Write The Unknown Number In The Equation:12. $3 \times 2 + \frac{2}{x} = 7 \frac{2}{4}$Also, Write Different Ways To Express $\frac{7}{3}$ As A Mixed Number.

Introduction to the Problem

When solving mathematical equations, it's essential to understand the concept of variables and how to manipulate them to find the unknown value. In this article, we will focus on solving the equation $3 \times 2 + \frac{2}{x} = 7 \frac{2}{4}$ to find the unknown number. Additionally, we will explore different ways to express the fraction $\frac{7}{3}$ as a mixed number.

Understanding the Equation

The given equation is $3 \times 2 + \frac{2}{x} = 7 \frac{2}{4}$. To solve for the unknown number, we need to simplify the equation and isolate the variable. The first step is to convert the mixed number $7 \frac{2}{4}$ to an improper fraction. A mixed number is a combination of a whole number and a fraction, and it can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator.

Converting Mixed Numbers to Improper Fractions

To convert the mixed number $7 \frac{2}{4}$ to an improper fraction, we multiply the whole number by the denominator and then add the numerator.

$$7 \frac{2}{4} = \frac{(7 \times 4) + 2}{4} = \frac{30 + 2}{4} = \frac{32}{4}$$

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

$$3 \times 2 + \frac{2}{x} = \frac{32}{4}$$

Simplifying the Equation

The next step is to simplify the equation by evaluating the expression $3 \times 2$. Multiplication is a basic arithmetic operation that involves finding the product of two numbers.

$$3 \times 2 = 6$$

Now that we have simplified the expression, we can rewrite the equation as:

$$6 + \frac{2}{x} = \frac{32}{4}$$

Isolating the Variable

To isolate the variable, we need to get rid of the constant term on the left-hand side of the equation. We can do this by subtracting 6 from both sides of the equation.

$$\frac{2}{x} = \frac{32}{4} - 6$$

Evaluating the Expression

To evaluate the expression $\frac{32}{4} - 6$, we need to follow the order of operations (PEMDAS). First, we evaluate the division operation.

$$\frac{32}{4} = 8$$

Now that we have evaluated the division operation, we can rewrite the equation as:

$$\frac{2}{x} = 8 - 6$$

Simplifying the Expression

To simplify the expression $8 - 6$, we subtract 6 from 8.

$$8 - 6 = 2$$

Now that we have simplified the expression, we can rewrite the equation as:

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

Solving for the Unknown Number

To solve for the unknown number, we need to isolate the variable. We can do this by multiplying both sides of the equation by x.

$$2 = 2x$$

Dividing Both Sides by 2

To solve for x, we need to divide both sides of the equation by 2.

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

Evaluating the Expression

To evaluate the expression $\frac{2}{2}$, we can simplify it by dividing 2 by 2.

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

Now that we have evaluated the expression, we can conclude that the unknown number is 1.

Expressing $\frac{7}{3}$ as a Mixed Number

In addition to solving the equation, we will also explore different ways to express the fraction $\frac{7}{3}$ as a mixed number. A mixed number is a combination of a whole number and a fraction, and it can be expressed in the form $a \frac{b}{c}$, where a is the whole number, b is the numerator, and c is the denominator.

Converting Fractions to Mixed Numbers

To convert the fraction $\frac{7}{3}$ to a mixed number, we need to divide the numerator by the denominator.

$$\frac{7}{3} = 2 \frac{1}{3}$$

Alternative Ways to Express $\frac{7}{3}$ as a Mixed Number

In addition to $2 \frac{1}{3}$, there are other ways to express $\frac{7}{3}$ as a mixed number. We can also express it as $2 \frac{1}{3}$, $2 \frac{1}{3}$, or $2 \frac{1}{3}$.

Conclusion

In this article, we solved the equation $3 \times 2 + \frac{2}{x} = 7 \frac{2}{4}$ to find the unknown number. We also explored different ways to express the fraction $\frac{7}{3}$ as a mixed number. By following the steps outlined in this article, you can solve similar equations and convert fractions to mixed numbers.

Introduction

In our previous article, we solved the equation $3 \times 2 + \frac{2}{x} = 7 \frac{2}{4}$ to find the unknown number. We also explored different ways to express the fraction $\frac{7}{3}$ as a mixed number. In this article, we will answer some frequently asked questions (FAQs) related to solving equations and converting fractions to mixed numbers.

Q1: What is the difference between a variable and a constant in an equation?

A1: In an equation, a variable is a letter or symbol that represents a value that can change, while a constant is a value that remains the same. For example, in the equation $x + 2 = 5$, x is a variable and 2 and 5 are constants.

Q2: How do I simplify a mixed number?

A2: To simplify a mixed number, you need to convert it to an improper fraction. To do this, multiply the whole number by the denominator and add the numerator. For example, to simplify the mixed number $3 \frac{2}{4}$, you would multiply 3 by 4 and add 2 to get $\frac{14}{4}$.

Q3: How do I convert a fraction to a mixed number?

A3: To convert a fraction to a mixed number, you need to divide the numerator by the denominator. For example, to convert the fraction $\frac{7}{3}$ to a mixed number, you would divide 7 by 3 to get $2 \frac{1}{3}$.

Q4: What is the order of operations (PEMDAS)?

A4: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

• P: Parentheses (evaluate expressions inside parentheses first)
• E: Exponents (evaluate any exponential expressions next)
• M: Multiplication and Division (evaluate multiplication and division operations from left to right)
• A: Addition and Subtraction (finally, evaluate any addition and subtraction operations from left to right)

Q5: How do I solve an equation with a variable on both sides?

A5: To solve an equation with a variable on both sides, you need to isolate the variable by performing the same operation on both sides of the equation. For example, to solve the equation $x + 2 = 5 - x$, you would add x to both sides to get $2x + 2 = 5$.

Q6: What is the difference between a linear equation and a quadratic equation?

A6: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $x + 2 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q7: How do I graph a linear equation?

A7: To graph a linear equation, you need to find two points on the line and plot them on a coordinate plane. You can then draw a line through the two points to represent the equation.

Q8: What is the concept of slope in linear equations?

A8: The concept of slope in linear equations refers to the rate at which the line rises or falls as you move from left to right. A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Q9: How do I find the slope of a linear equation?

A9: To find the slope of a linear equation, you need to use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q10: What is the concept of y-intercept in linear equations?

A10: The concept of y-intercept in linear equations refers to the point at which the line crosses the y-axis. The y-intercept is the value of y when x is equal to 0.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to solving equations and converting fractions to mixed numbers. We hope that this article has provided you with a better understanding of these concepts and has helped you to improve your math skills.