Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
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.
### 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.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
