squaring a fraction

How many squares would you color to get the fraction half? => 2 or 3 or 1 or 4..

There are 32 black and 32 white squares on a chessboard. Find the fraction of black squares on the chessboard. => 1 5 or 1 4 or 1 3 or 1 2..

How many squares would you color to get the fraction one-third? => 6 or 1 or 9 or 3..

1 3 of a square is colored pink. A green colored square is inscribed in it, which is 1 3 part of the pink colored portion. What fraction of the area of larger square does the green colored square occupy? => 3 or 1 ..

If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all approximately zer..

Rational numbers Problems involving markups, commissions, profits Squares and square roots Operations on fractions, decimals, integers Rates and ratios Order of operations, exponents Scientific notation, radicals, absolute value, irrational/real numbers Numb..

Different forms of numbers Scientific notation, square roots, exponents, radicals, absolute value, factorial, logarithms Properties of numbers Estimation of solutions Sequences and series Proportionality/direct variation, exponential/fractional expressions Patterns, rela..

In this theory, the rate constant is related to three factors Z, f and p by the equation k = Zfp b (19) where Z is the collision frequency f is the fraction of collisions having energy greater than the threshold energy and p is the fraction of the collisions that occurs with the..

>, on the other hand, is coated so as to be slightly "leaky," so that a small fraction of the laser light can escape at each reflection to form the useful beam. The windows W, W in the above figure, which close the ends of the discharge tube, are slanted so that their normals make an angl..

The last terms in (ii) and (iii) depends upon the fact whether n is even or odd. The binomial theorem for fractional index states that General term For r 0, T r + 1 in the expansion of (1+x) n , |x|<1,n Q is given by If x be so small that its squares and higher powers may be ..