Solve For A A A . A 3 = 5 1 3 \frac{a}{3} = 5 \frac{1}{3} 3 A = 5 3 1

Mar 11, 2025 by ADMIN 74 views

Solving for $a$ : A Step-by-Step Guide to Understanding the Equation $\frac{a}{3} = 5 \frac{1}{3}$

In mathematics, solving for a variable is a fundamental concept that helps us understand and manipulate equations. In this article, we will focus on solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ . This equation is a great example of how to solve for a variable in a simple algebraic equation.

Before we dive into solving for $a$ , let's take a closer look at the equation $\frac{a}{3} = 5 \frac{1}{3}$ . This equation is a simple algebraic equation that involves a fraction. The left-hand side of the equation is $\frac{a}{3}$ , which means that $a$ is divided by 3. The right-hand side of the equation is $5 \frac{1}{3}$ , which is a mixed number that represents the sum of 5 and $\frac{1}{3}$ .

Converting the Mixed Number to an Improper Fraction

To make it easier to work with the equation, let's convert the mixed number $5 \frac{1}{3}$ to an improper fraction. To do this, we multiply the whole number part (5) by the denominator (3) and then add the numerator (1). This gives us:

5 \frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3}

Now that we have converted the mixed number to an improper fraction, we can rewrite the equation as:

\frac{a}{3} = \frac{16}{3}

Now that we have the equation in a simpler form, we can solve for $a$ . To do this, we can multiply both sides of the equation by 3 to get rid of the fraction. This gives us:

a = 16

Therefore, the value of $a$ is 16.

To make sure that our answer is correct, let's plug it back into the original equation and see if it works. If we substitute $a = 16$ into the equation, we get:

\frac{16}{3} = 5 \frac{1}{3}

This is true, so we can be confident that our answer is correct.

In this article, we solved for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ . We started by converting the mixed number to an improper fraction, and then we multiplied both sides of the equation by 3 to get rid of the fraction. Finally, we checked our answer by plugging it back into the original equation. We hope that this article has helped you understand how to solve for a variable in a simple algebraic equation.

When solving for a variable, make sure to follow the order of operations (PEMDAS).
When working with fractions, make sure to simplify them before solving for the variable.
When checking your answer, make sure to plug it back into the original equation to see if it works.

Forgetting to simplify fractions before solving for the variable.
Not following the order of operations (PEMDAS).
Not checking the answer by plugging it back into the original equation.

Solving for a variable is a fundamental concept that has many real-world applications. For example, in physics, we use equations to describe the motion of objects. In economics, we use equations to model the behavior of markets. In engineering, we use equations to design and optimize systems.

In conclusion, solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ is a simple algebraic equation that involves a fraction. By following the steps outlined in this article, we can solve for $a$ and check our answer by plugging it back into the original equation. We hope that this article has helped you understand how to solve for a variable in a simple algebraic equation.
Solving for $a$ : A Q&A Guide to Understanding the Equation $\frac{a}{3} = 5 \frac{1}{3}$

In our previous article, we solved for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ . In this article, we will answer some common questions that readers may have about solving for $a$ in this equation.

Q: What is the first step in solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ ?

A: The first step in solving for $a$ is to convert the mixed number $5 \frac{1}{3}$ to an improper fraction. This is done by multiplying the whole number part (5) by the denominator (3) and then adding the numerator (1).

Q: Why do we need to convert the mixed number to an improper fraction?

A: We need to convert the mixed number to an improper fraction because it makes it easier to work with the equation. Improper fractions are easier to add, subtract, multiply, and divide than mixed numbers.

Q: How do we multiply both sides of the equation by 3 to get rid of the fraction?

A: To multiply both sides of the equation by 3, we simply multiply the left-hand side of the equation by 3 and the right-hand side of the equation by 3. This gives us:

3 \times \frac{a}{3} = 3 \times \frac{16}{3}

Q: What is the result of multiplying both sides of the equation by 3?

A: The result of multiplying both sides of the equation by 3 is:

a = 16

Q: How do we check our answer by plugging it back into the original equation?

A: To check our answer, we simply substitute $a = 16$ into the original equation and see if it works. If we substitute $a = 16$ into the equation, we get:

\frac{16}{3} = 5 \frac{1}{3}

This is true, so we can be confident that our answer is correct.

Q: What are some common mistakes to avoid when solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ ?

A: Some common mistakes to avoid when solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ include:

Forgetting to simplify fractions before solving for the variable.
Not following the order of operations (PEMDAS).
Not checking the answer by plugging it back into the original equation.

Q: What are some real-world applications of solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ ?

A: Solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ has many real-world applications, including:

Physics: We use equations to describe the motion of objects.
Economics: We use equations to model the behavior of markets.
Engineering: We use equations to design and optimize systems.

When solving for a variable, make sure to follow the order of operations (PEMDAS).
When working with fractions, make sure to simplify them before solving for the variable.
When checking your answer, make sure to plug it back into the original equation to see if it works.

Forgetting to simplify fractions before solving for the variable.
Not following the order of operations (PEMDAS).
Not checking the answer by plugging it back into the original equation.

Solving for $a$ in the equation $\frac{a}{3} = 5 \frac{1}{3}$ has many real-world applications, including:

Physics: We use equations to describe the motion of objects.
Economics: We use equations to model the behavior of markets.
Engineering: We use equations to design and optimize systems.