Maths-
General
Easy
Question
Express
in standard form
Hint:
Solve by finding the greatest common divisor.
The correct answer is: -3/4
Complete step by step solution:
Given rational number = ![fraction numerator negative 33 over denominator 44 end fraction](data:image/png;base64,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)
The greatest common divisor of 33 and 44 is 11.
Now, divide numerator and denominator of
by 11,
we get ![fraction numerator negative 33 divided by 11 over denominator 44 divided by 11 end fraction equals fraction numerator negative 3 over denominator 4 end fraction](data:image/png;base64,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)
The standard form of
is
.
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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
Maths-
The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?
The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?
Maths-General
Maths-
Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?
Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?
Maths-General