- \n
- Multiplication and Division<\/a><\/li>\n
- Divide by 10, 100 and 1000 Divisors<\/a><\/li>\n
- Counting Numbers in Proper Pattern<\/a><\/li>\n
- Concept of Pattern<\/a><\/li>\n<\/ul>\n
Patterns in Mathematics<\/h3>\n
Below provided is the pattern for counting numbers from 1 to 100.<\/p>\n
![\"Patterns](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/patterns-and-mental-mathematics.png\")
<\/p>\nThe following are the observations that can be read from a pattern.<\/p>\n
- \n
- The numbers in every column increase by 1.<\/li>\n
- The numbers in every row increase by 10.<\/li>\n
- The diagonally located numbers from the left to right from least to highest have a difference of 9. Those are 10, 19, 28, 37, 46, 55, 64, 73, 82, 91.<\/li>\n
- And the diagonally located numbers from left to right from top to bottom have a difference of 11. Those numbers are 1, 12, 23, 34, 56, 67, 78, 89, 100.<\/li>\n
- All the numbers in the first row have 1 in their unit’s place, the second row have 2, the third row has 3, and so on.<\/li>\n<\/ul>\n
Mental Math Tricks – Addition, Subtraction, Multiplication, Division<\/h3>\n
Addition:<\/strong>
\nThe most used and best trick to solve the addiction problem is to expand the given numbers. Add the numbers in hundred’s places, tens place, units place together. Again add the obtained numbers to get the sum of the numbers.
\nExample:<\/strong>
\nSolve 1256 + 563 + 78
\n1256 + 563 + 78 = 1000 + 200 + 50 + 6 + 500 + 60 + 3 + 70 +\u00a0 8
\n= 1000 + 700 + 180 + 17
\n= 1700 + 197
\n= 1897<\/p>\nSubtraction:<\/strong>
\nFor solving subtraction problems, we need to expand the given numbers and provide the sign. Subtract the numbers in the hundreds place, ten place, unit’s place.
\nExample:<\/strong>
\nSolve 875 – 232
\n875 – 232 = 800 + 70 + 5 – 200 – 30 – 2
\n= 600 + 40 + 3
\n= 643<\/p>\nMultiplication:<\/strong>
\nFor solving the multiplication of smaller numbers, we can use the repeated addition method. For getting the product of larger numbers, expand the numbers and perform the multiplication. At the end add or subtract those numbers.
\nExamples:<\/strong>
\n8 x 6 = 8 + 8 + 8 + 8 + 8 + 8 = 48
\n82 x 5 = (90 – 8) x 5 = 90 x 5 – 8 x 5
\n= 450 – 40 = 410
\n105 x 8 = (100 + 5) x 8
\n= 100 x 8 + 5 x 8
\n= 800 + 40 = 840<\/p>\nDivision:<\/strong>
\nFor dividing the numbers, divide every digit of the dividend by the divisor and write the quotient.
\nExample:<\/strong>
\n156\/4 = 39<\/p>\nExamples on Patterns and Mental Math Strategies<\/h3>\n
Question 1:<\/strong>
\nSolve the following
\n(i) 27 x 6
\n(ii) 49 x 50
\n(iii) 53 x 47
\nSolution:<\/strong>
\n(i) Given that,
\n27 x 6
\nExpand 27 = 20 + 7
\n27 x 6 = (20 + 7) x 6
\n= 120 + 42
\n= 162
\nTherefore, 27 x 6 = 162
\n(ii) Given that,
\n49 x 50
\nRepresent 49 as 50 – 1
\n49 x 50 = (50 – 1) x 50
\n= (50 x 50) – 50
\n= 2500 – 50
\n= 2450
\nTherefore, 49 x 50 = 2450
\n(iii) Given that,
\n53 x 47
\nRepresent 53 as 50 + 3 and 47 as 50 – 3
\n53 x 62 = (50 + 3) x (50 – 3)
\n= 2500 – 9 = 2491
\nTherefore, 53 x 47 = 2491.<\/p>\nQuestion 2:<\/strong>
\nFind the sum of the numbers.
\n(i) 85 + 162 + 569
\n(ii) 145 + 75
\n(iii) 1453 + 2563 + 4326
\nSolution:<\/strong>
\n(i) Given that,
\n85 + 162 + 569
\nExpand all the numbers
\n85 + 162 + 569 = 80 + 5 + 100 + 60 + 2 + 500 + 60 + 9
\n= 600 + 200 + 16
\n= 816
\nSo, 85 + 162 + 569 = 816
\n(ii) Given that,
\n145 + 75
\nExpand all the numbers
\n145 + 75 = 100 + 40 + 5 + 70 + 5
\n= 100 + 110 + 10
\n= 220
\nSo, 145 + 75 = 220
\n(iii) Given that,
\n1453 + 2563 + 4326
\nExpand all the numbers
\n1453 + 2563 + 4326 = 1000 + 400 + 50 + 3 + 2000 + 500 + 60 + 3 + 4000 + 300 + 20 + 6
\n= 7000 + 1200 + 130 + 12
\n= 8200 + 142
\n= 8342
\nSo, 1453 + 2563 + 4326 = 8342<\/p>\nQuestion 3:<\/strong>
\nSubtract the numbers.
\n(i) 356 – 182
\n(ii) 1563 – 823
\n(iii) 526 – 230
\nSolution:<\/strong>
\n(i) Given that,
\n356 – 182
\nExpand all the numbers
\n356 – 182 = 300 + 50 + 6 – 100 – 80 – 2
\n= 200 – 30 + 4
\n= 170 + 4 = 174
\nSo, 356 – 182 = 174
\n(ii) Given that,
\n1563 – 823
\nExpand all the numbers
\n1563 – 823 = 1000 + 500 + 60 + 3 – 800 – 20 – 3
\n= 700 + 40 = 740
\nSo, 1563 – 823 = 740
\n(iii) Given that,
\n526 – 230
\nExpand all the numbers
\n526 – 230 = 500 + 20 + 6 – 200 – 30
\n= 300 – 10 + 6
\n= 296
\nSo, 526 – 230 = 296<\/p>\nQuestion 4:<\/strong>
\nDivide the following numbers.
\n(i) \\(\\frac { 500 }{ 5 } \\)
\n(ii) \\(\\frac { 1492 }{ 2 } \\)
\n(iii) \\(\\frac { 768 }{ 8 } \\)
\nSolution:<\/strong>
\n(i) Given that,
\n\\(\\frac { 500 }{ 5 } \\) = 100
\n(ii) Given that,
\n\\(\\frac { 1492 }{ 2 } \\) = \\(\\frac { 1400 }{ 2 } \\) + \\(\\frac { 90 }{ 2 } \\) + \\(\\frac { 2 }{ 2 } \\)
\n= 700 + 45 + 1
\n= 746
\n(iii) Given that,
\n\\(\\frac { 768 }{ 8 } \\) = 96<\/p>\n","protected":false},"excerpt":{"rendered":"The pattern is a scheme that helps to solve math questions easily and fastly. Mental mathematics is a skill that allows students to do maths in their heads without using pen and paper or a calculator. Get the simple patterns that make addition, subtraction, multiplication, and division problems easier. Also, find the solved examples on … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":117247,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Patterns-and-Mental-Mathematics-1.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117145"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=117145"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117145\/revisions"}],"predecessor-version":[{"id":135473,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117145\/revisions\/135473"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/117247"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=117145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=117145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=117145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Divide by 10, 100 and 1000 Divisors<\/a><\/li>\n