Problem 9 · 2019 Math Kangaroo
Medium
Fractions, Decimals & Percents
area-fractiongrid-counting
A big square is divided up into smaller squares of different sizes, as shown. Some of the smaller squares are shaded grey. Which fraction of the big square is shaded grey?
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Answer: D — 49
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Hint 1 of 2
Pick a unit so the smallest cells are 1 by 1 and the whole square is a whole number of them.
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Hint 2 of 2
Count grey units and divide by the total units.
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Approach: count equal area units
- Let the big square be 6×6 = 36 small units.
- The fully grey square in the lower-right quarter covers 9 units, and the grey cells in the small 3×3 block cover another 7 units.
- Grey total = 9 + 7 = 16 units, so the fraction is 16/36 = 4/9.
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