Modulus gives a remainder: M(373,5) = 3, since 5*74 = 370 Rounding rounds to the nearest integer: so R(3.4) = 3, and R(5.8) = 6 and Truncation 'rounds' to an integer by removing any decimal fractions, so T(7.7) = 7 adding the answers above gives 3+3+6+7 = 19
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A student's grade in a course is determined by 6 quizzes and one examination. If the examination counts thrice as much as each of the quizzes, what fraction of final grade is determined by the examination?
Solution: On two racks there are 80 books in total.
Number of books issued on the day = 30
Fraction of books remaining: 50/80 =5/8
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After loading a dock, each worker on the night crew loaded \(\frac{3}{4}\) as many boxes as each worker on the day of the crew. If the night crew has \(\frac{4}{5}\) as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
If there are x workers in day and each loaded y boxes
then boxes loaded in day = xy
boxes loaded in night = \(\frac{3}{4} \times y \times \frac{4}{5} \times x = \frac{3}{5} \times xy\)
Total boxes loaded = \(xy + \frac{3}{5} \times xy = \frac{8}{5} xy\)
fraction of all the boxes loaded by two crews did the day crew load = \(\frac{xy}{(\frac{8}{5} \times xy)} = \frac{5}{8}\)
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\(\frac{2}{3}\)rd of the balls in a bag are blue, the rest are pink. if \(\frac{5}{9}\)th of the blue balls and \(\frac{7}{8}\)th of the pink balls are defective, find the total number of balls in the bag given that the number of non-defective balls is 146?
Let total no of balls = x blue = \(\frac{2x}{3}\)
pink = \(\frac{x}{3}\)
Total no of defective balls = \(\frac{10x}{27} + \frac{7x}{24}\)
= \(\frac{143x}{216}\)
Non defective balls = \(x - \frac{143x}{216} = 146\)
=> x = 432
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How many \(\frac{1}{5}\) are there in \(\frac{243}{5}\)?
243 is 3 raise to 5 ;
729 is 3 raise to 6.
both can be multiple of \(\frac{1}{5}\), as multiple is what you say how much part of this is there is that.
so the ans is 729.
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