (product of unit digits of both the number)<br \/>\n<\/span><span style=\"font-weight: 400;\">= ( 2 x 3 ) ( 4 x 6)<br \/>\n<\/span><span style=\"font-weight: 400;\">= 624<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, 24 x 26 = 624.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">You see the answer above has come without doing any elaborate calculation.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_2_Nikhilam_Navatashcaramam_Dashatah\"><\/span><span style=\"font-weight: 400;\">Sutra 2: Nikhilam Navatashcaramam Dashatah<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(All from 9 last from 10)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This Sutra is commonly used to subtract the numbers from the power of 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;<br \/>\n<\/span><span style=\"font-weight: 400;\">\u00a010000 <\/span><span style=\"font-weight: 400;\">&#8211; 7688 =<\/span><span style=\"font-weight: 400;\">\u00a02312<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now if we analyse this situation, the last number is 8 and it is subtracted from 10 and the next 8 is subtracted from 9, whereas all other numbers are subtracted by 9 and the result comes out almost orally.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_3_Urdhva-Tiryagbyham\"><\/span><span style=\"font-weight: 400;\">Sutra 3: Urdhva-Tiryagbyham<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(Vertically and crosswise)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used For multiplication.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Formula used for this sutra is ab \u00d7 cd =(ac) (ad + bc) (bd)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The example is given below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">24 x 12<br \/>\n<\/span><span style=\"font-weight: 400;\">= (2 x 1) (2 x 2 + 4 x 1) (4 x 2 )<br \/>\n<\/span><span style=\"font-weight: 400;\">= 288<\/span><\/p>\n<p><span style=\"font-weight: 400;\">And the answer is 288.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">You can see how simple multiplication can become using this sutra.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_4_Parvaartya_Yojayet\"><\/span><span style=\"font-weight: 400;\">Sutra 4: Parvaartya Yojayet<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(Transpose and adjust)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used for division, when the divisor is greater than the power nearest to 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us see an example using 434\\12<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The very first thing that we need to see is that the number 12 which is divisor is greater than 10, in that case this sutra can be applied easily. Next we need to check is that how many digits are there in a divisor, this one has two digits so the dividend needs to split into two, 43 and 4, other process is given below;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">As shown above, the divisor is written and leaving 1 apart, 2 is taken down as 2 bar, i.e. vinculum 2. The dividend is divided into two parts 43 and 4. 4 of 43 is taken down and to this four, the vinculum 2 is multiplied to get vinculum 8 which is written under 3 of 43. 3 vinculum 8 would be vinculum 5 which is taken down. Vinculum 2 of the divisor is multiplied with this vinculum 5 and the result 10 is written under 4 and totalled to 14.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">14 is taken down as it is. Now 45 is a vinculum number because 5 is vinculum. According to Vedic maths rules vinculum, 5 is complemented with 10 to get normal 5 which is taken down. The number next to the vinculum number should be reduced by 1. So, 4 becomes 3 and comes down<\/span><\/p>\n<p><span style=\"font-weight: 400;\">And the answer is quotient =35 and remainder = 14 when 434\/12.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_5_Shunyam_Saamyasamuuaye\"><\/span><span style=\"font-weight: 400;\">Sutra 5: Shunyam Saamyasamuuaye<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(When the sum is the same the sum is zero)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used to solve equations in the forms given below:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">ax + b = cx + d<br \/>\n<\/span><span style=\"font-weight: 400;\">So, x = d &#8211; b\/a &#8211; c<br \/>\n<\/span><span style=\"font-weight: 400;\">(x+a)(x+b) =(x+c)(x+d)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, x = cd-ab\/a+b-c-d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Some applications<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A term which occurs as a common factor in all the terms is equated to zero e.g. : 14x + 9x = 4x + 12x. <\/span><span style=\"font-weight: 400;\">Here x occurs as a common factor with all terms and hence the value of x according to this sutra is zero.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"> If the product of the independent term on either side of the equation is equal the value of the variable will be zero, which is the second interpretation of this sutra.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">E.g.<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">(x +8) (x+3) = (x + 12 ) (x + 2 )<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">8 x 3 = 24 = 12 x 2 and hence value of x in this equation would be 0\u00a0<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_6_Anurupyena-Sunyamanyat\"><\/span><span style=\"font-weight: 400;\">Sutra 6 : Anurupyena-Sunyamanyat<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(If one is in ratio, the other is zero)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is also used to solve equations.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suppose:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2x + 4y = 8<br \/>\n<\/span><span style=\"font-weight: 400;\">And<br \/>\n<\/span><span style=\"font-weight: 400;\">4x + 6y = 16,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The ratio of terms with x = 2x\/4x = \u00bd<br \/>\n<\/span><span style=\"font-weight: 400;\">The ratio of the R.H.S term is also 8\/16 = \u00bd<br \/>\n<\/span><span style=\"font-weight: 400;\">Therefore, the other variable, in this case y = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Substituting this value of y in any other of the two equations, we can get value of x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2x + 4(0)=8<br \/>\n<\/span><span style=\"font-weight: 400;\">2x = 8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore x= 8\/4 = 2.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_7_Sankalana-Vayavakalanabyham\"><\/span><span style=\"font-weight: 400;\">Sutra 7: Sankalana-Vayavakalanabyham<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(By addition and by subtraction)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used to solve equations but with a condition and the condition is that if the coefficient of 1 variable is same in both the equations,\u00a0 irrespective of the signs being used.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Wait, no need to get confused, what it means is that the coefficient of 1 variable in 1<\/span><span style=\"font-weight: 400;\">st<\/span><span style=\"font-weight: 400;\"> equation should be equal to the 2 variable in 2<\/span><span style=\"font-weight: 400;\">nd<\/span><span style=\"font-weight: 400;\"> equation and in the same way the coefficient of 2<\/span><span style=\"font-weight: 400;\">nd<\/span><span style=\"font-weight: 400;\"> variable in first equation should be equal to the 1<\/span><span style=\"font-weight: 400;\">st<\/span><span style=\"font-weight: 400;\"> variable in second equation. If the condition matches, the equations can be easily added and subtracted.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">4x + 2y = 6\u2026\u2026\u2026\u2026 equation 1 and<br \/>\n<\/span><span style=\"font-weight: 400;\">2x + 4y = 7 \u2026\u2026\u2026\u2026.equation 2.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now add equation 1 and 2 we get<\/span><\/p>\n<p><span style=\"font-weight: 400;\">6x + 6y = 13 or<br \/>\n<\/span><span style=\"font-weight: 400;\">6 (x + y) = 13 or<\/span><\/p>\n<p><span style=\"font-weight: 400;\">X + y = 13\/7\u2026\u2026\u2026\u2026we get equation 3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Subtract equation 2 for equation 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2x -2y = -1<br \/>\n<\/span><span style=\"font-weight: 400;\">2 (x -y ) = -1 or\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">X \u2013 y = &#8211; 1 \/ 2 \u2026\u2026 we get equation 4\u2026\u2026.therefore<br \/>\n<\/span><span style=\"font-weight: 400;\">Y = x + 1 \/ 2\u2026\u2026\u2026\u2026equation 5 substitute this in equation 3.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So we get<\/span><\/p>\n<p><span style=\"font-weight: 400;\">X + (x + \u00bd) = 13\/7\u2026 solving for x, we get<br \/>\n<\/span><span style=\"font-weight: 400;\">X = 19\/7 = 2.71\u2026\u2026.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">And y = x + 0.5\u2026.. from equation 5<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, y = 2.71 +0.5= 3.21<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_8_Purana_Purana_Byham\"><\/span><span style=\"font-weight: 400;\">Sutra 8: Purana Purana Byham<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(By the completion or non-completion)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra can be used to solve problems of addition but with a condition, which is; when the unit digits of the numbers add up to 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Numbers 22 and 18 the unit digits add up to 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let try to add 295 + 46 + 28 + 15 + 44 + 22 =?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now we need to check and number and pair them in such a way that their unit places add up to 10. So\u2026.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">295 + 46 + 28 + 15 + 44 + 22 =?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Rearrange to put the paired number together.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(295 + 15) + (46 + 44) + (28 + 22)<br \/>\n<\/span><span style=\"font-weight: 400;\">300 + 90 + 50 = 440.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This happened in easy steps instead of long calculations.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_9_Chalana_kalanabyham\"><\/span><span style=\"font-weight: 400;\">Sutra 9: Chalana kalanabyham<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(difference and similarities)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The application of this sutra can be found in calculus to find roots of a quadratic equation and the another application is in differential calculus for factorizing 3<\/span><span style=\"font-weight: 400;\">rd<\/span><span style=\"font-weight: 400;\">, 4<\/span><span style=\"font-weight: 400;\">th<\/span><span style=\"font-weight: 400;\">, and 5<\/span><span style=\"font-weight: 400;\">th<\/span><span style=\"font-weight: 400;\"> degrees expression. This sutra finds very specialized applications in the area of higher mathematics.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_10_Yavadunam\"><\/span><span style=\"font-weight: 400;\">Sutra 10: Yavadunam<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(Whatever the extent of its deficiency)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used to find squares of numbers that are close to the powers of base 10.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">You need to compare the number with the closed base to the number and find the deficiency or excess. After which you need to square the difference of numbers and this is one part of the answer after which you reduce the given number or increase the same by the difference the number has to the power of base 10.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us understand this with an example;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us try to find the square of 12<\/span><\/p>\n<p><span style=\"font-weight: 400;\">12 is near to 10 and it is 2 excess than 10.<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> Square the difference (excess in this case). So 2 x2 = 4\u2026.this is the unit place<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> Now add the excess to the number. The number is 12 so 12 + 2 = 14\u2026this is the left part of the answer<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> Combining both of them we get = 144<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> Solving it in equation form<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 122 = (12 + 2) ( 2)2 = 144<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_11_Vyashtisamanstih\"><\/span><span style=\"font-weight: 400;\">Sutra 11: Vyashtisamanstih<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(Part and whole)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra helps in the factorization of quadratic equations.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_12_Shesanyankena_charamena\"><\/span><span style=\"font-weight: 400;\">Sutra 12: Shesanyankena charamena<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(The remainders by the last digit)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra gives you the process of converting fractions to decimals.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example; 1\/29\u00a0<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> The last digit of the divisor should be 9. It is in this case, now increase the value by 1 of the number next to 9. So, the number is 2 and increasing it by 1 makes it 3<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> The dividend is 1 now it has to be divided by 3 so,<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 1 \/ 3<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> Doing it mentally it will be 0.0 and remainder 1 and it is written as<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 0.10 and 10 is divided by 3 and it will be written as 3 and remainder 1 written to left<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 0.1 01 3 now 13 is to be divided by 3 and it will be written as 4 and remainder 1 written to left<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 0.101314 and keep on dividing it by 3 to as many decimal places as needed. For three decimal places the answer is 0.034<\/span><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_13_Sopaantyadvayamantyam\"><\/span><span style=\"font-weight: 400;\">Sutra 13: Sopaantyadvayamantyam<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(The ultimate and twice the penultimate.)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is used to find solution of equations in the following form<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1\/ ab + 1\/ac = 1\/ad + 1\/bc<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Where a, b, c and d are in arithmetic progression<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B= a + z<br \/>\n<\/span><span style=\"font-weight: 400;\">C = a + 2z<br \/>\n<\/span><span style=\"font-weight: 400;\">D = a + 3z<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Solution for such equations is 2c + d = 0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1. g.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1\/ (x+1)(x+2) + 1\/ (x +1)(x+3) = 1\/ (x+1)(x + 4) + 1\/ (x+2)(x +3)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now according to the above sutra the solution would be<\/span><\/p>\n<p><span style=\"font-weight: 400;\">2(x +3) + (x+4) = 0<br \/>\n<\/span><span style=\"font-weight: 400;\">2x + 6 + x + 4 = 0<br \/>\n<\/span><span style=\"font-weight: 400;\">3x + 10 = 0<br \/>\n<\/span><span style=\"font-weight: 400;\">X = -10\/3<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_14_Ekanyunena_Purvena\"><\/span><span style=\"font-weight: 400;\">Sutra 14: Ekanyunena Purvena<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(By one less than the previous.)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Multiplication problems can be solved using this sutra.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The product of two number can be calculated using this sutra when the multiplier consists of only 9<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">12 x 99 = ?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The process to do it is<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> Reduce 1 from multiplicand i.e. 12-1=11<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> The other part of the answer would be 99-11 = 88 (complement of 99)<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Hence the answer is 1188<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_15_Gunita_Samuchaya\"><\/span><span style=\"font-weight: 400;\">Sutra 15: Gunita Samuchaya<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(The product of the sum is equal to the sum of the product)\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra is useful to find the correctness and accuracy of the answers in factorization problems and it states that the sum of the coefficients in the product is equal to the sum of coefficients of the factors and if this condition is satisfied then the equation can be considered to be balanced.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example;\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">let us consider a quadratic equation<\/span><\/p>\n<p><span style=\"font-weight: 400;\">8&#215;2 + 11x + 3 = (x+1)(8x+3)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In this case, the sum of coefficients is 8+11+3=22<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Product of the sum of coefficients of the factors =2 (8+3)= 2 x 11 = 22<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Since both, the totals tally the equation is balanced and correct.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sutra_16_Gunakasamuchya\"><\/span><span style=\"font-weight: 400;\">Sutra 16: Gunakasamuchya<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">(The factor of the sum is equal to the sum of the factors.)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This sutra holds good for a perfect number.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us find the factors of number 28,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">1 x 28= 28<br \/>\n<\/span><span style=\"font-weight: 400;\">2 x 14 = 28<br \/>\n<\/span><span style=\"font-weight: 400;\">4 x 7 = 28<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, in this case, the sum of factors is 1+2+4+7+14 = 28<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The sum of factors equals the factor of the sums, so 28 is said to be a perfect number.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span><span style=\"font-weight: 400;\">Frequently Asked Questions<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>Q1. How is Vedic Mathematics useful?<\/b><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Ans. Vedic mathematics helps in making one\u2019s calculation more accurate and also helps in speeding up one&#8217;s calculation abilities. Having this skill in oneself can automatically boost up the confidence and one do not have to run from the situations where there is any kind of calculation required.\u00a0<\/span><\/p>\n<p><b>Q2. Is Vedic Mathematics a part of our education curriculum?<\/b><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Ans. Vedic Mathematics is not officially included in our education curriculum, but students opt Vedic m mathematics to prepare for certain competitive exams like SSC, RRB, UPSC, IBPS, etc. Because during these examinations students need to have fast calculation skills as there is a limited time for competitive exams and questions are more.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vedic Maths has gained a lot of popularity in some of the last years because of its fast and accurate calculations. Calculation is a crucial part of every profession nowadays, and people with fast calculation abilities seems to have special skill, as not everybody has this ability to calculate fast and accurate. Everybody wants to &#8230; <a title=\"Vedic Maths Tricks\" class=\"read-more\" href=\"https:\/\/www.saralstudy.com\/blog\/vedic-maths-tricks\/\" aria-label=\"Read more about Vedic Maths Tricks\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":2438,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[64],"tags":[],"class_list":["post-625","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-knowledge"],"_links":{"self":[{"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/posts\/625","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/comments?post=625"}],"version-history":[{"count":5,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/posts\/625\/revisions"}],"predecessor-version":[{"id":2440,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/posts\/625\/revisions\/2440"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/media\/2438"}],"wp:attachment":[{"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/media?parent=625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/categories?post=625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.saralstudy.com\/blog\/wp-json\/wp\/v2\/tags?post=625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}