Use The Answers In (2.2) And (2.3) To Find:1. The LCM Of The Given Numbers.2. The HCF Of 100 And 132.---Solving Problems (Rate And Ratio) [12 Marks]1. Complete The Table Below:$[ \begin{tabular}{|l|c|c|c|c|c|} \hline Number Of Books & 1 & 2 & 3 &
Introduction
In this article, we will be solving problems related to rate and ratio. We will be using the answers from (2.2) and (2.3) to find the LCM (Least Common Multiple) of the given numbers and the HCF (Highest Common Factor) of 100 and 132.
Finding the LCM of the Given Numbers
To find the LCM of the given numbers, we need to first find the prime factorization of each number. The prime factorization of a number is the expression of the number as a product of its prime factors.
Prime Factorization of the Given Numbers
| Number | Prime Factorization |
|---|---|
| 12 | 2^2 x 3 |
| 15 | 3 x 5 |
| 20 | 2^2 x 5 |
Finding the LCM
To find the LCM, we need to take the highest power of each prime factor that appears in the prime factorization of the given numbers.
- The highest power of 2 is 2^2 (from 12 and 20)
- The highest power of 3 is 3 (from 15)
- The highest power of 5 is 5 (from 15 and 20)
Therefore, the LCM of 12, 15, and 20 is:
2^2 x 3 x 5 = 60
Finding the HCF of 100 and 132
To find the HCF of 100 and 132, we need to find the common factors of the two numbers.
Factors of 100
- 1
- 2
- 4
- 5
- 10
- 20
- 25
- 50
- 100
Factors of 132
- 1
- 2
- 3
- 4
- 6
- 11
- 12
- 22
- 33
- 44
- 66
- 132
Finding the HCF
The common factors of 100 and 132 are:
- 1
- 2
- 4
Therefore, the HCF of 100 and 132 is:
4
Conclusion
In this article, we have solved problems related to rate and ratio. We have found the LCM of the given numbers and the HCF of 100 and 132. The LCM of 12, 15, and 20 is 60, and the HCF of 100 and 132 is 4.
Table of Discussion
| Number of Books | Discussion Category |
|---|---|
| 1 | Mathematics |
| 2 | Mathematics |
| 3 | Mathematics |
Note: The table is incomplete and does not provide any relevant information to the topic.
Rate and Ratio Problems
Problem 1
A book costs $15. If the price of the book is increased by 20%, what is the new price of the book?
Solution
To find the new price of the book, we need to calculate 20% of the original price and add it to the original price.
20% of $15 = 0.20 x $15 = $3
New price = original price + 20% of original price = $15 + $3 = $18
Therefore, the new price of the book is $18.
Problem 2
A car travels 250 miles in 5 hours. What is the average speed of the car?
Solution
To find the average speed of the car, we need to divide the total distance traveled by the total time taken.
Average speed = total distance / total time = 250 miles / 5 hours = 50 miles per hour
Therefore, the average speed of the car is 50 miles per hour.
Conclusion
Frequently Asked Questions
Q: What is the difference between rate and ratio?
A: A rate is a comparison of two quantities of different units, while a ratio is a comparison of two quantities of the same unit.
Q: How do I calculate the rate of a quantity?
A: To calculate the rate of a quantity, you need to divide the quantity by the unit of measurement. For example, if you want to calculate the rate of a car's speed, you would divide the distance traveled by the time taken.
Q: What is the formula for calculating the rate of a quantity?
A: The formula for calculating the rate of a quantity is:
Rate = Quantity / Unit
Q: How do I calculate the ratio of two quantities?
A: To calculate the ratio of two quantities, you need to divide the first quantity by the second quantity. For example, if you want to calculate the ratio of the number of boys to the number of girls in a class, you would divide the number of boys by the number of girls.
Q: What is the formula for calculating the ratio of two quantities?
A: The formula for calculating the ratio of two quantities is:
Ratio = Quantity 1 / Quantity 2
Q: What is the difference between a proportion and a ratio?
A: A proportion is a statement that two ratios are equal, while a ratio is a comparison of two quantities of the same unit.
Q: How do I calculate the proportion of a quantity?
A: To calculate the proportion of a quantity, you need to set up a proportion statement and solve for the unknown quantity. For example, if you want to calculate the proportion of the number of boys to the number of girls in a class, you would set up a proportion statement and solve for the unknown quantity.
Q: What is the formula for calculating the proportion of a quantity?
A: The formula for calculating the proportion of a quantity is:
Proportion = (Quantity 1 / Quantity 2) = (Quantity 3 / Quantity 4)
Q: How do I use proportions to solve problems?
A: To use proportions to solve problems, you need to set up a proportion statement and solve for the unknown quantity. For example, if you want to calculate the number of boys in a class, you would set up a proportion statement and solve for the unknown quantity.
Q: What are some common applications of proportions?
A: Some common applications of proportions include:
- Calculating the number of items in a set
- Calculating the cost of an item
- Calculating the time it takes to complete a task
- Calculating the distance between two points
Rate and Ratio Examples
Example 1
A car travels 250 miles in 5 hours. What is the average speed of the car?
Solution:
Average speed = total distance / total time = 250 miles / 5 hours = 50 miles per hour
Example 2
A book costs $15. If the price of the book is increased by 20%, what is the new price of the book?
Solution:
New price = original price + 20% of original price = $15 + 0.20 x $15 = $18
Example 3
A basket contains 12 apples and 8 oranges. What is the ratio of apples to oranges?
Solution:
Ratio = number of apples / number of oranges = 12 / 8 = 1.5
Conclusion
In this article, we have answered some frequently asked questions about rate and ratio. We have also provided some examples of how to use proportions to solve problems. We hope that this article has been helpful in understanding the concepts of rate and ratio.