The diagram shows a grid of identical squares, some of which are shaded. (a) Write down the fraction of the grid that is shaded, in its lowest terms. [1] (b...

This question tests writing a fraction in its lowest terms, converting it to a percentage, and applying the same fraction to a larger total.

(a) The shaded squares as a fraction of all the squares in the grid simplify to

\[ \frac{3}{5} \] [B1]

A fraction is in its lowest terms when the numerator and denominator share no factor other than \(1\), which is true of \(3\) and \(5\).

(b) A percentage is a fraction out of \(100\), so scale the denominator to \(100\):

\[ \frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100} = 60\% \] [B1]

(c) The larger grid is shaded in the same proportion, so take the same fraction of its \(340\) squares:

\[ 340 \times \frac{3}{5} \] [M1]

\[ = \frac{340}{5} \times 3 = 68 \times 3 = 204 \] [A1]

So \(204\) squares are shaded in the larger grid.

Part (c) works because a fraction records a proportion rather than a count, so it transfers to any size of grid. Dividing by the denominator first, as above, keeps the numbers small and avoids the decimal work of \(340 \times 0.6\).