Solve The Equation { \frac{1}{3} B = \frac{4}{5}$}$. Which Of The Following Equals { B$}$ In This Equation?A. ${ 2 \frac{2}{5}\$} B. ${ 1 \frac{1}{8}\$} C. { \frac{2}{5}$}$ D. { \frac{1}{4}$}$

Introduction

In mathematics, equations are a fundamental concept that help us solve problems and understand relationships between variables. In this article, we will focus on solving a specific equation involving fractions, and we will explore the different steps involved in finding the solution.

The Equation

The given equation is:

$\frac{1}{3} b = \frac{4}{5}$

Our goal is to solve for the variable $b$.

Step 1: Multiply Both Sides by 3

To isolate $b$, we need to get rid of the fraction $\frac{1}{3}$ that is being multiplied by $b$. We can do this by multiplying both sides of the equation by 3.

$\frac{1}{3} b \times 3 = \frac{4}{5} \times 3$

This simplifies to:

$b = \frac{12}{5}$

Step 2: Simplify the Fraction

The fraction $\frac{12}{5}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

$b = \frac{12}{5}$

Step 3: Convert the Fraction to a Mixed Number

To make the solution more understandable, we can convert the fraction to a mixed number.

$b = \frac{12}{5} = 2 \frac{2}{5}$

Conclusion

In conclusion, the solution to the equation $\frac{1}{3} b = \frac{4}{5}$ is $b = 2 \frac{2}{5}$.

Answer

The correct answer is:

A. $2 \frac{2}{5}$

Discussion

This equation involves fractions, and we used the concept of multiplying both sides of the equation by a common factor to isolate the variable $b$. We also simplified the fraction and converted it to a mixed number to make the solution more understandable.

Related Topics

• Solving equations with fractions
• Multiplying and dividing fractions
• Simplifying fractions
• Converting fractions to mixed numbers

Practice Problems

Try solving the following equation:

$\frac{2}{3} x = \frac{3}{4}$

What is the value of $x$?

Solution

To solve for $x$, we can multiply both sides of the equation by 3.

$\frac{2}{3} x \times 3 = \frac{3}{4} \times 3$

This simplifies to:

$x = \frac{9}{4}$

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

$x = \frac{9}{4}$

We can convert the fraction to a mixed number.

$x = \frac{9}{4} = 2 \frac{1}{4}$

Conclusion

In conclusion, the solution to the equation $\frac{2}{3} x = \frac{3}{4}$ is $x = 2 \frac{1}{4}$.

Answer

The correct answer is:

$$

Introduction

In our previous article, we explored the concept of solving equations with fractions. We learned how to isolate the variable by multiplying both sides of the equation by a common factor and simplifying the fraction. In this article, we will continue to explore this topic by answering some frequently asked questions.

Q&A

Q: What is the first step in solving an equation with fractions?

A: The first step in solving an equation with fractions is to identify the variable and the fraction that is being multiplied by it. We then need to determine the common factor that will allow us to isolate the variable.

Q: How do I multiply fractions?

A: To multiply fractions, we simply multiply the numerators and the denominators. For example, if we have the equation $\frac{1}{2} x = \frac{3}{4}$, we can multiply both sides by 2 to get rid of the fraction on the left-hand side.

Q: What is the difference between a fraction and a mixed number?

A: A fraction is a way of expressing a part of a whole, where the numerator is less than the denominator. A mixed number, on the other hand, is a way of expressing a part of a whole, where the numerator is greater than or equal to the denominator.

Q: How do I convert a fraction to a mixed number?

A: To convert a fraction to a mixed number, we need to divide the numerator by the denominator and write the result as a whole number and a remainder. For example, if we have the fraction $\frac{17}{4}$, we can divide the numerator by the denominator to get 4 with a remainder of 1. We can then write the result as a mixed number: $4 \frac{1}{4}$.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 15 is 3, because 3 is the largest number that divides both 12 and 15 without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. For example, if we have the fraction $\frac{12}{16}$, we can find the GCD of 12 and 16, which is 4. We can then divide both numbers by 4 to get the simplified fraction: $\frac{3}{4}$.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that says two things are equal, where the two things are expressions. An expression, on the other hand, is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value.

Q: How do I evaluate an expression?

A: To evaluate an expression, we need to follow the order of operations (PEMDAS) and perform the mathematical operations in the correct order. For example, if we have the expression $2 + 3 \times 4$, we need to follow the order of operations to get the correct result.

Conclusion

In conclusion, solving equations with fractions requires a good understanding of fractions, mixed numbers, and the order of operations. By following the steps outlined in this article, you can become proficient in solving equations with fractions and improve your math skills.

Practice Problems

Try solving the following equation:

$\frac{2}{3} x = \frac{5}{6}$

What is the value of $x$?

Solution

To solve for $x$, we can multiply both sides of the equation by 3.

$\frac{2}{3} x \times 3 = \frac{5}{6} \times 3$

This simplifies to:

$x = \frac{15}{6}$

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

$x = \frac{5}{2}$

We can convert the fraction to a mixed number.

$x = \frac{5}{2} = 2 \frac{1}{2}$

Conclusion

In conclusion, the solution to the equation $\frac{2}{3} x = \frac{5}{6}$ is $x = 2 \frac{1}{2}$.

Answer

The correct answer is:

A. $2 \frac{1}{2}$