Sure! Let's tackle each part of the problem step-by-step.
### Question 16
Out of 60 students in a class, 40 are boys. We need to find the simplest form of the following ratios:
#### (a) Number of boys to the number of girls
- Number of boys: 40
- Total number of students: 60
- Number of girls: Total number of students - Number of boys = 60 - 40 = 20
The ratio of the number of boys to the number of girls is:
- Ratio: 40 boys / 20 girls = 40:20
To simplify this, we need to find the greatest common divisor (GCD) of 40 and 20, which is 20.
- Simplified ratio: [tex]\( \frac{40}{20} : \frac{20}{20} \)[/tex] = 2:1
Answer: The simplest form of the ratio of the number of boys to the number of girls is 2:1.
#### (b) Number of boys to the number of total students
- Number of boys: 40
- Total number of students: 60
The ratio of the number of boys to the number of total students is:
- Ratio: 40 boys / 60 students = 40:60
To simplify this, we need to find the greatest common divisor (GCD) of 40 and 60, which is 20.
- Simplified ratio: [tex]\( \frac{40}{20} : \frac{60}{20} \)[/tex] = 2:3
Answer: The simplest form of the ratio of the number of boys to the number of total students is 2:3.
#### (c) Number of girls to the number of total students
- Number of girls: (as calculated earlier) 20
- Total number of students: 60
The ratio of the number of girls to the number of total students is:
- Ratio: 20 girls / 60 students = 20:60
To simplify this, we need to find the greatest common divisor (GCD) of 20 and 60, which is 20.
- Simplified ratio: [tex]\( \frac{20}{20} : \frac{60}{20} \)[/tex] = 1:3
Answer: The simplest form of the ratio of the number of girls to the number of total students is 1:3.
### Question 17
A line segment 45 cm long is to be divided into two parts in the ratio 4:5. Find the length of each part.
First, we need to determine how many parts the line segment is divided into:
- Sum of the parts of the ratio: 4 + 5 = 9 parts
Each part is calculated as:
- Total length of the line segment: 45 cm
- Length of each part: [tex]\( \frac{Total\ length}{Sum\ of\ the\ parts} = \frac{45\ cm}{9} = 5\ cm\ per\ part \)[/tex]
Now we calculate the length of each section based on the ratio.
- Length of the first part (4 parts):
- [tex]\(4\ parts \times 5\ cm\ per\ part = 20\ cm\)[/tex]
- Length of the second part (5 parts):
- [tex]\(5\ parts \times 5\ cm\ per\ part = 25\ cm\)[/tex]
Answer: The length of the first part is 20 cm and the length of the second part is 25 cm.
