Using the Division Property of Equality

Oct 13, 2025 by windailys.com 7 views

Solving the Equation: The Quotient of a Number and 18 is 109.2

Understanding the Problem

The given sentence states that the quotient of a number and 18 is 109.2. This can be translated into a mathematical equation as:

x / 18 = 109.2

where x is the unknown number.

Analyzing the Equation

To solve this equation, we need to isolate the variable x. We can start by multiplying both sides of the equation by 18 to eliminate the fraction.

x = 109.2 * 18

This will give us the value of x.

Using the Division Property of Equality

The division property of equality states that if two fractions are equal, then their cross-products are also equal. In this case, we can use the division property of equality to solve the equation.

x / 18 = 109.2

Multiplying both sides by 18 gives us:

x = 109.2 * 18

This is the same as the previous step.

Using the Multiplication Property of Equality

The multiplication property of equality states that if two expressions are equal, then their products are also equal. In this case, we can use the multiplication property of equality to solve the equation.

x / 18 = 109.2

Multiplying both sides by 18 gives us:

x = 109.2 * 18

This is the same as the previous step.

Checking the Statements

Based on the analysis above, we can conclude that:

It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.

Therefore, both statements are correct.

Conclusion

In this article, we have solved the equation that represents the sentence "The quotient of a number and 18 is 109.2." We have analyzed the equation and used the division property of equality and the multiplication property of equality to solve it. We have also checked the statements and concluded that both are correct.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

Write the equation: x / 18 = 109.2
Multiply both sides by 18: x = 109.2 * 18
Simplify the equation: x = 1965.6

Answer

The value of x is 1965.6.

Key Takeaways

The division property of equality can be used to solve equations involving fractions.
The multiplication property of equality can be used to solve equations involving fractions.
To solve an equation, we need to isolate the variable.

Frequently Asked Questions

Q: What is the quotient of a number and 18? A: The quotient of a number and 18 is 109.2.
Q: How can we solve the equation x / 18 = 109.2? A: We can use the division property of equality or the multiplication property of equality to solve the equation.
Q: What is the value of x in the equation x / 18 = 109.2? A: The value of x is 1965.6.

Related Topics

Solving equations involving fractions
Division property of equality
Multiplication property of equality
Isolating variables in equations

Conclusion

Frequently Asked Questions

We have received many questions about the equation x / 18 = 109.2. Here are some of the most frequently asked questions and their answers:

Q: What is the quotient of a number and 18?

A: The quotient of a number and 18 is 109.2.

Q: How can we solve the equation x / 18 = 109.2?

A: We can use the division property of equality or the multiplication property of equality to solve the equation.

Q: What is the value of x in the equation x / 18 = 109.2?

A: The value of x is 1965.6.

Q: Can we use other methods to solve the equation x / 18 = 109.2?

A: Yes, we can use other methods such as the inverse operation method or the algebraic method to solve the equation.

Q: What is the inverse operation method?

A: The inverse operation method involves using the inverse operation of the given operation to solve the equation. In this case, we can use the inverse operation of division, which is multiplication, to solve the equation.

Q: How do we use the inverse operation method to solve the equation x / 18 = 109.2?

A: To use the inverse operation method, we can multiply both sides of the equation by 18 to eliminate the fraction. This gives us x = 109.2 * 18.

Q: What is the algebraic method?

A: The algebraic method involves using algebraic operations to solve the equation. In this case, we can use the algebraic method to solve the equation by multiplying both sides of the equation by 18 to eliminate the fraction.

Q: How do we use the algebraic method to solve the equation x / 18 = 109.2?

A: To use the algebraic method, we can multiply both sides of the equation by 18 to eliminate the fraction. This gives us x = 109.2 * 18.

Q: Can we use the algebraic method to solve other types of equations?

A: Yes, we can use the algebraic method to solve other types of equations, such as linear equations and quadratic equations.

Q: What is the difference between the division property of equality and the multiplication property of equality?

A: The division property of equality states that if two fractions are equal, then their cross-products are also equal. The multiplication property of equality states that if two expressions are equal, then their products are also equal.

Q: How do we use the division property of equality to solve the equation x / 18 = 109.2?

A: To use the division property of equality, we can multiply both sides of the equation by 18 to eliminate the fraction. This gives us x = 109.2 * 18.

Q: How do we use the multiplication property of equality to solve the equation x / 18 = 109.2?

A: To use the multiplication property of equality, we can multiply both sides of the equation by 18 to eliminate the fraction. This gives us x = 109.2 * 18.

Conclusion

In this article, we have answered some of the most frequently asked questions about the equation x / 18 = 109.2. We have discussed the division property of equality, the multiplication property of equality, and the algebraic method, and how they can be used to solve the equation. We have also provided examples of how to use these methods to solve the equation.

Related Topics

Solving equations involving fractions
Division property of equality
Multiplication property of equality
Algebraic method
Inverse operation method

Key Takeaways

The division property of equality can be used to solve equations involving fractions.
The multiplication property of equality can be used to solve equations involving fractions.
The algebraic method can be used to solve equations involving fractions.
The inverse operation method can be used to solve equations involving fractions.

Frequently Asked Questions

Q: What is the quotient of a number and 18? A: The quotient of a number and 18 is 109.2.
Q: How can we solve the equation x / 18 = 109.2? A: We can use the division property of equality, the multiplication property of equality, or the algebraic method to solve the equation.
Q: What is the value of x in the equation x / 18 = 109.2? A: The value of x is 1965.6.

Conclusion

In this article, we have provided answers to some of the most frequently asked questions about the equation x / 18 = 109.2. We have discussed the division property of equality, the multiplication property of equality, and the algebraic method, and how they can be used to solve the equation. We have also provided examples of how to use these methods to solve the equation.