In a class 2/5 of the pupils wear sprctacles.(a)What fraction of the pupils do not wear spectacles?
(b)If 16 pupils wear spectacles, how many pupils are there altogether?
a) 2/5ths of the pupils are wearing spectacles.
b) 2/5 = 0.4. 1/5 = 0.2. So you can tell, 0.2 is half of 0.4, meaning 1/5th is half of 16, meaning 8. You can then multiply 8 by 5 to get 40 - the number of students in the class.
a) 1 - 2/5 = 3/5 who do not wear specs
b) 16 = 2/5 x
x = 16 * 5/2 = 40
Step 1: Find the fraction of pupils who wear spectacles.
Given that 2/5 of the pupils wear spectacles, this means that 2 out of every 5 pupils wear spectacles.
(a) What fraction of the pupils do not wear spectacles?
To find the fraction of pupils who do not wear spectacles, we need to subtract the fraction who do wear spectacles from 1 (whole).
Step 2: Subtract the fraction who wear spectacles from 1.
Whole - Fraction that wear spectacles = Fraction that do not wear spectacles
1 - 2/5 = 5/5 - 2/5 = 3/5
Therefore, (a) 3/5 of the pupils do not wear spectacles.
(b) If 16 pupils wear spectacles, how many pupils are there altogether?
We know that 2/5 of the pupils wear spectacles, and this fraction is equivalent to 16 pupils.
So, to find out the total number of pupils, we need to find a fraction that is equivalent to 16 pupils but has a denominator of 5.
Step 3: Find the equivalent fraction with a denominator of 5.
To find an equivalent fraction, we multiply both the numerator and denominator by the same number.
We know that 2/5 = 16 pupils, so to find the total number of pupils, we can use a proportion:
2/5 = 16/x
To solve this proportion, we can cross multiply:
2 * x = 5 * 16
2x = 80
Finally, divide both sides by 2 to solve for x:
x = 80 / 2
x = 40
Therefore, (b) there are 40 pupils altogether.
To answer these questions, we'll break down the problem step by step.
(a) What fraction of the pupils do not wear spectacles?
First, we need to find the fraction of pupils who wear spectacles. We are given that 2/5 of the pupils wear spectacles. So, to find the fraction of pupils who do not wear spectacles, we subtract this fraction from 1 (whole).
1 - 2/5 = 5/5 - 2/5 = 3/5
Therefore, 3/5 of the pupils do not wear spectacles.
(b) If 16 pupils wear spectacles, how many pupils are there altogether?
To find the total number of pupils, we need to determine the value of one fraction in relation to the other fraction.
We know that the fraction of pupils who wear spectacles is 2/5, and we are given that this fraction represents 16 pupils. So, we can set up a proportion to solve for the total number of pupils.
2/5 = 16/x
To solve this proportion, we cross-multiply:
2 * x = 5 * 16
2x = 80
Dividing both sides of the equation by 2, we find:
x = 80/2
x = 40
Therefore, there are 40 pupils in total.