2/3 of the pupils in a hall are boys and the rest are girls. 1/4 of the boys and 1/3 of the girls wear spectacles. what fraction of the pupils in a hall does not wear spectacles?
1/4 * 2/3 + 1/3 * 1/3 wear
1/6 + 1/9 wear
3/18 + 2/18 wear
5/18 wear
so
13/18 do not wear
To find the fraction of pupils in the hall that do not wear spectacles, we need to determine the fraction of boys and girls who wear spectacles and then subtract it from 1.
Let's denote the total number of pupils in the hall as "x".
The fraction of boys in the hall is given as 2/3. So, the number of boys in the hall is (2/3) * x.
The fraction of girls in the hall is given as the remaining 1/3. So, the number of girls in the hall is (1/3) * x.
Now, let's find the number of boys who wear spectacles. It is given that 1/4 of the boys wear spectacles. So, the number of boys wearing spectacles is (1/4) * (2/3) * x.
Similarly, the number of girls who wear spectacles is (1/3) * (1/3) * x, as 1/3 of the girls wear spectacles.
Now, let's find the total number of pupils wearing spectacles by adding the number of boys and girls wearing spectacles:
(1/4) * (2/3) * x + (1/3) * (1/3) * x.
Now, to find the fraction of pupils not wearing spectacles, we subtract the fraction of pupils wearing spectacles from 1:
1 - [(1/4) * (2/3) * x + (1/3) * (1/3) * x].
Simplifying the expression further, we get:
1 - [(2/12) * x + (1/9) * x].
1 - [(1/6) * x + (1/9) * x]
1 - [(3/18) * x + (2/18) * x]
1 - [(5/18) * x].
Therefore, the fraction of pupils in the hall who do not wear spectacles is: (5/18) * x.
To find the fraction of pupils in a hall who do not wear spectacles, we need to subtract the fraction of pupils who do wear spectacles from 1.
Let's break down the problem step by step:
Step 1: Find the fraction of boys who wear spectacles.
We know that 1/4 of the boys wear spectacles. Since 2/3 of the pupils are boys, we can calculate the fraction of boys who wear spectacles as follows:
(1/4) * (2/3) = 2/12 = 1/6
Step 2: Find the fraction of girls who wear spectacles.
We know that 1/3 of the girls wear spectacles. To find the fraction of girls, we subtract the fraction of boys from 1:
1 - (2/3) = 1/3
Now, we can calculate the fraction of girls who wear spectacles:
(1/3) * (1/3) = 1/9
Step 3: Add the fractions of boys and girls who wear spectacles.
1/6 + 1/9 = 3/18 + 2/18 = 5/18
Step 4: Subtract the fraction of pupils who wear spectacles from 1.
1 - 5/18 = 18/18 - 5/18 = 13/18
Therefore, the fraction of pupils in a hall who do not wear spectacles is 13/18.