Which Property Should Remus Use To Solve The Equation Below?$7q = 49$A. Division Property Of Equality B. Addition Property Of Equality C. Subtraction Property Of Equality D. Identity Property Of Equality

Introduction

Remus is a math enthusiast who is trying to solve the equation $7q = 49$. He has several properties of equality at his disposal, but he is not sure which one to use. In this article, we will explore the different properties of equality and determine which one is the most suitable for solving the equation.

Understanding the Properties of Equality

Before we dive into the solution, let's briefly review the properties of equality. There are four main properties of equality:

• Addition Property of Equality: If $a = b$, then $a + c = b + c$.
• Subtraction Property of Equality: If $a = b$, then $a - c = b - c$.
• Multiplication Property of Equality: If $a = b$, then $ac = bc$.
• Division Property of Equality: If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.
• Identity Property of Equality: For any number $a$, $a + 0 = a$ and $a \cdot 1 = a$.

Analyzing the Equation

Now that we have reviewed the properties of equality, let's analyze the equation $7q = 49$. We can see that the equation is a linear equation, where the variable $q$ is multiplied by the constant $7$. Our goal is to isolate the variable $q$ and find its value.

Choosing the Right Property

To solve the equation, we need to isolate the variable $q$. We can do this by dividing both sides of the equation by $7$. This will give us the value of $q$.

The correct property to use in this case is the Division Property of Equality. This property states that if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. In our case, we have $7q = 49$ and $7 \neq 0$, so we can divide both sides of the equation by $7$.

Solving the Equation

Now that we have chosen the correct property, let's solve the equation.

$$7q = 49$$

We can divide both sides of the equation by $7$ to get:

$$q = \frac{49}{7}$$

Simplifying the right-hand side of the equation, we get:

$$q = 7$$

Therefore, the value of $q$ is $7$.

Conclusion

In conclusion, Remus should use the Division Property of Equality to solve the equation $7q = 49$. This property allows us to isolate the variable $q$ by dividing both sides of the equation by $7$. By using this property, we can find the value of $q$ and solve the equation.

Key Takeaways

• The Division Property of Equality states that if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.
• To solve the equation $7q = 49$, we need to isolate the variable $q$ by dividing both sides of the equation by $7$.
• The correct property to use in this case is the Division Property of Equality.

Final Answer

Q: What is the Division Property of Equality?

A: The Division Property of Equality states that if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. This property allows us to isolate the variable in an equation by dividing both sides of the equation by a non-zero constant.

Q: Why is the Division Property of Equality important in solving equations?

A: The Division Property of Equality is important in solving equations because it allows us to isolate the variable and find its value. By dividing both sides of the equation by a non-zero constant, we can eliminate the constant and find the value of the variable.

Q: Can I use the Division Property of Equality to solve any equation?

A: No, you cannot use the Division Property of Equality to solve any equation. The Division Property of Equality only applies when the equation is in the form $a = b$ and $c \neq 0$. If the equation is not in this form, you may need to use a different property of equality or a different method to solve the equation.

Q: What are some examples of equations that can be solved using the Division Property of Equality?

A: Some examples of equations that can be solved using the Division Property of Equality include:

• $7q = 49$
• $4x = 32$
• $9y = 81$

Q: How do I apply the Division Property of Equality to solve an equation?

A: To apply the Division Property of Equality to solve an equation, follow these steps:

1. Check if the equation is in the form $a = b$ and $c \neq 0$.
2. If the equation is in this form, divide both sides of the equation by $c$.
3. Simplify the right-hand side of the equation to find the value of the variable.

Q: What are some common mistakes to avoid when using the Division Property of Equality?

A: Some common mistakes to avoid when using the Division Property of Equality include:

• Dividing both sides of the equation by a zero constant.
• Not checking if the equation is in the form $a = b$ and $c \neq 0$ before applying the Division Property of Equality.
• Not simplifying the right-hand side of the equation after dividing both sides by $c$.

Q: Can I use the Division Property of Equality to solve equations with fractions?

A: Yes, you can use the Division Property of Equality to solve equations with fractions. However, you need to be careful when dividing fractions to avoid making mistakes.

Q: How do I divide fractions using the Division Property of Equality?

A: To divide fractions using the Division Property of Equality, follow these steps:

1. Check if the equation is in the form $a = b$ and $c \neq 0$.
2. If the equation is in this form, invert the fraction on the right-hand side of the equation and multiply both sides of the equation by the inverted fraction.
3. Simplify the right-hand side of the equation to find the value of the variable.

Conclusion

In conclusion, the Division Property of Equality is an important property of equality that allows us to isolate the variable in an equation by dividing both sides of the equation by a non-zero constant. By understanding how to apply the Division Property of Equality, we can solve a wide range of equations and find the value of the variable.