Maths-
General
Easy
Question
Which of the two rational numbers is greater in the given pair
and ![fraction numerator 7 over denominator negative 12 end fraction](data:image/png;base64,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)
Hint:
Find the least common multiple of denominators.
The correct answer is: 9/-13
Given rational numbers are
and
.
Here,
and ![fraction numerator 7 over denominator negative 12 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 12 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 12 end fraction](data:image/png;base64,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)
So we have
and ![fraction numerator negative 7 over denominator 12 end fraction](data:image/png;base64,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)
By taking LCM of denominators 13 and 12, we get LCM as 156
On multiplying
with 12, we get ![fraction numerator negative 9 cross times 12 over denominator 13 cross times 12 end fraction equals fraction numerator negative 108 over denominator 156 end fraction](data:image/png;base64,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)
On multiplying
with 13, we get ![fraction numerator negative 7 cross times 13 over denominator 12 cross times 13 end fraction equals fraction numerator negative 91 over denominator 156 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH4AAAAjCAYAAABSM76hAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA0xJREFUeNrtWz1oFEEUHo4jBBFBRA5JIRwhiEgIhCByyBEIQUQkBA6RFCKBIFZiK1ZiY2UrlhZCkCASgiASjmARCEHEQgSxsrCxCCLHIsT3uG9hPffnZnZnb8Z9H3xF9jZ7b+bb9+bN3rdKFYfDDNrAFPE+8X3C5/PELeIvYo/4mfiYeEL5gzZxB/HzOF4Qm4bzUSo6xKeWrv2MuJZyY20Tl4ljkWMzxNeeiL5I/EicI9aIdeIq8ROxYTAfpaGBu3Xc8vfoDvTAE+H3ErKbk+lRgfNROF4hw5JwD9T9LM9Am8gYH/A74Thn/76rwt/CepOFOIF1RB92oFx9bmKdv+yJ8F+IszHHT2O9d054DmwXa5LSFF9X9KyBDjaZdzxq7Likf0WDVwOvINsDW8IfKvNOvYuOWgcs9hsD0Ycd6HHiEm7I9oiENJnTNprUHrhOnHQx4zvYQinHhA9xFOL7jPGMMZQufA2N04yB6LZKfRx6ngvP1fSBS8Ivocybim6zuQsxjQbPZzwkTrgk/HN0znlEL3I718XSU0c1mkezdMMTgd+qvx9ATWCndLXgCpgb39FEjbJZiuIicTPSGG2jK/YFC4iZ9/MHSKzpHPMhEAgEAoEgfd2UdVRQjTv7f2ZV5lQgpV4gEAgEAkFVkWXbbam+7ZefJwc4b2XEMblurc6KX7eZZCfuOjTg8bLfMbfhJMu2y7+CXVd9kwPjLPEdjtmC79bqrPh1dgtrEHoKfx9D4u0UubUZFuy7+1DSdksHrlmr8wrPSbbn2iSnOV3EWl2M8E8sV1btSb6Acq80xa+atTqv8Hwjn3JF+NAM2Bri3Kpbq9OED7A0cZN6N9JDDVZVXts30MgGKP0rZQvPDpyXqv/e17CogrXaNH62jc1iB8DZfSbm//dRyUKLWQvV7XZZQTYh+qTmdatsrdaJf1H9a2blihBnvOQdzLcyguQ7kd+KPWIgepWt1Xnj30KWxyGwHWQDDw/qOUS32dyFcNFarRP/OdV/ny4KLufXEhJx13aQmzFrj4noRW7nfLFWJ8W/gZ1R+M7cJYi+PHDeGMa6Gkm883iGslBEcGmPDUfxW7Xv1uqs+DuoTmyt/oGKOpdwrZNYZn/i/C7Gn4g/EBCrtakHN2UAAAEQdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjc8L21uPjxtbz4mI3hENzs8L21vPjxtbj4xMzwvbW4+PC9tcm93Pjxtcm93Pjxtbj4xMjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjEzPC9tbj48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjkxPC9tbj48L21yb3c+PG1uPjE1NjwvbW4+PC9tZnJhYz48L21hdGg+Ct0OTwAAAABJRU5ErkJggg==)
On comparing the above fractions with same denominator,
we have -91 > -108
Hence ![fraction numerator negative 91 over denominator 156 end fraction greater than fraction numerator negative 108 over denominator 156 end fraction equals fraction numerator 7 over denominator negative 12 end fraction greater than fraction numerator 9 over denominator negative 13 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN8AAAAjCAYAAAAUqd9OAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABKdJREFUeNrtXV9EXmEYfyVJEjOTdBFJZuYzkvnkk0gySSIzXUwi2cWk2+lqxswupouRmV3MjCQzk26SZBeRzMxkzC5mppsuJvl8oj2P7/fp7Oyc73TOd87pvM/7/vhdfG+nvvP8e9/nec97npSKF/3EbWKReExcIXb6XNtNXCB+UvrhPPfeQnxO3AGXMOZGE3GReAS9rRPbNdDBaQClIIxPXxiGiF+IvcQ6Yj1xmrhPbPW4/jVxRlNDnefeN4ijjs8jGHPjJfER9NVAfIxg1RUTxBdCAi+sT18Ydn1mBDbGk4AZVFecVnHARY/xZ8Q7rrGi6zMbuaSpPlqxSjQKCb6oPp06TnzG2Zn2DAu+FcyabgzgZ05wutns0tdPTfXxnnhDUMoZ1adTx3dij8d4B3Jlk4LvECmkGzx24BrjFfK+43Oe+FRDXcyiDpaEqD59Ibn+DxSodeAIZoiSYcF3UuV33LrIYYy5RfxNLGimhw7UqfXCgi+qT8fiWGF3tPgmN1HHMJeJXRle+aLIWGvwFV1O+4bY5lgpezDj5jRy0i2k1BIRxaczg0ZVffdO4sp34JN2NrrSzlWfIBuAwXVZHdaUWQjy6cyAHemhgRsuwx7jQ64Nl+I5V8isgtOwfWGbLHH4dGbAz7DaDQu+ceX9rOuV+vdRw1ekMG5cQ+2XdYwh5TQNQT6dOjbgdJV0i2+Od79GIzqwzsGnkDbOqbOH5w88HHUcATjgKOgHUPPNaiD/W+KU4CCL6tOpYxAOx5sNf2CYXMjNDp2CLujeL6ny6ZXKsSQ+XtbsUzNVds+KCNAxTfRwADmlIqxPW1hYWCQHXh36rBqszS3SRx75uDWItblFBgySN1QHtR4UsDa3iMUgm9Yg1uZSZ9C0GRbzAb93qjGtzeXYXNwsuGnoymecsa3Ns2WAbWsAa3OL9A1QsOqwNrdID9YA1uYWFhYWySKoVV7YYp+7QfFLiXxejs8zcu+Pfiu3WP/gh+IrkLuE6yaFycgH4vm9xmPY9psqN8y6XOsXB7XKC7OjNgOn68bnFhhiO4MKN1XuuPXED8T5VarKwXJ+Zeqj+r+Tm84ycj3qfAOCwe85rsd1A7U6ISt9V0PnMlXuuPTkBW6h8Vm4jAqrfSaccEmz2c50uZN2zKJwGbnn535WnJBvpM3A4NNV7iQdM4/UU6KM3Dx4CnXfrTScsIQllovOeeX94mgRNc8qCtMS0rFJjYNPstxJBV+lAVGfMBndm25zaSqXWyZw67sFzPZXPX5/D7MBX1sHA/AMcU9jp5Iid1KtFJ3gN9/fKe+O3pJkHMME05+WEzrByt3yKD69Gs/wrtAvIemUJLnj1lMnAq/LkNS6WcXYYrDWgnoNs74XSkIULknuOPXE2QB3dGsyqK718oVUvvi6KnfhcoJTrNs+htkRonBJcselJ96AWFYy2smH8YUcSotEv5g3EvLqrP3dMBxw3HVdA1KyaYchbqry855BDRUuXe649PTBow6WJiPbd8JR0/OJF/4/D3eTKFKdmECEc4u1Q8xyvT5/6wrSjyNczzddyLCiTZQ7bj1JeNcw6N4LmGQq/9OBT7yMVPuDfwGey3shOSsvXgAAAXB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+OTE8L21uPjwvbXJvdz48bW4+MTU2PC9tbj48L21mcmFjPjxtbz4mZ3Q7PC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTA4PC9tbj48L21yb3c+PG1uPjE1NjwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtbj43PC9tbj48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4xMjwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPiZndDs8L21vPjxtZnJhYz48bW4+OTwvbW4+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTM8L21uPjwvbXJvdz48L21mcmFjPjwvbWF0aD4xUITUAAAAAElFTkSuQmCC)
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Without doing any actual division, find which of the following is a terminating decimal or not:![6 over 125](data:image/png;base64,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)
Without doing any actual division, find which of the following is a terminating decimal or not:![6 over 125](data:image/png;base64,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)
Maths-General
Maths-
Without doing any actual division, find which of the following is a terminating decimal or not:![7 over 8](data:image/png;base64,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)
Without doing any actual division, find which of the following is a terminating decimal or not:![7 over 8](data:image/png;base64,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)
Maths-General
Maths-
Without doing any actual division, find which of the following is a terminating decimal or not:![123 over 125](data:image/png;base64,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)
Without doing any actual division, find which of the following is a terminating decimal or not:![123 over 125](data:image/png;base64,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)
Maths-General
Maths-
If
Find the values of a and b
If
Find the values of a and b
Maths-General
Maths-
Rationalize the denominator:![fraction numerator 1 over denominator square root of 3 plus square root of 2 minus 1 end fraction](data:image/png;base64,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)
Rationalize the denominator:![fraction numerator 1 over denominator square root of 3 plus square root of 2 minus 1 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Simplify ![fraction numerator 1 plus square root of 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 minus square root of 2 over denominator square root of 5 minus square root of 3 end fraction](data:image/png;base64,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)
Simplify ![fraction numerator 1 plus square root of 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 minus square root of 2 over denominator square root of 5 minus square root of 3 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?
Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?
Maths-General
Maths-
The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?
The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?
Maths-General