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This question is asking you to find the common denominator.
Number of boys = Number of girls. --- the class is half boys and half girls.
3/4 boys + 5/6 girls can swim
Therefore, those who cannot swim = (1 - 3/4 boys) + (1- 5/6 girls) = 1/4 boys + 1/6 girls = 3/12 boys and 2/12 girls
Recall, the class is half boys and half girls, therefore, fraction of total class that cannot swim = 3/12 X 1/2 + 2/12 X 1/2 = 3/24 + 2/24 = 5/24 of the class.
Number of boys = Number of girls. --- the class is half boys and half girls.
3/4 boys + 5/6 girls can swim
Therefore, those who cannot swim = (1 - 3/4 boys) + (1- 5/6 girls) = 1/4 boys + 1/6 girls = 3/12 boys and 2/12 girls
Recall, the class is half boys and half girls, therefore, fraction of total class that cannot swim = 3/12 X 1/2 + 2/12 X 1/2 = 3/24 + 2/24 = 5/24 of the class.