Solve For $a$ In The Proportion.${ \frac{1.7}{10} = \frac{3.4}{a} }$a =$

Mar 13, 2025 by ADMIN 77 views

Solving for $a$ in the Proportion

Understanding the Concept of Proportion

A proportion is a statement that two ratios are equal. It is often expressed as a fraction or a decimal, and it can be used to solve for unknown values in a variety of mathematical problems. In this article, we will focus on solving for $a$ in the given proportion: $\frac{1.7}{10} = \frac{3.4}{a}$.

Setting Up the Equation

To solve for $a$, we need to set up the equation based on the given proportion. We can start by writing the proportion as an equation: $\frac{1.7}{10} = \frac{3.4}{a}$.

Cross-Multiplying

To solve for $a$, we can use the method of cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us the equation: $1.7a = 3.4 \times 10$.

Simplifying the Equation

Now that we have the equation $1.7a = 3.4 \times 10$, we can simplify it by multiplying $3.4$ by $10$. This gives us: $1.7a = 34$.

Solving for $a$

To solve for $a$, we need to isolate the variable $a$ on one side of the equation. We can do this by dividing both sides of the equation by $1.7$. This gives us: $a = \frac{34}{1.7}$.

Calculating the Value of $a$

Now that we have the equation $a = \frac{34}{1.7}$, we can calculate the value of $a$. To do this, we can divide $34$ by $1.7$. This gives us: $a = 20$.

Conclusion

In this article, we have solved for $a$ in the given proportion: $\frac{1.7}{10} = \frac{3.4}{a}$. We started by setting up the equation based on the proportion, and then used the method of cross-multiplication to solve for $a$. Finally, we simplified the equation and calculated the value of $a$. The final answer is $a = 20$.

Frequently Asked Questions

What is a proportion? A proportion is a statement that two ratios are equal.
How do you solve for $a$ in a proportion? To solve for $a$, you can use the method of cross-multiplication and then simplify the equation.
What is the final answer to the problem? The final answer is $a = 20$.

Additional Resources

For more information on proportions, see the article on "Understanding Proportions".
For more information on solving equations, see the article on "Solving Equations".
For more information on math problems, see the article on "Math Problems".

Final Answer

The final answer is: 20

Understanding the Concept of Proportion

Q&A: Solving for $a$ in the Proportion

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal.

Q: How do you solve for $a$ in a proportion?

A: To solve for $a$, you can use the method of cross-multiplication and then simplify the equation.

Q: What is the final answer to the problem?

A: The final answer is $a = 20$.

Q: What is the method of cross-multiplication?

A: The method of cross-multiplication involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.

Q: How do you simplify the equation?

A: To simplify the equation, you can multiply the numbers and then divide both sides of the equation by the coefficient of the variable.

Q: What is the coefficient of the variable?

A: The coefficient of the variable is the number that is multiplied by the variable.

Q: How do you calculate the value of $a$?

A: To calculate the value of $a$, you can divide the product of the two numbers by the coefficient of the variable.

Q: What is the final answer to the problem in decimal form?

A: The final answer is $a = 20.0$.

Q: What is the final answer to the problem in fraction form?

A: The final answer is $a = \frac{34}{1.7}$.

Real-World Applications of Proportions

Proportions have many real-world applications, including:

Finance: Proportions are used to calculate interest rates and investment returns.
Science: Proportions are used to calculate the concentration of solutions and the amount of a substance in a mixture.
Engineering: Proportions are used to calculate the size and shape of structures and the amount of materials needed.
Business: Proportions are used to calculate the cost of goods sold and the amount of profit made.