Maths-
General
Easy
Question
Which of the numbers
and
is greater
Hint:
Find the least common multiple of denominators.
The correct answer is: -5/6
Complete step by step solution:
Given rational numbers are
and
.
Here, ![fraction numerator 3 over denominator negative 4 end fraction equals fraction numerator 3 cross times negative 1 over denominator negative 4 cross times negative 1 end fraction equals fraction numerator negative 3 over denominator 4 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAAjCAYAAADrC/qsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAeFJREFUeNrtnKFLBEEYxQcRk0UMRkHEKHYRscoFEcwigslgF7vRavZfEBFExGCwiUHE4v9gkG3rG51wyIE7s7ez8z7fg1+5C/fum3e73+7Od87FawNcgU9QgTdwBmYdh1j9L4ET8ORsKMs63IFtMDX02gq4JikSq/8LcABqI2HtdR0+yIvH4t9KWHtbhwXwSlygv/wfB2LfU1gLytEc2Av9xiZhcWL8jwpl7qBaDWunOap/cURWnFT/w+HsI6jWwpo1RzNgCzyCdcJipfj3Ab1JCGrdAOawtvl+WXM0HT6IVTH+U8OqI2tBOarIC1U1DKraAPIcLYfmmFVN/OsCq4x1iNI92AGTYML9PIl4B7skBUnxr1tXZaxDtNbAZThce/yTiAFRkVj9p16QaR0kSZIkSZK678ss9WmqtyTpV9Yd7P7ZUF50WlIbIEmSJEmSJElSHg3IG3QW/2wj2sXV1W+ifSEOK5N/phHtIut6DvaJw8rov1Zd47UKbokK2Ma/9rkS58L/u8YzmCcNa4p/TRCQ5uIUHJKdmsbhX7NZPeci9lGcn595KKiAuf1rRHu0SsvFt/wI7SJh0z8u/xrRJsoF+4aINv7VBhjIBfuuHV1g/SOv1sOqW1cKq/y3PM2arOsXT12mzKuc8UYAAAF3dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4zPC9tbj48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj40PC9tbj48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbj4zPC9tbj48bW8+JiN4RDc7PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21yb3c+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48L21yb3c+PG1uPjQ8L21uPjwvbWZyYWM+PC9tYXRoPiQenSoAAAAASUVORK5CYII=)
So we have
and ![fraction numerator negative 5 over denominator 6 end fraction](data:image/png;base64,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)
By taking LCM of denominators 4 and 6, we get LCM as 12
On multiplying
with 3, we get ![fraction numerator negative 3 cross times 3 over denominator 4 cross times 3 end fraction equals fraction numerator negative 9 over denominator 12 end fraction](data:image/png;base64,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)
On multiplying
with 2, we get ![fraction numerator negative 5 cross times 2 over denominator 6 cross times 2 end fraction equals fraction numerator negative 10 over denominator 12 end fraction](data:image/png;base64,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)
On comparing the above fractions with same denominator,
we have -9 > -10
Hence ![fraction numerator negative 9 over denominator 12 end fraction greater than fraction numerator negative 10 over denominator 12 end fraction equals fraction numerator 3 over denominator negative 4 end fraction greater than fraction numerator negative 5 over denominator 6 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALcAAAAjCAYAAADWmZvKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA8hJREFUeNrtXEFoU0EQXUooRUpBRER6KIRSRKQIUiSUEgpFSglFCkWKB5FAD+JBepWeRBBP4kEoIh48CCGIlFK8hFCCh0AQERERxJOHXnooUkIIxBkywa/8n5/85P+dHefBO2RJSGbmZWZn/+4aM1xkgRVgHXgCLALTxh3MALeBH7u8ZwL4DFgl7tAYJywC9ykGGItvwCfAM8ZdtLowdlwDfgbOAUeAKWAe+BV4zhEHvgJuhjisBFz1vM7RGCeUgWvAUc/YZeA7x8VtDbWALL0OfCzEkWjLU59xzIobDth1rOKOhmbAOGbxD0IcWaQK5TcNKDK3KU1VVMUdAd+BV3zGp2juJ8GRR/+U+g5w7JCpLTglvE3z7hUVdzRgyf5BTeUIMUdZuyHEkc0un2kwtMHLe8ZttMjHx9QsbwHH4+hOg7rULDUzdWIBOG0hc0f57YOKu85UFKeB1017ZSfryOpHtxilaIawTdOsCzaNGCPHSsjchwHTkjHG05IOxh2MQxiw/zmw+QOw2XogqKFcDnBy0QG76kYerNr0EDgpRNy4dvzcZ/yl4b8UOEtNpSRcooWM2FEyfz84mKR50aqwzrxMzVmKbL1vuzT64IAa/BQ19ovU7N9yWMhvgBnPYsUyCXstiS9fosA3qaN9TdnCNVGHNTXYoL0wf7YY7AzStceEBeCep7HHuOQcz9LrVHlQX0e0WDFnFAoFj3I6r27QGElEhubu6kCN0X/hwIww2wZ9wKQxEibysjpQYxR3RhkW+8VWyOdaDKkxcue3W8sKZWGZW0xwBMcoEYdV1GEaI4kOW1B3aIwkQR2mMVIoFMNC2JUHuJiPWz5xT0mD3ndT7WGPHOMGFveNFCgGuD9m18R02CLsygNcyMctn50NRBeB7w3fbaDS7IkCtO0LU3Fvkphn6PUEJZdKnF/ajyPwYPAn5gGWZk8/wN2MeYbixkRS4y4GY/if/JBmT6/AaVcpog+S+NNtcBdDhkq5FHG7YE8vGKUKNMVU3Hjo9zxnMXQOBc8LEbcr9vSCR8C7A1SvuFGnuTaevDmhhr6WREPfiyPwpMpb438zk4vi5mxPv4/yZ32qT4uhTXjXDV4g1Dkmh0kFT+HcsSmGNAlh2pEsJs2eMFR9bOEmblz68ztQjhd5/rQlBrwcBU+Gn3Io2NLsGTTTc8A+ZWs/NGyIAe+jK1AZMQLE7ao9cTfVSQCnHjcCkk3VhiP2jOVrrdQeMeLG1Rx8iJb3JJerpr3Cs5RUOeu13LlSnl22R5K4EWdpSvjLtK9yQLH3vVnrNz67ycDeGbLqAAABanRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj45PC9tbj48L21yb3c+PG1uPjEyPC9tbj48L21mcmFjPjxtbz4mZ3Q7PC9tbz48bWZyYWM+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTA8L21uPjwvbXJvdz48bW4+MTI8L21uPjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bW4+MzwvbW4+PG1yb3c+PG1vPiYjeDIyMTI7PC9tbz48bW4+NDwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPiZndDs8L21vPjxtZnJhYz48bXJvdz48bW8+JiN4MjIxMjs8L21vPjxtbj41PC9tbj48L21yb3c+PG1uPjY8L21uPjwvbWZyYWM+PC9tYXRoPqqfa7kAAAAASUVORK5CYII=)
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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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)
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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
Maths-
Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?
Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?
Maths-General
Maths-
A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?
A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?
Maths-General
Maths-
The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds
The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds
Maths-General
Maths-
At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?
At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?
Maths-General
Maths-
Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?
Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?
Maths-General