in a boy's school,5/8 of the boys play football and 4/7 play rugby.if every boy play atleast one of the two games,ind the fraction of the boys who play both ?
To find the fraction of boys who play both football and rugby, we need to determine the common fraction of boys who play football and rugby.
Let's analyze the given information:
In the boy's school:
- 5/8 of the boys play football
- 4/7 of the boys play rugby
To find the common fraction, we need to find the greatest common divisor (GCD) of the two denominators, 8 and 7.
The prime factors of 8 are 2 x 2 x 2.
The prime factors of 7 are 7.
Since there are no common factors between 8 and 7, their GCD is 1.
Now, we can find the common fraction of boys who play both football and rugby by multiplying the fractions:
(5/8) x (4/7) = (5 x 4) / (8 x 7) = 20 / 56
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
20 ÷ 4 / 56 ÷ 4 = 5 / 14
Therefore, the fraction of boys who play both football and rugby is 5/14.
5/8 + 4/7 = 67/56
so, 11/56 play both