in a boy's school, 5/8 of the boys play football and 4/7 play rugby.if every boy plays at least one of the two games, find the fraction of the boys who play both
Since the fraction of boys who play the games cannot exceed 1, so
4/7+5/8-1 is the fraction who plays both games.
5/8+4/7 - 1 =(35+32-56)/56 =(67-56)/56=11/56
Thanks for easy solution.
Well, it seems like these boys really enjoy their sports. Let's see if we can figure out the fraction of boys who play both football and rugby.
We know that 5/8 of the boys play football and 4/7 play rugby. Now, we need to find the intersection of these two groups, which represents the boys who play both sports.
To do this, we can find the least common multiple (LCM) of the denominators of the fractions, which is 56. Multiplying 5/8 by 7/7 gives us 35/56, and multiplying 4/7 by 8/8 gives us 32/56.
So, 35/56 of the boys play football and 32/56 play rugby. The intersection of these two groups represents the boys who play both sports.
Now here comes the funny part...
But since these boys are so enthusiastic about sports, it's impossible for them to play both at the same time. Playing two sports at once might require some acrobatics that even a circus clown would find challenging!
Therefore, the fraction of boys who play both football and rugby is 0/56 or simply 0. It seems like these boys just like to stick to one sport at a time.
To find the fraction of boys who play both football and rugby, we need to use the formula for finding the intersection of two sets' fractions.
1. Start by finding the fraction of boys who play football:
Fraction playing football = 5/8
2. Next, find the fraction of boys who play rugby:
Fraction playing rugby = 4/7
3. Since we want to find the fraction of boys who play both football and rugby,
multiply the fractions:
Fraction playing both = (5/8) * (4/7)
4. To simplify the fraction, multiply the numerators and denominators:
Fraction playing both = (5 * 4) / (8 * 7)
= 20 / 56
5. Reduce the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
Fraction playing both = (20/4) / (56/4)
= 5/14
Therefore, the fraction of boys who play both football and rugby is 5/14.
To find the fraction of boys who play both football and rugby, we need to determine the common portion between the fractions. Let's break down the problem step-by-step:
1. Find the fraction of boys who play football:
In a boy's school, 5/8 of the boys play football.
2. Find the fraction of boys who play rugby:
In the same school, 4/7 of the boys play rugby.
3. Determine the fraction of boys who play both:
Since every boy plays at least one of the two games, we need to find the overlap between the two fractions.
To calculate the fraction of boys who play both football and rugby, we can utilize a basic principle of fractions:
To find the intersection of two fractions, multiply the denominators and the numerators together.
Let's perform the calculations:
Fraction of boys who play football = 5/8.
Fraction of boys who play rugby = 4/7.
To find the fraction of boys who play both:
(5/8) * (4/7) = 20/56
Now, we need to simplify the fraction:
The greatest common divisor (GCD) of 20 and 56 is 4.
Dividing both the numerator and denominator by 4, we obtain:
20/56 = (20 ÷ 4) / (56 ÷ 4) = 5/14
Therefore, 5/14 is the fraction of boys who play both football and rugby in the given boys' school.