0

enter image description here

I want to solve this question within minute but bcz of fraction it take more than a minute. does any one know a trick to solve this type question.plz share thanks

IOv
  • 9
  • Can you give a rough estimate of the fractions you multiply without much thinking? – Andrea Mori Jan 14 '14 at 10:03
  • @Andrea: That doesn't help. – TonyK Jan 14 '14 at 10:27
  • I now realize that there must be a major misunderstanding about notation here. What does $5\frac{17}{37}$ mean? The usual understanding is that it means $(5\cdot17)/37\simeq2.29$, but maybe for the questioner means $5+\frac{17}{37}\simeq5.46$. – Andrea Mori Jan 14 '14 at 11:28
  • 1
    @Andrea: Your interpretation never occurred to me. I would always write $5 \times \frac{17}{37}$ or $5 \cdot \frac{17}{37}$ if that is what I meant. (Perhaps this is a cultural thing.) – TonyK Jan 14 '14 at 13:20
  • @TonyK: The standard mathematical convention is that whenever you write $ab$ where $a$ and $b$ are numbers (or other entities in an algebraic structure where a multiplication is defined) that is to be understood as "*$a$ multiplied $b$", unless there is an ambiguity (thus, "$2$ times $3$" should be written $2\cdot3$ and not $23$). Writing $5\frac{17}{37}$ has no ambiguity and would universally interpreted (by mathematicians) as a multiplication. The number which has integral part $5$ and fractional part $\frac{17}{37}$ is to be written $5+\frac{17}{37}$. – Andrea Mori Jan 14 '14 at 14:53
  • 1
    Well, I'm a mathematician. So you are demonstrably wrong. – TonyK Jan 14 '14 at 14:58
  • @AndreaMori "...universally interpreted" in Italy, perhaps. I cannot remember seeing your interpretation in a German textbook, for example. See also http://en.wikipedia.org/wiki/Fraction_(mathematics)#Mixed_numbers . The multiplication-x-signs in the original task make little sense if one is to be inserted between every number and fraction bar anyway. – arne.b Jan 14 '14 at 17:00

1 Answers1

2

Notice that answer (1) and (3) are equal. Notice also that, if you write the factors as non-mixed (improper) fractions, two numerators are even (and not divisible by 4), and only one denominator is even (and divisible by 4). Thus, if your answer is not (5), it must be (2), as the product is either a fraction without $1/4$ in it or an integer.

To find out whether it is (2) or (5), you have to be quick with numbers, I am afraid (not sure whether it took me less than a minute):

The numerators are $5*37+17=202$, $5*52-1=260-1=280-21=7*(40-3)=7*37$ and $7*11+1=78=6*13$. The second denominator is $52=4*13$, which leaves you with $202*6/4$ for the product term, which can still be done in the head.

arne.b
  • 395