Which Equations Could You Use The Division Property Of Equality To Solve? Check All That Apply.1. $2.35y = 4.70$ 2. $\frac{k}{3} = 17$ 3. $4 = 10w$ 4. $55x = 111$ 5. $8 = \frac{a}{5}$

The division property of equality is a fundamental concept in algebra that allows us to isolate a variable in an equation by dividing both sides of the equation by a non-zero constant. This property is essential in solving equations and is widely used in various mathematical applications. In this article, we will explore which equations can be solved using the division property of equality.

Understanding the Division Property of Equality

The division property of equality states that if we have an equation of the form:

a = b

where a and b are algebraic expressions, we can multiply both sides of the equation by a non-zero constant c to get:

ac = bc

Similarly, if we have an equation of the form:

a = b

we can divide both sides of the equation by a non-zero constant c to get:

a/c = b/c

This property is crucial in solving equations, as it allows us to isolate a variable by performing operations on both sides of the equation.

Applying the Division Property of Equality

Now that we have a clear understanding of the division property of equality, let's apply it to the given equations.

Equation 1: $2.35y = 4.70$

To solve this equation using the division property of equality, we can divide both sides of the equation by 2.35.

\frac{2.35y}{2.35} = \frac{4.70}{2.35}

Simplifying the equation, we get:

y = 2

Therefore, the solution to the equation is y = 2.

Equation 2: $\frac{k}{3} = 17$

To solve this equation using the division property of equality, we can multiply both sides of the equation by 3.

\frac{k}{3} \cdot 3 = 17 \cdot 3

Simplifying the equation, we get:

k = 51

Therefore, the solution to the equation is k = 51.

Equation 3: $4 = 10w$

To solve this equation using the division property of equality, we can divide both sides of the equation by 10.

\frac{4}{10} = \frac{10w}{10}

Simplifying the equation, we get:

w = 0.4

Therefore, the solution to the equation is w = 0.4.

Equation 4: $55x = 111$

To solve this equation using the division property of equality, we can divide both sides of the equation by 55.

\frac{55x}{55} = \frac{111}{55}

Simplifying the equation, we get:

x = 2

Therefore, the solution to the equation is x = 2.

Equation 5: $8 = \frac{a}{5}$

To solve this equation using the division property of equality, we can multiply both sides of the equation by 5.

8 \cdot 5 = \frac{a}{5} \cdot 5

Simplifying the equation, we get:

40 = a

Therefore, the solution to the equation is a = 40.

Conclusion

In conclusion, the division property of equality is a powerful tool in solving equations. By applying this property, we can isolate a variable in an equation and find its solution. In this article, we have explored which equations can be solved using the division property of equality and have applied it to five different equations. We have seen that the division property of equality can be used to solve equations with variables on both sides, as well as equations with fractions.

Key Takeaways

• The division property of equality states that if we have an equation of the form a = b, we can multiply both sides of the equation by a non-zero constant c to get ac = bc.
• The division property of equality can be used to solve equations with variables on both sides, as well as equations with fractions.
• To solve an equation using the division property of equality, we can divide both sides of the equation by a non-zero constant.
• The division property of equality is a fundamental concept in algebra and is widely used in various mathematical applications.

Final Thoughts

The division property of equality is a fundamental concept in algebra that allows us to isolate a variable in an equation by dividing both sides of the equation by a non-zero constant. In this article, we will answer some frequently asked questions about the division property of equality.

Q: What is the division property of equality?

A: The division property of equality states that if we have an equation of the form a = b, we can multiply both sides of the equation by a non-zero constant c to get ac = bc. Similarly, if we have an equation of the form a = b, we can divide both sides of the equation by a non-zero constant c to get a/c = b/c.

Q: When can I use the division property of equality?

A: You can use the division property of equality when you have an equation with a variable on both sides, or when you have an equation with fractions. The division property of equality can be used to isolate a variable in an equation.

Q: How do I apply the division property of equality?

A: To apply the division property of equality, you can divide both sides of the equation by a non-zero constant. For example, if you have the equation 2x = 6, you can divide both sides of the equation by 2 to get x = 3.

Q: What if the equation has fractions?

A: If the equation has fractions, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction. For example, if you have the equation 1/2x = 3, you can multiply both sides of the equation by 2 to get x = 6.

Q: Can I use the division property of equality with negative numbers?

A: Yes, you can use the division property of equality with negative numbers. However, you must be careful when dividing by a negative number, as it can change the sign of the result. For example, if you have the equation -2x = 6, you can divide both sides of the equation by -2 to get x = -3.

Q: What if the equation has decimals?

A: If the equation has decimals, you can multiply both sides of the equation by a power of 10 to eliminate the decimals. For example, if you have the equation 0.5x = 3, you can multiply both sides of the equation by 10 to get 5x = 30.

Q: Can I use the division property of equality with variables on both sides?

A: Yes, you can use the division property of equality with variables on both sides. For example, if you have the equation 2x + 3 = 5, you can subtract 3 from both sides of the equation to get 2x = 2, and then divide both sides of the equation by 2 to get x = 1.

Q: What if I get a negative result when using the division property of equality?

A: If you get a negative result when using the division property of equality, it means that the equation has no solution. For example, if you have the equation x = -2, you can divide both sides of the equation by -2 to get 1 = -1, which is a contradiction.

Conclusion

In conclusion, the division property of equality is a powerful tool in solving equations. By understanding when and how to use the division property of equality, you can isolate a variable in an equation and find its solution. We hope that this article has provided a clear understanding of the division property of equality and its applications in solving equations.

Key Takeaways

• The division property of equality states that if we have an equation of the form a = b, we can multiply both sides of the equation by a non-zero constant c to get ac = bc.
• The division property of equality can be used to solve equations with variables on both sides, as well as equations with fractions.
• To apply the division property of equality, you can divide both sides of the equation by a non-zero constant.
• The division property of equality can be used with negative numbers, decimals, and variables on both sides.

Final Thoughts

The division property of equality is a crucial concept in algebra that allows us to isolate a variable in an equation. By understanding when and how to use the division property of equality, you can solve equations with variables on both sides, as well as equations with fractions. We hope that this article has provided a clear understanding of the division property of equality and its applications in solving equations.