Maths-
General
Easy
Question
𝑉𝑒𝑟𝑖𝑓𝑦 ![open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator 10 over denominator negative 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator 10 over denominator negative 3 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses](data:image/png;base64,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)
Hint:
Solve the LHS part and RHS part separately and then compare.
The correct answer is: verified.
To verify ![open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator 10 over denominator negative 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator 10 over denominator negative 3 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses](data:image/png;base64,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)
Express the rational numbers with positive denominator by multiplying with -1.
Here, ![fraction numerator 10 over denominator negative 3 end fraction equals fraction numerator 10 x minus 1 over denominator negative 3 x minus 1 end fraction equals fraction numerator negative 10 over denominator 3 end fraction](data:image/png;base64,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)
Consider the LHS part, we have
…(i)
Determine the LCM of the denominators of rational numbers inside the brackets.
LCM of 5 and 3 = 15
On multiplying
with 3, we get ![fraction numerator negative 9 cross times 3 over denominator 5 cross times 3 end fraction equals fraction numerator negative 27 over denominator 15 end fraction](data:image/png;base64,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)
On multiplying
with 5, we get ![fraction numerator negative 10 cross times 5 over denominator 3 cross times 5 end fraction equals fraction numerator negative 50 over denominator 15 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAjCAYAAABSM76hAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnhJREFUeNrtWz1LA0EQPUSCRRDEwt5CLEQEsbAQsZEgQSSQwkpsrIOt+B/EQhARCzsJViKCiKS0sxRBrG0sUkgQIc6QEY6wd7cfd+vN3Tx4hXvJZWaetzu7eQmC9DEDPAQ+x7xmHHgCfCKe0lja6MeQA0zi91XTSFwC9xKK+wDcDP1dp7EsCscZJvH7qql10E3gsWL8CLgtwlvF77Om1kG3geuK8TW6psIB0fRaWYS3qan3oD+BFcU4jn3E3E8lcJzoZRLetqZeg/6Jec93wj3DQieJ/hcD3rMLvAXuA6vMhNeJ36WmRh2lTmdsI3xPIy4U+15D9DBGgYu023gBzuawS4+raVL8rjX18sR/RExLY5rTko3wYeBa2GE8/avid62pt+auFpFQW0N0k6k+N09ByuilWFNvwjeAZ4rxi4Sth01zp8Ic8I2x6Kr4bWvqvSN9BLZo7aqQeB1D0XWuXQOXgSPEGhWtwURkk/hNa+qlgRnGBPCcpqyvYHC8mEW3jQcbr9T84JbnCrjE6Ok2id9XTQUCgUAgKApcD7IEAr7/2UVmWWoqkKleIBAIBAKBQA30dqFDBM+I8awYz5fR6DfpudnijiRreu5yx2+G8BujsBlgAXiXkfBFRZI1nU3uXRE+1RxZ5D4dDPxhUSirZbqwwk8Bd2md30h4bRkt04UTfrjZaGm+r2yWaVfhc5s7OkG2gsEP91YNxOdqmfYpPIvcqyR+VsKHwd0y7TKl5zJ33R9IiGXabS3PVe7z1OCl3dypwN0y7SL8v+aOU02T1h60AeNJ3jtwJ4PtHHfLtIvwuct9BXhDUw4ST/LqGX0Wd8u0yc6on1XuvxkBfpMzhUSxAAABDXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4xMDwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjU8L21uPjwvbXJvdz48bXJvdz48bW4+MzwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjU8L21uPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTA8L21uPjwvbXJvdz48bW4+MTU8L21uPjwvbWZyYWM+PC9tYXRoPgMwYUYAAAAASUVORK5CYII=)
On adding, we get ![fraction numerator negative 27 over denominator 15 end fraction plus fraction numerator negative 50 over denominator 15 end fraction equals fraction numerator negative 77 over denominator 15 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAjCAYAAACO5gjTAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnRJREFUeNrtW7FKA0EQXUQkSBCsLAURCWIhiIVY2UgKEQlYiJWNWIqt+A9iIYiIhYUgIiJiJyJiYResRPAD0qSwkBCEOIsjHGHvMhdjdud8D16RzZLs2ze7s3PJGtM5zBLPie/EOrFMXHX0a7Rg6Egz9gHiPvGJecBtRrnORih+3hNXiHl+PU585DYJlomHSsyQ4pa4GHm9wG2aIfXJm5/DxGdBvyHiAzGXoaCzk77naN9NsRBDg9Qn737WBH2uiJOK0o4E9qgx72if4/c0QuqTVz9nOMUmYYO4o2jipUFXJfY52m1bRWHASX3y6meOD8+zLdKv7dOrLOjqXDDdELci59goPhM+o64s4KQ+/drPhmm/MhkkXsakl+biYy7wKi1Op53YKV7VL8RCiqCrKdKZxidvfo5wwI0KDto3JhuY5wmPohKTXnPK0qvUJ29+FrhM7m/Rr4d3h0mTHdQchUQxJkC1FBJSn7z5acvkM2E+X3LsDJoxQXxraisZ93OqY0WPTKQ+efPz2nGuicMpcU1pgF1wVd7DLHLAlRx974ibvBBtqt1WttikPnnzM80BtcLFhkbYs8srFwpV3t2nEwqqI069H+b7Z7C8Iq1SnzT7CQB60MAUAAg6AEGnWJf2v4Ih6AB9q6rb/IsdQJPO/+IndjqkVwDpFUDQAQCCDgCAv8OY+f4DY7mNQzB0QmdbOCGuJ3xpVlIedAaoM+tmQCeCDjqhE2ZAZ2CDlFzVy4IZ0BnIIH/Q6qqedjOgM8BBRuG6qpcVM6Az0EFa1P6BGdAZ0CBdV/WyaAZ0ehpkmqt6ms2Azi4PLunnkDRX9UI3ATo7qPMLV2ew2Ghw87sAAAEcdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjI3PC9tbj48L21yb3c+PG1uPjE1PC9tbj48L21mcmFjPjxtbz4rPC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTA8L21uPjwvbXJvdz48bW4+MTU8L21uPjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj43NzwvbW4+PC9tcm93Pjxtbj4xNTwvbW4+PC9tZnJhYz48L21hdGg+4Nl0ZgAAAABJRU5ErkJggg==)
On substituting this in (i), we get ![fraction numerator negative 77 over denominator 15 end fraction plus fraction numerator negative 21 over denominator 4 end fraction](data:image/png;base64,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)
Determine the LCM of the denominators of rational numbers.
LCM of 15 and 4 = 60
On multiplying
with 4, we get ![fraction numerator negative 77 cross times 4 over denominator 15 cross times 4 end fraction equals fraction numerator negative 308 over denominator 60 end fraction](data:image/png;base64,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)
On multiplying
with 15, we get ![fraction numerator negative 21 cross times 15 over denominator 4 cross times 15 end fraction equals fraction numerator negative 315 over denominator 60 end fraction](data:image/png;base64,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)
On adding, we get ![fraction numerator negative 308 over denominator 60 end fraction plus fraction numerator negative 315 over denominator 60 end fraction equals fraction numerator negative 623 over denominator 60 end fraction](data:image/png;base64,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)
Thus we have LHS to be ![open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator negative 10 over denominator 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 623 over denominator 60 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAAmCAYAAAA7tVwMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAY00gKyAAABWFJREFUeNrtXV+EVFEYP9ZIkkhWkkTWSpJIkrHWkqysZBnJStaSrB6SXpIkK9JTklhJkkRWkqSXZKWHSJJkRXrqYS3JyBprmb7P/EbT2DvznXPvnT3nzPfj97DX7HXOd853vj9z53eNWRmTxNtG0Qncgr0VikQMED8RCxnfd5D4llghLhJniDsCs00/8TLsk4QNxDvE9+A0riWB7fwZ9vEZRaxZmbgEG4yltJXP2E98gvnynn3etEZSewwRX2LP832+EW8SN0kHso74g7g34wkeJn7BRHuwESeIc8TNAS3UQ+JpYrXFZ14Tjzb8PYJrrbAbdl/v8dxniScaxriL+A7XXG3lK07DCfsbDtoxBBVbe7whjhLXNFxj/3olHcwUTvms8SEhKpaINwJctKSNVkI62oybLTZvYxo7FZgdtiPKu9jKV+zCfs3LHnWUJR/qJf4mbs1hossJ1zlqfozIKWeQFayUwsy0uecWLFRvYLaoROaU04IDNI09DALUnORml5By5IHvxH0JJ8tiRE75qylNqYOvzQvuew91WCg4iJQtJqecwwGZhz24VBtHXXlEcsOvaPLkgRJqpkFExx7UWh9RJMfilMst/kcyz6L0BPUAa02tkVWMzCkrqCWfImAsIZ0dS2GPahPPSQbCg1iw3JTt2IxBFL0VkDtbfasUKV3Gn9YpK8KxcUTd6bkNNhKfJaTqvjml7TyrCBYcyQoIIEVEt8mU9uDPHYPztu22c0h9tIqnbSyRcj4hfV0rTF8N1mHc47nvwAbsS2krX1FO6Ktwx/RnBvZgrJfs+wfEM6tgAG6ATEXklNzMGV7h+mFBo6eOCayHj+AIftfUvjozkTrlS0RHSQniYg9x5vRCWnhmjGsmn27vajnlKBapGfeNvKM3jI3hGzaj5ChkZCtfwSnq8YQD6X0G9mDsQTrcElxP5tmKf23+/wKVHZG7jEdNmGi10d6gkC9gvtzVnrVMbRY8nPMLx1o3NKdcg/WaaHC4A6b2/eMhB3vwvUoN9Slnh9z0PNXuHxdbhOwscAibdRk5+2OcFiE6Y7tmCBfz98y/xwmnjd2TOj3Gz6+JbBtCts0zn9CLjOcP9iw71oCjPQbgwPUGJ/vBSIynWexYUhMoqjrmIOemh6luAh2zOqVCN7g6ZTfaIO3DHeqUOmZ1SkXnN0G1g8zj9Kx6SJf16CYb5BllqyHYQyOlRkpNX3WDq1OqUyrUKdUpFbrBdczqlArd4Loeikiw3IECPVSklgh0gO+P2Y1EfnC0k5dk2EqJWiOrB9JjXKjUEoGWKBi/dYv44fqvETulRF6S4SIlagX+RfVGdUorlHO6L0fgBY/nzRFhItK1lspLppESFYN/WjKsTimGWCLQAUeMnz9yZhQbokGMay2Vl0wjJSoG/zJ+XJ2yLawlAh3Tp/sezp3Td/6h7/aI11oqL5lWSlSEkyYbzdcqmhRlnPbnjd9S/DbzspYIdMRj46dw1nXi2cgPYKm8ZFopURH6s/RwNCtYfPkyTp+dkSyalUSgIxY8tBerRLzrgqxIKi+ZhZSoCJyaHMxhopx7z0a2eCKJQAcMGT/FmHmufV3glFJ5ySykREW4YGraMnmlBTGmOlmDS4iLAaTvsT4cLpWXzEJKVARuxefxgh9+zdv3yBxSJBFoiW2mJtS0KRAbxBgppfKSWUiJinHFpHuD81OkwPX3hQzDIUcDXihniUBL8CJfDaz+ig1SeUlGWilRMdbBiVzlH0uIIFwIc9uYH1XaH/hCOUsEWmCv8f+lsd3glAyJvCQjrZSoFbjblMfr1RXJp/Nnk98bzxSRgL/AvqNm6Ai4XDijZlDU8RfqLngnJMKfWAAAAZV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+OTwvbW4+PC9tcm93Pjxtbj41PC9tbj48L21mcmFjPjxtbz4rPC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTA8L21uPjwvbXJvdz48bW4+MzwvbW4+PC9tZnJhYz48L21yb3c+PC9tZmVuY2VkPjxtbz4rPC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjE8L21uPjwvbXJvdz48bW4+NDwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjYyMzwvbW4+PC9tcm93Pjxtbj42MDwvbW4+PC9tZnJhYz48L21hdGg+OknragAAAABJRU5ErkJggg==)
Consider the RHS part, we have
…(ii)
Determine the LCM of the denominators of rational numbers inside the brackets.
LCM of 3 and 4 = 12
On multiplying
with 4, we get ![fraction numerator negative 10 cross times 4 over denominator 3 cross times 4 end fraction equals fraction numerator negative 40 over denominator 12 end fraction](data:image/png;base64,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)
On multiplying
with 3, we get ![fraction numerator negative 21 cross times 3 over denominator 4 cross times 3 end fraction equals fraction numerator negative 63 over denominator 12 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAjCAYAAABSM76hAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAqpJREFUeNrtm8FLG0EUxgeRICIFKSLSgxBCKB6CFykiIoXSQ8mhFEqRHEQCORQP3sW7x17FozcRESlSKKWU0kOglNJDES89+Q+EIiEI6TfwAkvZmHmTnd2Z3feD75B1JfPm23k7u34qlRxr0CnUgXrQT6hxz/lVaJ/Oc8VT6BK6hbrQNfQOeqjCYgU6obnVdVxAG77U+QXahGbo8xL0jY7FcQy1oL7DMX2GXkGlyLFl6ENAprfI6Cp9fkAL6qvPdS5Cv0ac089gXJ1ATNeL53uodXYTMH6PxP1ZHGXoKhDjD+/pmF7XuUrtPokVH2cwx/R5aJvufy8CMV4bt8D8nczrnILatOlLqtVHjTY1vf+fdgO6v3fp3n5GG7cetf6Gyzr7BhrGLHQOPTf8HsU0/yOzvQ/G9JIuxo2MjOTOqf78g1buJDRBC0mv5re+1Vkm0yuMyUjD+AEzNCkhoDdnj2KO6x37jU91PoaOoGnmKnDZ6m02nL5wSas8jp4vdc7TS4ZJi/aXxuZuQI1aZQjodv5myAJr+1LnexqQcmC87eOcfqn0OnJ/1G+4/kBbgRhfohqakQX1hN6NPPOlTu4mkLNZtGWdLsguSb/hqquwmKPb51/ojkxez2GdgiAIgpA247zIEoSwr+w8qyhzKkirFwRBEARBMKPucNOTl8h0HKMi59wIe6roAMBvh8bnITI9jFGRc26EPVV0MrSZwWNOR+UHztyZRNido1vRJ8PBFzUynbTxSmWcKCrRlbfIGHwRI9NJG28SYXfKAbRjMfiiRaaTNN40wu6MWsxVxw1RhhqZzsp4ToTdGXriKxkYH32SaBfIeG6E3elAbf+IUbTI9LjG20TYvWtXRYxMjzN3thF2r4wvamR6nLmzjbB7/SxqSp6jxCb/S5dIJuAffjV2/q/1Fz0AAAENdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjIxPC9tbj48bW8+JiN4RDc7PC9tbz48bW4+MzwvbW4+PC9tcm93Pjxtcm93Pjxtbj40PC9tbj48bW8+JiN4RDc7PC9tbz48bW4+MzwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj42MzwvbW4+PC9tcm93Pjxtbj4xMjwvbW4+PC9tZnJhYz48L21hdGg+cghFvQAAAABJRU5ErkJggg==)
On adding, we get ![fraction numerator negative 40 over denominator 12 end fraction plus fraction numerator negative 63 over denominator 12 end fraction equals fraction numerator negative 103 over denominator 12 end fraction](data:image/png;base64,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)
On substituting this in (ii), we get ![fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator negative 103 over denominator 12 end fraction](data:image/png;base64,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)
Determine the LCM of the denominators of rational numbers.
LCM of 5 and 12 = 60
On multiplying
with 12, we get ![fraction numerator negative 9 cross times 12 over denominator 5 cross times 12 end fraction equals fraction numerator negative 108 over denominator 60 end fraction](data:image/png;base64,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)
On multiplying
with 5, we get ![fraction numerator negative 103 cross times 5 over denominator 12 cross times 5 end fraction equals fraction numerator negative 515 over denominator 60 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAAAjCAYAAAB/7VNeAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA2NJREFUeNrtXE1rFEEQbUIIQYIgIiIehCBBREQQkRCCBESCBBFhEfEgIuTgSbwG/4N4EBYRD96WICIhCBKCiAchiHgSIXjykIsHkTAsgbGKrYFm09NTPR9JV6YevMP29u7U9ryprp7pt8bUjyngE+A3T5/DwOfAL8QutdmYA64Ct4EJ8CfwKfBoAzGnHkpAaPxF5yiK8XgNXCw46BrwhvV6gdpsrANvAcestgvA9w2dCMlIaz5HqYQf1wE+c7RjtrnD+N6/KqTa4hctpGXgNUf7HL3nwyTwh+f9JWLoeyokgUL6MzRdZcC2rZzPHAfepzrpesFxXYLxiUiFJFRIO57P9AuKvkfMY9vCKRJRdpw+TZtY4D8GTggTUpn4070Yj5TBuoWU5LQfAd6kFd6VADF9YIjIxijwIq1ocAo9E+EqzDf2ofGnEsYjL8itnKlt3DO1ZZggMTUlJBtYx30UPN1x4k8ljIev2J7PCXSZ8b1JA1NblWPFjKRGIe3beOQFifeGXjjaXzGW/+ep4K672HbhHHBTsIg48acSxsMX5DoVzqM0zS050ia+7lCfEbo98At4r4Hl/xvgNB1nhDLmJoleAsrGn8Y8HpzCEIvnl5Qq8RFI17EqmAWuUJ+ExLfQUMwdynQ7dHuiB7wkKPuExl90jqSPh0KhUCgUinhQ9QauQqEIvaKUOvaaZXVqUygUCoVCoVBIRpHNZcYMtorgzrs+9bu7D8XvQQQ+C+vR2OKzyXdm9yZAjg0sChTZXPCJPm4VyR7QngV+Njz3SBkhtQWLJJwpSzB4gX4a6sexgUW3FObiFPC7Cqk08GLcYPSragOLXkjG+HfetdVixEWXKYQqNjARQpqm6c0EiumgW4y4wE35Jxj9ytjAxAhpnIq+GUbftlmMQrI51ka4q3GbfvOGYxETYgMTJSTcJfk2J936xCTVYtTkWH81A+Noti0ZL0zc4fiQKaREqpAmSUSnA7+37RYjFzDjnnS04x9u/LZeV7GBRSkkzAjoIjlUQkRqMdqNVcpCRVNWVRtYVEJCD3+PUnBZEZkKYpJuMXIBp6/bOResbSatYgOLTkgrJWqUtlqMuBij6fqBdYFeNoN7c1eH+nJsYNEIyPc4Yi8fW7TJUnOMss0/+r0ojtmcBU6RDawU/gMO0dbK+Lqm8wAAARB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTAzPC9tbj48bW8+JiN4RDc7PC9tbz48bW4+NTwvbW4+PC9tcm93Pjxtcm93Pjxtbj4xMjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjU8L21uPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTE1PC9tbj48L21yb3c+PG1uPjYwPC9tbj48L21mcmFjPjwvbWF0aD72R8sUAAAAAElFTkSuQmCC)
On adding, we get ![fraction numerator negative 108 over denominator 60 end fraction plus fraction numerator negative 515 over denominator 60 end fraction equals fraction numerator negative 623 over denominator 60 end fraction](data:image/png;base64,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)
Thus we have RHS to be ![fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator negative 10 over denominator 9 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses equals fraction numerator negative 623 over denominator 60 end fraction](data:image/png;base64,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)
So we get LHS = RHS = ![fraction numerator negative 623 over denominator 60 end fraction](data:image/png;base64,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)
Hence verified.
Related Questions to study
Maths-
Diameter of a circle is 21 cm. Calculate its circumference.
Diameter of a circle is 21 cm. Calculate its circumference.
Maths-General
Maths-
The circumference of the given circle is _____.
![](data:image/png;base64,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)
The circumference of the given circle is _____.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAAC4CAYAAABUxvb6AAAV6ElEQVR4nO2df2gb9/nH3/lyAw00uIACMshDpgpRqMP0h8IUrDGl04ghovOYRgsz1DAXDM1AoS5LIMEM/9ENU+ySjhSckRRvdMUddtFGXOJWKU6whzfsYgfJ2MamMlgggQ4s0IEOnv3h713s+GesO92d9LwgkFrufZ5ILz33fH7c53OKiAgMU+f8n9kBMEwtYNGZhoBFZxoCFp1pCFh0piFg0ZmGgEVnGgIWnWkIWHSmIWDRmYaARWcaAhadaQgEswOwM6VSCZlMBouLi3j27BkKhQIURcHGxgYAYGNjA4qioFAooFQqwel0wuVyQRAEeDweAIDH44EgCHC5XHj11VfR2toKv98Pp9Np5j+t7jjFqxePx8rKCp48eYJnz55pcq+vrxvWntfr1aR/9dVXEQqF4Pf7DWuv3mHRD0CSJExMTOCbb77BxMTEvlI7HA74fD5NRq/XC+B5lna73XA4HBBFEaIoolQqoVAoQJZl5HI5ANCuu76+jqWlJWQyGWQyGciyvKc9j8eDaDSKK1euIBqNwuVyGfgO1Bcs+g5mZmbwr3/9C5OTk5iZmdn1msfjQSQSwY9+9CNNbiMz7MrKiib9t99+iydPnuz5sgWDQUSjUVy9ehXhcNiwWOqBhhe9UCjgwYMH+OSTT7C4uKj93Ol0IhwO48qVK2hvb7dE2ZDJZDA5OYkvv/wSjx8/RqlU0l7z+Xz47W9/i87OTq3+Z3ZADUilUqFkMknxeJwEQSAABIA8Hg/duHGDUqkUlctls8M8lEqlQqlUim7dukVer1f7NwiCQLFYjEZHR6lSqZgdpmVoKNGLxSL19fWRx+PZI0YymbS1GA8fPtzzxXW5XNTX10fFYtHs8EynIUQvl8v0/vvvkyiKmgRer5f6+/spm82aHZ6ubG5u0sDAAPn9fu3fKopiwwtf16KXy2UaHBwkt9utfeiBQIDGxsbMDq0mPHr0iCKRyC7h+/v7LV+WGUFdil6pVBpa8BdJpVIUDoe198LtdtPg4GBDCV93os/NzVEgEGDB92FsbGzXe+P3+2l6etrssGpC3YheLpept7dX64x5vV4W/ADGxsZ21fDXrl2jra0ts8MylLoQPZVKkc/n00ZRent76/6Dq5ZyuUy3bt3SEoPH46FkMml2WIZha9GLxSJ1d3fvKlNmZ2fNDstWLCwsUCgU0t7DN998k/L5vNlh6Y5tRV9YWNCyuMPhoIGBAVuPg5tJpVKhO3fukNPp1LJ7vSUMW4o+OjqqfSihUIjW1tbMDqkuyGazFI1GteRx//59s0PSDVuJXqlU6NatW9pttru7m7O4zlQqFert7d3VUa2H99g2oheLRWpvb9c6nMPDw2aHVNeMjIxod81IJEKbm5tmh1QVthA9nU5r9bjb7W6YsV+zmZub0xaM2b1ut7zoCwsL2gxnKBSyfWaxG/l8XqvbnU4nTU1NmR3SibC06FNTU9rtMx6P10WtaEcqlQrF43Fby25Z0Vlya1GpVKinp0cbkRkdHTU7pJfCkqInk0lN8q6uLpbcQiQSCW1AwE6yW0700dFRbVo6kUiYHQ6zD+rwo51kt5ToU1NTLLlNGBwc1GR/+PCh2eEciWVET6fT5HK5WHIb0dfXp3VQFxYWzA7nUCwhej6f15aNdnR0cE1uIzo7O7VxdisP/ZoueqVS0Z5+CQaDvLzWZtjl8zNddLtkBOZg7HBHNlX0/v5+29R4zOHs7GPduHHD7HD2YJro09PTJAiCbXrtzNHsHDWz2mdqiuhbW1vaYiErfvuZk/P+++9ri++s9KSSKaKrdXkwGLRkPcecnEqlou0l09HRYXY4GjUXfXR0VKvLl5eXa908UwOy2ay2K9rdu3fNDoeIaiy6Fd8Axhh2JrR0Om12OLUV3Yq3NMY41B0aAoGA6SVqzUQfGRnRxsut1ElhjGPnoMOdO3dMjaUmopfLZW2r5np6spw5mmQyqW1wauZuvjU5fvGPf/wjNjY2EAwG0dXVVYsmGYsQi8UQiUQgSRJu375tWhyGH+2ysbGBs2fPQpZlpFIpRCIRI5tjLMj8/DwuXrwIAFhYWDDlmBzDM/rNmzchyzLi8ThL3qAEAgF0dnZCURRcv37dlBgMzegzMzO4dOkSBEFAOp2Gz+czqinG4uRyOZw9exalUgkPHz5Ee3t7Tds3NKPfvHkTAJBIJFjyBsftduPdd98F8NyLWmJYRn/y5Al+8pOfQBRFrK2tQRRFI5phbIQsy2hpaUEul0MymUQsFqtZ24Zl9A8++AAA0N3dzZIzALZP2n7nnXcAPPejVhiS0VdWVnD+/HkIgoC1tTW43W69m2BsiiRJaGlpgSRJmJubQyAQqEm7hmT0Dz/8EIqi4M0332TJmV2IoqjNpdQyq+ue0QuFApqbmyHLMtLptCWOFmesRS6XQ3NzMwBgbW2tJke6657RP/74Y8iyjI6ODpac2Re3262Nq9cqq+ua0RVFQXNzM3K5HKanpxEKhfS6NFNnLC4u4sKFCxBFEdlsFk6n09D2dM3oExMTyOVyCIVCLDlzKK2trYhGo5AkCePj44a3p6von332GQDgjTfe0POyTJ2ieqJ6YyS6lS6lUglNTU0olUrIZrM16WAw9kaSJDQ1NUFRFGxubsLlchnWlm4ZfXx8HKVSCeFwmCVnjoUoimhvb4eiKPj8888NbUs30dXbz1tvvaXXJZkG4Fe/+hUA4G9/+5uh7ehSuhQKBTQ1NQGA4bcgpr4olUo4c+YMZFk2tOTVJaN//vnnUBQFkUiEJWdeCqfTiXg8DgB48OCBYe3oIvqXX34JgEdbmJPxi1/8AgDw1VdfGdaGLqXL6dOnIUkSlpeXed0589JIkoTTp0/D4XCgWCzC4XDo3kbVGX1+fh6SJMHtdrPkzIkQRRF+vx+yLGNmZsaQNqoW/fHjxwDAz4MyVaH68+TJE0OuX7Xo//73vwEAP/7xj6sOhmlc2traAABPnz415PpV1+hNTU3I5XI1XUTP1B/r6+toaWmB0+lEsViEIAi6Xr+qjJ7JZJDL5SCKIkvOVIXX64XX60WpVMJ//vMf3a9flehqfc4rFRk9UD0yok6vSvTV1VUAQDAY1CUYprFR+3lLS0u6X7sq0VdWVgAA586d0yUYprFRh6czmYzu19ZFdB4/Z/RA9Wh9fV33a1c16vL9738fsiwjn8/zGhemahRFwfe+9z0AQLlc1nWG9MQZfWNjA7IsQxRFlpzRBUEQtKyuVgt6cWLRuWxhjIBFZxoCy4muDi3yiIt1SKVSOHXq1L5/7MIrr7wC4LlfenHiedZcLgdge0aLsQaXL1/Gi2MLZm28f1LUDWllWdb1ujU5w4gxh9XVVQwNDeHatWsH/s7OrJ9KpQAA4XAYq6ure+4I4XBY+2+9M66KulfnxsaGrtetatQFAG8iamE++ugjJBIJrRx4kXA4jOHhYdD26YS7DtPy+Xzaz9va2nDq1Cn09/eDiJBIJAx7CF4dUlQURdfrnrh0UQMx4mkQRh+Ghobw9ddf7/va6uoqnj59umtdyc6/7/z/urq6cPHiRVy+fBkA8Prrr2NoaMigqLfRW/QTZ3RJkgCAN/m3KPfu3UNbW5sm54t89913NY7oeKh9PsuULiz68VAUBePj47h06RIuXbqk7ZhgNG+//Tb6+/sPfP2HP/yh4TFYiROLrn5Yei+Qrzf++c9/4pe//CVmZmYwMzODX//61/j73/9uaJv37t0DgAOzOfB8GE/9XWC7ZjcbdVfdUqmk63VPvNZF7YkbfB6v7bl06dKeB36DwaAhDxfUG3q6xcOLjK25d+/erqHRgzix6EaNd9Yb6tmaO3nnnXe0oTv+s/tPPp8HgGMtFFxdXcXbb7+t/f0wTlxgGzXeWW90dHRgZGQEH374IYBtyTs7O02OyrqotflxTsBQ5wkA4NmzZ4f+7olFVwNRR1+Y/REEAZ2dnSy3zqRSKQwNDYGIcO/evSP3bTxx6aLeWlh0Rk/Up4uO2lX39u3bGB4eBrA9gnTUfjBVd0b1XnzDMMDhw9bqkGh3dzeA53MCh9XpJy5d1BksdRUjw+iBmjgPE13tgL64/Pi77747cF0PDy8ylkJNnAeVLtevX0cikdgzWtPW1mZMRldrdB5eZPRE7fMdtFhwaGho36ePLl68eOjIy4lFV28RRmw2wzQualY+qAQ5aLZ0cHDw0OueuHQx6tm+emW/x9yMenjBzhj1LPKJRff7/QBY9ONw/fp1vPbaa7tqyuHhYfh8Ppb9BVSf9H5EU5cNjIrFIi/XPYBUKoXXXnsNKysre27Hp06dwtdff33oKsNGYucGRltbW8eaHT0uVY26qN86zuoHc/v27QMfZztqpKDRUD1yu926Sg5UKTrX6Ufz9OlTvP766we+dlCnqxExcq8gFt1A1Gy939M86rJSLlueo3qk9v/0pCrR1c2L/vvf/+oSTCOxc60Gs823334LwJhNsaoSXT1JTD35gtnNK6+8gra2Nnz00Ue7fq4+sqau1WC2UT0y4pG+qg/rUg/TXVhYQGtrq15x1RUvrskYHh5myV9gY2MDzc3NcDgc2NrastZhXYDx50PWAy+uy2DJ96L6EwqFDHngvmrRf/rTnwIAvvnmm6qDYRoX1R/VJ73RLaMbdbQ10xio/hh1AnnVNToA/OAHP0CpVMLa2hrvrsu8NJIk4fTp0xAEAcViUffJIkCn9ehqL5lHX5iTMDk5CWB7vxsjJAd0Ev3KlSsAgC+++EKPyzENhurN1atXDWtDl9Ill8uhubkZgiAgm83y4V3MsZFlGWfOnEGpVMLy8rJhRwXpktHdbjcikQhkWcb4+Lgel2QahImJCZRKJYRCIUPPw9LtmdHf/OY3AIDPPvtMr0syDcAnn3wCAHjjjTcMbUeX0gXY3mHpzJkzUBQFm5ubXL4wR7LTmWw2a+jpKbpldKfTiVgsBkVR8Ne//lWvyzJ1zPj4OGRZRiQSMfyIIF23u1DLl3/84x96XpapU9QyV/XGSHQrXYDtHnRTUxMkScLc3BwCgYBel2bqjJWVFZw/fx6CICCfzxs2fq6ia0Z3OBzaUX9/+tOf9Lw0U2d88MEHUBQFPT09hksO6JzRge0x9ZaWFiiKgnQ6zUeoM3swwxHdt6Rzu93o7OyEoijanuAMs5M///nPkGUZsVisZolQ94wOAIuLi7hw4QIcDgfW1tb40F1GQ5IktLS0QJIkTE9PIxQK1aRdQzYZbW1tRSwWgyzL+Pjjj41ogrEpDx48gCRJCIfDNZMcMCijA9srGS9fvgxRFJHNZmvS4WCsjSzLaGlpQS6Xw9jYGDo6OmrWtmHbRkciEQQCAUiSxCMwDIDtM4dyuRx8Ph9isVhN2zYsowPPs7rD4cDy8vKRx3Uw9UuhUMDZs2chSRJGR0cRj8dr2r6hBwFEIhHE43HIsoybN28a2RRjcf7whz9AkiTNiVpjaEYHtmfALly4AFmWMTs7i2AwaGRzjAXJZDK4cOECAGB2dtaUGXPDj3bx+XzaWZDXr183ujnGgrz33ntQFAVdXV2mLQsxPKMD22On58+fRy6XM6U+Y8xjcnISP//5zyGKItLptGlzKjU5rEsURfT39wPY/narpwMz9Y0sy/jd734HAPj9739v7sQh1YhKpULBYJAAUGdnZ62aZUzk2rVrBIBaW1upXC6bGkvNRCciWl5eJqfTSQDo008/rWXTTI1JJpMEgBwOB83NzZkdTm1FJyIaHh4mACSKIq2trdW6eaYG5PN5crlcBIAGBgbMDoeITBCdiCgejxMACofDVKlUzAiBMZBYLEYAKBqNmh2KhimiF4tF8ng8BID6+/vNCIExiDt37hAAcrlclM1mzQ5HwxTRiYgePXpEAEgQBJqamjIrDEZHZmdnyeFwEAAaGxszO5xdmCY6EdGtW7e0b386nTYzFKZKstksud1uAkA9PT1mh7MHU0WvVCrU0dFBAMjv91M+nzczHOaEbG1tUWtrq1aXW7HfZaroRNtvkjq+zp1T+1GpVKi9vV1LVltbW2aHtC+mi05EtLm5qXVOeTLJXvT09BAAcrvdlh4utoToREQLCwvaZFJfX5/Z4TDHYGBggACQ0+mk6elps8M5FMuITkT08OFDEgSBANDg4KDZ4TCHMDg4SAAIAI2OjpodzpFYSnQiok8//VST/caNG2aHw+zDTsntkpAsJzoR0ejoqCZ7IpEwOxxmB319fdr8x927d80O59hYUnSibdnVyYdr167xaIwFSCQSmuR2KFd2YlnRiYimpqa0Dmo8HmfZTcTOkhNZXHSi3bJHo1GeVKoxW1tb2iItp9NJjx49MjukE2F50YmIpqentellr9drifXNjUA6nSa/368t07DzmiRbiE60PakUCoW0zDIyMmJ2SHVNMpnU7qSBQMDSk0HHwTaiE21PN3d3d2tDW729vVy3G4A6sqLOVFt1Wv9lsJXoKsPDw9rwYzQatdS6ZzuTz+e1elwQBMs8HaQHthSdaHfdLoqircZ0rcj9+/e1x99cLpdtO50HYVvRibYzkPpYnrr6kde1vxxra2sUjUa19zAWi9XlHdLWoquMjY1pqx8dDgf19fVx7X4ElUqFBgYGtEk5l8tV1x38uhCdaPs5VHXJqLo2OpVKmR2WJUmlUhQIBHZ1OOt9fqJuRFdJpVLa2C8AikQiLPz/k0qlKBKJaO+N1+ulZDJpdlg1oe5EJyIql8vU19dHoiiy8EQ0Nzenjaaonfe+vr66GDY8LnUpukqxWNxXeDvP8L0Ms7Oz2jO5av+lt7eXisWi2aHVnLoWXaVYLNKNGze0jpe6H+CdO3fq7kPf2tqiu3fvas/hqoInEgna3Nw0OzzTaAjRVTY3NymRSOzK8A6Hg7q6umxf1kxPT1NPT482ba8ulWh0wVUaSnSVcrlMIyMjuzpm6khNf38/zc7Omh3isVhYWKCBgQFtq4md8wn3799vqBr8KGpyEICVWV9fx1/+8hc8ePAAGxsb2s9dLhei0SiuXLmCaDRqiYPGcrkcJicn8dVXX2FiYgK5XE57ze12o6urC2+99Rb8fr+JUVqThhddRVEUPH78GF988QUmJyeRyWR2ve73+9He3o5z587B7/ejtbUVLpfLsHgKhQJWVlYwPz+PpaUlPH78GPPz87t+x+v1or29HVevXkV7ezsEQTAsHrvDoh/A+vr6ruwpSdKe33G5XPD5fAgEAjh37hxEUYTb7YbD4YDD4dBOeFB/piiKdtcoFAoolUrazyRJwtLSEjKZDBYXF1EoFPa0J4oiotEofvaznyEajcLn8xn7JtQRLPoxmZmZwczMDJaWljA/P49MJrOv/HohiiL8fr/2JQqFQggGg5y1TwiLXgW5XE6TfmlpCbIsY319HQBQKpW0rJzL5SDLMgRB0Gp9URQhiiIAwOPxwOl0amVRIBAw97yfOoRFZxqCmpxKxzBmw6IzDQGLzjQELDrTELDoTEPAojMNAYvONAQsOtMQ/A9ryzz1MA8VoQAAAABJRU5ErkJggg==)
Maths-General
Maths-
Find the perimeter of a semicircle of radius 28 cm.
Find the perimeter of a semicircle of radius 28 cm.
Maths-General
Maths-
What is the circumference of a circular disc of radius 14 cm?
What is the circumference of a circular disc of radius 14 cm?
Maths-General
Maths-
The circumference of a circular piece of plot is 440 m. Find its area.
The circumference of a circular piece of plot is 440 m. Find its area.
Maths-General
Maths-
Find the area of a circle of radius 21 m.
Find the area of a circle of radius 21 m.
Maths-General
Maths-
Find the circumference and area of the circle with radius 14 cm.
Find the circumference and area of the circle with radius 14 cm.
Maths-General
Maths-
𝑉𝑒𝑟𝑖𝑓𝑦 ![open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses](data:image/png;base64,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)
𝑉𝑒𝑟𝑖𝑓𝑦 ![open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses](data:image/png;base64,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)
Maths-General
Maths-
Verify ![fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAAjCAYAAADv/iqRAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAeZJREFUeNrtnC9LBFEUxS/LBhGLySiIiIhhQQxisixGEQxisojZ7icxGgQREZHtIgabmETwA1gMJhFhPI93weK4O+46c9+758AJ+yf89pw3szPDzBUZvebgQ/i+5PNV+Ax+gz/0ezvSjMjitP9jeA8uSj6/hrfhCX29AN/qe3WLLL77L4X8SdPwg5GQyeKo/6Li998NBUwWJ/1XgVzRXb4FkcVR/4NCjsF3ekDdtMiSWP/FAB4WchK+gLsGQiWLw/77Qc4o4KyBRUEWp/3/BjkPH8HjBsIki+P+yyCn4FO4bSBIsvjuvxTySrckCyKL0/77HWD/9UC87pMDzyxe+qcoqurlDuZCsQzmQlktY9iL3lykXKTMJbcfZM3/sfcaNUsTmVvKpYn+ucfg3z3FMpgLy6CYC8tgLhRF1X3ykPIVDa8sWfaf29/KlsT7HcmSUf85LdJwv+ONxGdvyMJFalKXcIcsXKRWtS9xRAxZMl2kYa5PmO/Tgw/ke4xKKgpTNMKjtW2y5N1/CHVJ9wCPktbjEGFG0RpZfPXf1bBTOZvvkcVn/ynMMWrpVt8hi7/+F+HnBILcMLTFW2LJrv9ziUOnWup1BdxMIMwTeJcs+fcfjqOe4E/4VeLD/8uJBPwicSYRWYz2/wVKI37sg1AzRgAAASd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTI8L21uPjwvbXJvdz48bW4+NTwvbW4+PC9tZnJhYz48bW8+KzwvbW8+PG1mcmFjPjxtbj4yPC9tbj48bW4+NzwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtbj4yPC9tbj48bW4+NzwvbW4+PC9tZnJhYz48bW8+KzwvbW8+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjEyPC9tbj48L21yb3c+PG1uPjU8L21uPjwvbWZyYWM+PC9tYXRoPq0KxYEAAAAASUVORK5CYII=)
Verify ![fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Find the perimeter and area of a semicircle whose radius is 14 cm.
Find the perimeter and area of a semicircle whose radius is 14 cm.
Maths-General
Maths-
The diameter of a circular park is 98 m. Find the cost of fencing it at Rs 4 per metre.
The diameter of a circular park is 98 m. Find the cost of fencing it at Rs 4 per metre.
Maths-General
Maths-
The circumference of a circular park is 176 m. Find the area of the park.
The circumference of a circular park is 176 m. Find the area of the park.
Maths-General
Maths-
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
Maths-General
Maths-
Find the area of a circle whose radius is 14 cm.
Find the area of a circle whose radius is 14 cm.
Maths-General
Maths-
Find the circumference of the given circle.
![](data:image/png;base64,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)
Find the circumference of the given circle.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAB/CAYAAAB/hVkeAAAPVElEQVR4nO2dT2gbRxvGn3zsQYctrEEBFZwi4y1RqEtVSEAlBivEUEFzUMEHQwQN1IEcDHWgBR8cTAk9mSJDWlxQihIScIoCCuTgljaRTVJiSCABuSjGaxRigwUSaEECLUjwfgd3p1biNvEfzeyu5wcCU9HMs5pn35l5Z/bdQ0REkEgczv9EC5BI3gZpVIkrkEaVuAJpVIkrkEaVuAJpVIkrkEaVuAJFtAC3YFkWDMNgn+XlZRiGAQCoVCqo1+uwLAulUgkAEAgE4PP5oKoq/H4/AEDXdfT29kLXdYRCIei6Dp/PJ+ya3MQhmfDfnqWlJTx8+BALCwt48uQJM+V+EwwGEQ6HMTAwgGg0inA43JF23I406t+USiXcvn0b9+7dw/z8PEzTbPteURTous4+vb29CIVCUBQFmqZB0zQoioLu7m4AwPr6OlqtFkzThGmaaLVaMAwDq6urbZHZsqy2djRNQzQaxenTpxGPx9m/d9A50Eat1+u4c+cOrl+/jvn5ebRaLfZdMBhENBrFwMAAIpEIQqFQRzQYhsEi9/z8PF68eNH2fTQaxdmzZzE0NARN0zqiwRXQASSXy1EikSCfz0cACAApikLxeJzS6TQVi0Vh2orFIqXTaYrH4236fD4fxeNx+v3334VpE8mBMmo2m6VIJMI6HwD19/fTzMwMlctl0fJeo1qtUiqVomg02qY5HA5TJpOhZrMpWiI3PG/UZrNJ6XSaQqEQ62hN02hiYkJo5Nwpa2trNDk5SX6/n12Hrut05coVajQaouV1HE8bdW5urs2ggUCAkskkVatV0dJ2TaPRoGQyScFgkF1XMBikbDYrWlpH8aRRi8UixePxto5MpVKeijz2SKHrOrvOWCxGhUJBtLSO4CmjNhoNmpiYYIsQVVXp8uXLnjLoqzSbTZqamiJN09iicHx8nGq1mmhp+4pnjFooFCgcDrPokkgkaG1tTbQsbmxsbNDIyAgpikIAKBQK0dOnT0XL2jc8YdRUKkWqqrIFxqNHj0RLEsbjx4/ZDevz+SiZTIqWtC+42qjVapWGh4dZFD137pznhrzd0Gg0aHR0lP0uZ86ccWT6bSe41qiFQoGt6FVVpdnZWdGSHEc2m2XprO7ubsrn86Il7RpXGvXBgwesA44fP+6qfChv1tbW2CaHqqo0NzcnWtKucJ1RZ2dn2ao+Ho/Lof4taDablEgkWFYglUqJlrRjXGXUqakpNu8aGxs7UFuI+8HExAT7/cbHx0XL2RGuMWoymWQR4cqVK6LluJZ0Os1SWG4yqyuMOjMzwyJBJpMRLcf1ZDIZZla3pK8cb1Q3/qhuYHZ2lt38MzMzouW8EUcb9e7du8ykk5OTouV4jq3TKaePVI416srKCtu/HhsbEy3Hs4yPj7PUlZO3XB1p1FqtxrYBY7GYaDmex97d03Xdsek+Rxr13Llz7Hiem8+OuoVarUZ9fX0sN+1EHGfUVCrFDlQ4eSjyGoVCgR3smZqaEi3nNRxl1JWVFbbrlE6nRcs5cGQyGba4clqQcJRRY7EYO0sqEYN96ioSiYiW0oZjjGrn9fx+v+uPpLmZWq3GnsdyUn7VEUatVqsUCAQIgDyu5wDu3r3Lntbd2NgQLYeIHGJUe7g5c+aMaCmSv7FTVk6Zhgkv6WMYBo4dOwZFUVAoFBAMBkXKkfxNpVLB+++/D9M08fTpU+HF24TXR/3uu+/QarVw4cIFaVIH4ff78dVXXwEAvv32W8FqBBdJ2xpNi8UiAoGAKCmSbTBNEz09PY6IqkIj6tZoKk3qPDRNc0xUFRZRnz9/jg8//FBGU4fjlKgqLKL++OOPMpq6AE3TMDo6CgD4/vvvhekQElEty8KRI0dQqVSQz+fR19fHW4JkB6yvr6OnpweKoqBcLkNVVe4ahETUO3fuoFKpIBKJSJO6gO7ubgwODsKyLNy8eVOIBiFGvX79OgDgiy++ENG8ZBfYfWX3HW+4D/1OGEYkO2frdK1QKHTsnQb/BveIevv2bbRaLQwPD0uTugifz4fh4WEAwK1bt7i3z92oCwsLAIBPP/2Ud9OSPfLZZ58B+KcPecJ16G+1Wjh8+DBM08TGxoZMS7mMer2Orq4uKIqCarXK9a2DXCPqkydPYJom+vr6pEldiKqqiEQisCwL8/PzXNvmalT74gYHB3k2K9lHTp8+DYD/8M/VqPbF2RcrcR/RaBQAuEdUrnPUw4cPo1KpyPmpi6nX63jnnXegqipqtRq3drlF1EqlgkqlAk3TpEldjKqqCAaDqNfrr723tZNwM+rS0hIAcE8US/Yfuw/tPuWBNKpkx9h9+Pz5c25tcjPq8vIyAOCDDz7g1aSkQxw9ehQA8Ndff3Frk5tR7btPRlT3Y/ehJ+eorVYLAOT+/i7I5XI4dOjQth8RKIoCYDMDwK1NXg2ZpglAGnU3nDp1Cq9mES9evChIzeb5VGAzk8ML7kb1+/28mvQsq6urmJ6ehmEYoqVwg/vQbw8bXuLFixe4ePEi3n33XXz++ecdXw3/8MMPGBsbQ29vb0fb+TfsUdEOPjzgtjNlz6cEF2bpCJ988gkWFxdFyxACr/4UXinFC/BcVBxUuBnVnoCvr6/zapIb6XQasVgMfr8fIyMjKBQKoM0CdPv+AYD79+937N9/m0+5XAaw+Sg1N3ZfX21n2DU35Qt2d49dNl40xWKRvWPhTdia79+/v6c2uUVU++7jmdLwGufPn0cqlRIt461ZXV3F+fPn2d97gdsS3DaqnM/tHnLIQrRUKgF4c6rRzk4Ae99u5WZUEbsZks5gWRaA/968yeVymJ6eBhHh6tWruHbt2p7a5Db0izhxI+kMdh/+17niS5cusWlKb28v/vzzzz21yc2o9ombvc5VJOKx+/Cjjz7a9vurV68CAEZGRgAA7733Xtv/txu4Df12jalnz57xalLSId50Es5eQL16aObly5e73k3jFlFto8qh3/38l1EvXryIsbGx13KvJ0+e3FNE5WZUv98Pv98P0zQ9naLa7kiel6Y7lmXBMAz4fL5tjTo9Pc3qqW7lxIkTe1v57ykLu0MGBwcJAM3NzfFslhtjY2OvJeTthLdhGIJU7S+PHj0iABQOh7m2y3Wv/+TJkwCAe/fu8WyWC3Y65tWjd/aC4uXLlyJk7Tt//PEHAP5FRLgaNRaLAfjnYr3EpUuX/vXo3V7nZ07CDjK8i4hwL5LW1dWFer2OarXK91BDhzl06BDu37+PU6dO7eg7N2FZFrq6utBqtVCtVrk+rcE1oiqKgv7+fgDAr7/+yrPpjmJHSztfuJVcLgcArjcpsFnGx7IsRCIR7o8UcT+PatdF9eI8dTu27tC4nd9++w2AmNph3Eujv3jxAj09PVBVFRsbG5552K+/vx8nTpxAMpls+28A8PDhQ1Gy9o1Wq4UjR46gVCqJed8U1xzD30SjUQJA6XRaRPMdA0DbJ5VKiZa0b2SzWQJAx48fF9K+kEdRvvzySwDi3rDRKeiV3Rg7NeUFfv75ZwDi3mQj7IVohw8fRr1ex8rKCnRd5y1BsgNKpRKOHDkCRVGwtrYm5JF3IRHV5/MhkUgA+OdOlTiXa9euodVqIR6PC6vLIOylvc+ePcPHH38MTdNQLBY9lVP1EpZloaenB6VSCblcjlWc5o2wx6XD4TDi8ThM08T09LQoGZI38NNPP6FUKiEajQozKSAwogIyqjodp0RTQHABChlVnY1ToikgOKIC7VE1n8+zQhUSsZimiWPHjjkimgIOKOkTDodx7tw5mKYptJSipJ1vvvkGpVIJ8XhcuEkBOKDsBhGVy2Xy+/0EgLLZrGg5B55cLkcASFVVWltbEy2HiDZ3UByBfRK+u7ubqtWqaDkHlkajQbquEwBKJpOi5TAcY1Qiov7+fgJAo6OjoqUcWL7++mv2qEmz2RQth+EooxYKBVIUhQDQ7OysaDkHjrm5OVIUhRRFoUePHomW04ajjEpElEwm2fwon8+LlnNgKBaLbJ0wOTkpWs5rOM6oRERDQ0MEgEKhENVqNdFyPE+j0aDjx48TAIrFYo4a8m0cadRarUahUIgA0NDQkGg5nmdkZIQtZMvlsmg52+JIoxIR5fN5UlWVAND4+LhoOZ7FnmopikKPHz8WLedfcaxRiYgymQxbXDkpVeIV7JQgXPA0gqONStT+Y964cUO0HM/gtiDgeKMStQ9Pcudq7zx48IB8Ph8BoImJCdFy3gpXGJWIaGJigplVRtbdk81m2dx/bGxMtJy3xjVGJSIaHx9n0wAn5vqcztTUFBvu3WRSIpcZlYhoZmaG/diJRMKROT+n0Ww26cKFC+wmn5qaEi1px7jOqESbW3328NXf308bGxuiJTmWcrlMsViM7fZlMhnRknaFK41KRPT06VMKBAIEgPx+v2drru6FXC5H3d3dBIACgQA9ePBAtKRd41qjEhFtbGywaGHPu+RUYHOon5iYYFOk/v5+x5wr3S2uNqrN1kVCOBw+0IdZVlZW2HFJRVFocnLSEzevJ4xKRPT48WN24FdRFBodHT1QB7Cr1SqNj4+zG7a7u9vVQ/2reMaoRJuHWUZHR1lnaZpGMzMznogo/0UqlWLzdQA0MjLiuZvUU0a1yefzrGIgAOrr66NsNus5w2azWQqHw+w6I5GIow+W7AVPGtVmdnaWrXoBkK7rlEqlqNFoiJa2a5rNJqXTaerr62PXFQgEPFfC81U8bVSizelAMplsGxoDgQAlk0nHnr3cjnK5TMlkkoLBYNt1XL582XPD/HZ43qg220UiRVHozJkzdOPGDUdG2UajQZlMhuLxODtEYo8MMzMzjtTcKQ6MUbeSzWZpcHCQLbrsXZtEIkHZbFZohKpWq5TNZmlkZITtvtmfwcFBT8613wbhJX1EUqlUcPPmTfzyyy9YXFxs+y4cDiMajWJgYADRaLRjBdxM08T8/DwWFhYwPz//2kuNw+Ewzp49i+Hh4QNd7uhAG3UrhmHg1q1buHfvHhYXF2FZVtv3fr8fuq5D13UcPXoUuq4jEAhAVVVW3FbTNGZo0zRhmiaAzRuiXq+jVCrBMAwsLy/DMAwYhvHae2F9Ph8ikQgGBgYwNDTEXnZ80JFG3QbLsvDkyRM8fPgQCwsLWFxcZKbbbzRNQzgcZpE7EonA5/N1pC03I436llQqFRiGgaWlJayurrJouDVybv17a3S1/9Y0jUXkUCiEUCgkrNS425BGlbgC4WUnJZK3QRpV4gqkUSWuQBpV4gr+D9jMKjV5EQKwAAAAAElFTkSuQmCC)
Maths-General