in a class 1/3 of students play cricket 1/8 play volleyball, 1/6 play tennis and the rest don't play any games. what fraction of the students doesn't play any games?

To find the fraction of students who don't play any games, we need to determine the fraction of students who participate in any of the given games and subtract it from 1.

Given information:
- 1/3 play cricket
- 1/8 play volleyball
- 1/6 play tennis

We need to find the fraction that doesn't play any of these games.

Let's calculate the fraction of students who play any of the given games:

Fraction playing cricket: 1/3
Fraction playing volleyball: 1/8
Fraction playing tennis: 1/6

To find the total fraction of students playing any game, we add these fractions:
1/3 + 1/8 + 1/6

To simplify, we find a common denominator:
8 is a multiple of 4 and 6 is a multiple of 3, so let's use 24 as the common denominator.

Fraction playing cricket: 8/24
Fraction playing volleyball: 3/24
Fraction playing tennis: 4/24

Now, we can find the total fraction of students playing any game:
8/24 + 3/24 + 4/24 = 15/24

Therefore, the fraction of students who don't play any games is:
1 - 15/24

To find a common denominator, we multiply 1 by 24/24:
24/24 - 15/24 = (24 - 15)/24 = 9/24

The fraction of students who don't play any games is 9/24. This fraction can be simplified further if needed.

To find the fraction of students who don't play any games, we need to subtract the fraction of students who play games from 1 (since the total fraction of students is 1).

Let's calculate the fraction of students who play games:

Fraction of students who play cricket = 1/3
Fraction of students who play volleyball = 1/8
Fraction of students who play tennis = 1/6

Now, let's add these fractions together to find the fraction of students who play games:

1/3 + 1/8 + 1/6

To add these fractions, we need to first find a common denominator:

The common denominator of 3, 8, and 6 is 24.

Now, let's convert each fraction to have a denominator of 24:

8/24 + 3/24 + 4/24

Adding these fractions together, we get:

15/24

So, the fraction of students who play games is 15/24.

To find the fraction of students who don't play any games, we subtract this fraction from 1:

1 - 15/24

To subtract fractions, we need to have a common denominator:

24/24 - 15/24

Subtracting these fractions, we get:

9/24

Therefore, the fraction of students who don't play any games is 9/24, which can be simplified to 3/8.

first we add all the fractions:

1/3 + 1/8 + 1/6
to add them, we need the 'least common denominator' (LCD) of the three fractions. LCD is the smallest number that is divisible by 3, 8 and 6.
the LCD of 3, 8 and 6 is 24. then we change all the denominators by 24. to get the new numerator for each, we divide 24 by the original denominator then multiply by original numerator.
for example, 1/3. we divide 24 by 3 and we get 8, then multiply by original numerator (which is 1) and thus the new numerator is 8. and we can say that 1/3 is equivalent to 8/24. applying this to the other two fractions,
8/24 + 3/24 + 4/24
to add fractions, just copy the denominator and add the numerators:
15/24
finally, we are asked of the fraction that does NOT play games. therefore, we subtract this from 1 (because 1 or one whole represent the whole class). therefore,
1 - 15/24 = 9/24 or 3/8

hope this helps~ :)

vollyball