Increase 5200 Kg In The Ratio $2:5$.
Understanding Ratios and Proportions
In mathematics, a ratio is a way to compare two or more numbers. It is a fraction that shows the relationship between two quantities. A proportion, on the other hand, is a statement that two ratios are equal. In this article, we will explore how to increase a given quantity by a certain ratio.
The Given Problem
We are given a quantity of 5200 kg and asked to increase it in the ratio 2:5. This means that for every 2 units of the original quantity, we need to add 5 units to get the new quantity.
Breaking Down the Ratio
To solve this problem, we need to break down the ratio 2:5 into its simplest form. We can do this by finding the greatest common divisor (GCD) of 2 and 5, which is 1. Since the GCD is 1, the ratio 2:5 is already in its simplest form.
Finding the Increase
Now that we have the ratio in its simplest form, we can find the increase by multiplying the original quantity by the ratio. Let's call the original quantity x. Then, the increase is given by:
Increase = (5/2) * x
We are given that the original quantity is 5200 kg. So, we can substitute this value into the equation:
Increase = (5/2) * 5200
Calculating the Increase
To calculate the increase, we can simplify the equation by multiplying 5200 by 5 and then dividing by 2:
Increase = (5/2) * 5200 = (5 * 5200) / 2 = 26000 / 2 = 13000
The New Quantity
Now that we have found the increase, we can add it to the original quantity to get the new quantity:
New Quantity = Original Quantity + Increase = 5200 + 13000 = 17800
Conclusion
In this article, we have shown how to increase a given quantity by a certain ratio. We started by breaking down the ratio 2:5 into its simplest form and then found the increase by multiplying the original quantity by the ratio. Finally, we calculated the new quantity by adding the increase to the original quantity. We hope that this article has provided a clear understanding of how to increase a quantity by a ratio.
Example Problems
- Increase 3000 kg in the ratio 3:4.
- Increase 4000 kg in the ratio 2:3.
- Increase 2000 kg in the ratio 5:6.
Solutions
- Increase = (4/3) * 3000 = (4 * 3000) / 3 = 12000 / 3 = 4000 New Quantity = 3000 + 4000 = 7000
- Increase = (3/2) * 4000 = (3 * 4000) / 2 = 12000 / 2 = 6000 New Quantity = 4000 + 6000 = 10000
- Increase = (6/5) * 2000 = (6 * 2000) / 5 = 12000 / 5 = 2400 New Quantity = 2000 + 2400 = 4400
Tips and Tricks
- When increasing a quantity by a ratio, make sure to break down the ratio into its simplest form.
- Use the formula Increase = (ratio) * original quantity to find the increase.
- Add the increase to the original quantity to get the new quantity.
Common Mistakes
- Failing to break down the ratio into its simplest form.
- Using the wrong formula to find the increase.
- Not adding the increase to the original quantity to get the new quantity.
Conclusion
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about increasing a quantity by a ratio.
Q: What is a ratio?
A: A ratio is a way to compare two or more numbers. It is a fraction that shows the relationship between two quantities.
Q: How do I increase a quantity by a ratio?
A: To increase a quantity by a ratio, you need to break down the ratio into its simplest form, find the increase, and add it to the original quantity.
Q: What is the simplest form of a ratio?
A: The simplest form of a ratio is when the greatest common divisor (GCD) of the two numbers is 1.
Q: How do I find the increase?
A: To find the increase, you need to multiply the original quantity by the ratio.
Q: What is the formula for finding the increase?
A: The formula for finding the increase is:
Increase = (ratio) * original quantity
Q: How do I add the increase to the original quantity?
A: To add the increase to the original quantity, you simply add the two numbers together.
Q: What if the ratio is not in its simplest form?
A: If the ratio is not in its simplest form, you need to break it down into its simplest form before finding the increase.
Q: Can I use a calculator to find the increase?
A: Yes, you can use a calculator to find the increase. However, make sure to follow the correct formula and steps.
Q: What if I make a mistake while increasing a quantity by a ratio?
A: If you make a mistake while increasing a quantity by a ratio, you need to go back and recheck your work. Make sure to follow the correct formula and steps.
Q: Can I increase a quantity by a ratio with decimals?
A: Yes, you can increase a quantity by a ratio with decimals. However, make sure to follow the correct formula and steps.
Q: What if I need to increase a quantity by a ratio with fractions?
A: Yes, you can increase a quantity by a ratio with fractions. However, make sure to follow the correct formula and steps.
Q: Can I use a ratio to decrease a quantity?
A: Yes, you can use a ratio to decrease a quantity. Simply use the reciprocal of the ratio.
Q: What is the reciprocal of a ratio?
A: The reciprocal of a ratio is when you swap the two numbers.
Q: How do I use the reciprocal of a ratio to decrease a quantity?
A: To use the reciprocal of a ratio to decrease a quantity, you need to multiply the original quantity by the reciprocal of the ratio.
Q: What is the formula for using the reciprocal of a ratio to decrease a quantity?
A: The formula for using the reciprocal of a ratio to decrease a quantity is:
Decrease = (1/ratio) * original quantity
Conclusion
In conclusion, increasing a quantity by a ratio is a simple process that involves breaking down the ratio into its simplest form, finding the increase, and adding it to the original quantity. By following these steps and using the correct formula, you can easily increase a quantity by a ratio. We hope that this article has provided a clear understanding of how to increase a quantity by a ratio.
Example Problems
- Increase 3000 kg in the ratio 3:4.
- Increase 4000 kg in the ratio 2:3.
- Increase 2000 kg in the ratio 5:6.
Solutions
- Increase = (4/3) * 3000 = (4 * 3000) / 3 = 12000 / 3 = 4000 New Quantity = 3000 + 4000 = 7000
- Increase = (3/2) * 4000 = (3 * 4000) / 2 = 12000 / 2 = 6000 New Quantity = 4000 + 6000 = 10000
- Increase = (6/5) * 2000 = (6 * 2000) / 5 = 12000 / 5 = 2400 New Quantity = 2000 + 2400 = 4400
Tips and Tricks
- When increasing a quantity by a ratio, make sure to break down the ratio into its simplest form.
- Use the formula Increase = (ratio) * original quantity to find the increase.
- Add the increase to the original quantity to get the new quantity.
- Use the reciprocal of the ratio to decrease a quantity.
- Make sure to follow the correct formula and steps when increasing or decreasing a quantity by a ratio.