Rewrite The Ratio $15:39$ As An Equivalent Ratio Of The Form $1:n$.Give Any Decimals In Your Answer To 1 Decimal Place.
Understanding Equivalent Ratios
In mathematics, equivalent ratios are ratios that have the same value, but are expressed in different forms. To rewrite a ratio in the form 1:n, we need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD.
Finding the Greatest Common Divisor (GCD)
To find the GCD of 15 and 39, we can use the Euclidean algorithm or list the factors of each number. The factors of 15 are 1, 3, 5, and 15, while the factors of 39 are 1, 3, 13, and 39. The greatest common factor of 15 and 39 is 3.
Rewriting the Ratio
To rewrite the ratio 15:39 as an equivalent ratio of the form 1:n, we need to divide both numbers by the GCD, which is 3.
# Import necessary modules
import math
numerator = 15
denominator = 39
gcd = math.gcd(numerator, denominator)
new_numerator = numerator / gcd
new_denominator = denominator / gcd
print(f"The equivalent ratio is new_numerator}")
Calculating the New Ratio
When we divide both numbers by the GCD, we get:
15 ÷ 3 = 5 39 ÷ 3 = 13
So, the equivalent ratio of 15:39 is 5:13.
Rounding Decimals
Since we are asked to give any decimals in our answer to 1 decimal place, we need to check if the new ratio has any decimals. In this case, the new ratio is 5:13, which is a whole number ratio. Therefore, we do not need to round any decimals.
Conclusion
In conclusion, we have successfully rewritten the ratio 15:39 as an equivalent ratio of the form 1:n. We found the GCD of 15 and 39, which is 3, and then divided both numbers by the GCD to get the new ratio of 5:13.
Example Use Case
This concept of equivalent ratios is useful in real-world applications such as cooking, where we need to scale up or down a recipe. For example, if a recipe calls for 15 cups of flour and 39 cups of water, we can rewrite the ratio as 5:13 and use this new ratio to scale up or down the recipe.
Tips and Variations
- To rewrite a ratio in the form 1:n, we need to find the GCD of the two numbers and divide both numbers by the GCD.
- We can use the Euclidean algorithm or list the factors of each number to find the GCD.
- If the new ratio has decimals, we need to round them to 1 decimal place.
- This concept of equivalent ratios is useful in real-world applications such as cooking, where we need to scale up or down a recipe.
Q: What is an equivalent ratio?
A: An equivalent ratio is a ratio that has the same value, but is expressed in a different form. In other words, two ratios are equivalent if they have the same proportion.
Q: How do I find the greatest common divisor (GCD) of two numbers?
A: There are several ways to find the GCD of two numbers. You can use the Euclidean algorithm, list the factors of each number, or use a calculator.
Q: Why do I need to find the GCD to rewrite a ratio?
A: Finding the GCD is necessary to rewrite a ratio in the form 1:n. By dividing both numbers by the GCD, you can simplify the ratio and express it in a more convenient form.
Q: Can I use a calculator to find the GCD?
A: Yes, you can use a calculator to find the GCD. Most calculators have a built-in function to calculate the GCD of two numbers.
Q: How do I know if a ratio is equivalent to another ratio?
A: To determine if two ratios are equivalent, you can compare their proportions. If the proportions are the same, then the ratios are equivalent.
Q: Can I use equivalent ratios in real-world applications?
A: Yes, equivalent ratios are useful in real-world applications such as cooking, where you need to scale up or down a recipe. You can also use equivalent ratios in science, engineering, and finance.
Q: How do I round decimals in an equivalent ratio?
A: If an equivalent ratio has decimals, you need to round them to 1 decimal place. This is because the problem statement asks for decimals to be rounded to 1 decimal place.
Q: Can I use equivalent ratios with fractions?
A: Yes, you can use equivalent ratios with fractions. To rewrite a fraction as an equivalent ratio, you can multiply both the numerator and denominator by the same number.
Q: How do I determine if a ratio is in its simplest form?
A: A ratio is in its simplest form if the greatest common divisor (GCD) of the two numbers is 1. If the GCD is greater than 1, then the ratio is not in its simplest form.
Q: Can I use equivalent ratios to solve problems in mathematics?
A: Yes, equivalent ratios are a fundamental concept in mathematics and can be used to solve a wide range of problems, including algebra, geometry, and trigonometry.
Q: How do I apply equivalent ratios in real-world situations?
A: Equivalent ratios can be applied in real-world situations such as cooking, science, engineering, and finance. You can use equivalent ratios to scale up or down a recipe, calculate proportions, and make informed decisions.
Q: Can I use equivalent ratios with negative numbers?
A: Yes, you can use equivalent ratios with negative numbers. However, you need to be careful when working with negative numbers, as they can change the sign of the ratio.
Q: How do I determine if two ratios are equivalent?
A: To determine if two ratios are equivalent, you can compare their proportions. If the proportions are the same, then the ratios are equivalent.
Q: Can I use equivalent ratios to solve problems in finance?
A: Yes, equivalent ratios can be used to solve problems in finance, such as calculating interest rates, investment returns, and stock prices.
Q: How do I apply equivalent ratios in science and engineering?
A: Equivalent ratios can be applied in science and engineering to calculate proportions, scale up or down experiments, and make informed decisions.
Q: Can I use equivalent ratios with decimals?
A: Yes, you can use equivalent ratios with decimals. However, you need to be careful when working with decimals, as they can affect the accuracy of the ratio.
Q: How do I determine if a ratio is in its simplest form with decimals?
A: A ratio is in its simplest form with decimals if the greatest common divisor (GCD) of the two numbers is 1, and the decimals are rounded to 1 decimal place.