Maths-
General
Easy
Question
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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)
Hint:
Solve LHS and RHS and then compare both.
The correct answer is: verified.
To 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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)
On LHS part, we have ![fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAjCAYAAAA+NeykAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAYhJREFUeNrtmi9LREEUxS+LQcRiMgoiImJYEIOYLItRBIOYLGLe7icxGgQREZHtIgabmETwA1gMpocIzzPMBYvjju767pnlHviF9wfe4bw3M7w7V2T4mgeH4D5xfQ2cgTfwrvftio0ovByDfVAnrl+DHTCpx4vgVs81LSYvycC+0wx4EA6Zeal/eX8lPKrYA1vVocAgMy+5gY2DO52ArTWQlzqDQQObAhegQxCWuZd+gc2qwTmCsCi8/BTYAjgCEwRh0XhJBTYNTsEYQVhMXpKBXelbZRCFl36Lw18Xkaa8WnlxMcu/CA/MA/PAakL+47dt2F78C/Mh6fLAPDDXaP6Tma2MozYktiXWyDywDIUa2Y3E+r4HlqFL0PZVKk8HEtscGpk8Q29C6FHoga58bb+XorDjHbbYGi1Xh4ct61t6FJ5SdI5Cn8W6pYGOmihlVewxGKkKCKulo6FtbWQJPBcQ2KbFSDiX2MTRUjY0rK0CAjsBexZzwBP4AK8SN0dXCpm/XiT2VWTpEwActniSLOrXAAAArnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4xMjwvbW4+PC9tcm93Pjxtbj41PC9tbj48L21mcmFjPjxtbz4rPC9tbz48bWZyYWM+PG1uPjI8L21uPjxtbj43PC9tbj48L21mcmFjPjwvbWF0aD4h/oxzAAAAAElFTkSuQmCC)
Here by taking LCM of denominators 5 and 7, we get it as 35.
On multiplying
with 7, we get ![fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction](data:image/png;base64,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)
On multiplying
with 5, we get ![fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35](data:image/png;base64,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)
On adding, we get
…(i)
On RHS part, we have ![2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction](data:image/png;base64,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)
Here by taking LCM of denominators 7 and 5, we get it as 35.
On multiplying
with 5, we get ![fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35](data:image/png;base64,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)
On multiplying
with 7, we get ![fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction](data:image/png;base64,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)
On adding, we get
…(ii)
We have LHS = RHS.
Hence verified.
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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,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)
Maths-General
Maths-
Evaluate ![3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction](data:image/png;base64,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)
Evaluate ![3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAjCAYAAACKE9juAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAl9JREFUeNrtXLFKA0EQXUKQIGnEwlIIIkFEAmIhQSSNiFiEQAqxEBuxDPb+g72lhSAiIhLsJIiFnViJINY2FinkCEKc5Qa0EDxye9k3m3nwCsO53Jt5mZ3NZWLM36gR28RPYkR8IR4RJ83w0f+HUjBLPCQ+OroODVXiObFL7PH9bw+y0C2xQRz79VqFeAMktkk8FpScE+JegjdM0uvQ0CFuEYv89xzxnl9zgi6I0CniHbFg5KHv+DpkTBOfXCxUIj6DiLriSmzUfPCI0laZXe77NgDE7HNPZNR88FjmrTd1o98CKeMPxLyaDx4FzlU1zSITxDovtArQ1NYAzJPmBC7FfGl0Ws9cEtdc3UyRDejzdNsOYCsKvfKV2HgzUM1jCuT4sFNR80GjbOKPv8ZdL7zAhw4fqPOWa9R8sLAH0zMX/XiHt7k8Vx3bZ70RdzwJO+UTt5oPF9dc+VJjhReLmPaJx6ZHYe/cxEo3XZKGXeojxBAegSoU/rabUbsX1anm05hrIDQpqlPNpzFHOa0McpLJ+n/R7yVLSteplU8rn267mhTVqebTmGsgNCmqU6HAO/kOG0hjnJLjKCYfSMGRMMY5Stte5vmQELSumi/MfKAHDWmMU83nOB+oQUMb4xx182WSDxu0HpdS21wemJ+fQUBo3FtCkoMWR1H5sF+jXzTxkLYtq2XPopHGOCXHUVw+7AwmyhCP7zHOUOIoKh8RkOBIcLIiEx4y1TRPfAUR6nOMM6Q4QubjwsQ/8pJjrnPAGh6EoY1xSo2jmHw02clfxA8TDwMveRKLNsYpNY5w+fgG/RVrVVp1iegAAAEmdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4zPC9tbj48bW4+NTwvbW4+PC9tZnJhYz48bW8+KzwvbW8+PG1mcmFjPjxtbj43PC9tbj48bW4+MzwvbW4+PC9tZnJhYz48bW8+KzwvbW8+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjExPC9tbj48L21yb3c+PG1uPjU8L21uPjwvbWZyYWM+PG1vPis8L21vPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48L21yb3c+PG1uPjM8L21uPjwvbWZyYWM+PC9tYXRoPgyiTekAAAAASUVORK5CYII=)
Maths-General
Maths-
The sum of two rational numbers is -5. If one of them is,
find the other.
The sum of two rational numbers is -5. If one of them is,
find the other.
Maths-General
Maths-
Arrange the following rational numbers in descending order
and
.
Arrange the following rational numbers in descending order
and
.
Maths-General
Maths-
8 Arrange the following rational numbers in ascending order
and
.
8 Arrange the following rational numbers in ascending order
and
.
Maths-General
Maths-
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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)
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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)
Maths-General
Maths-
Find the circumference of the circle whose diameter is 21 cm.
Find the circumference of the circle whose diameter is 21 cm.
Maths-General
Maths-
Express
as a rational number with denominator 5
Express
as a rational number with denominator 5
Maths-General
Maths-
Arrange the numbers
and
in ascending order
Arrange the numbers
and
in ascending order
Maths-General
General
Which of the following structures represent propanoic acid?
Which of the following structures represent propanoic acid?
GeneralGeneral