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. $8 = \frac{a}{5}$

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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 dividing both sides of the equation by a non-zero constant.

Which Equations Can Be Solved Using the Division Property of Equality?

Now that we have a clear understanding of the division property of equality, let's examine the given equations and determine which ones can be solved using this property.

Equation 1: 2.35y=4.702.35y = 4.70

This equation can be solved using the division property of equality. To isolate the variable y, we can divide both sides of the equation by 2.35.

# Given equation: 2.35y = 4.70
# Divide both sides by 2.35
y = 4.70 / 2.35

By dividing both sides of the equation by 2.35, we can isolate the variable y and find its value.

Equation 2: k3=17\frac{k}{3} = 17

This equation can also be solved using the division property of equality. To isolate the variable k, we can multiply both sides of the equation by 3.

# Given equation: k/3 = 17
# Multiply both sides by 3
k = 17 * 3

However, we can also solve this equation by dividing both sides by 1/3, which is equivalent to multiplying both sides by 3.

Equation 3: 4=10w4 = 10w

This equation cannot be solved using the division property of equality. To isolate the variable w, we would need to divide both sides of the equation by 10, but this would result in a fraction on the right-hand side, which is not allowed in this equation.

Equation 4: 55x=11155x = 111

This equation can be solved using the division property of equality. To isolate the variable x, we can divide both sides of the equation by 55.

# Given equation: 55x = 111
# Divide both sides by 55
x = 111 / 55

By dividing both sides of the equation by 55, we can isolate the variable x and find its value.

Equation 5: 8=a58 = \frac{a}{5}

This equation can be solved using the division property of equality. To isolate the variable a, we can multiply both sides of the equation by 5.

# Given equation: 8 = a/5
# Multiply both sides by 5
a = 8 * 5

However, we can also solve this equation by dividing both sides by 1/5, which is equivalent to multiplying both sides by 5.

Conclusion

In conclusion, the division property of equality is a powerful tool in solving equations. By understanding this property, we can isolate variables in equations and find their values. The equations that can be solved using the division property of equality are:

  • 2.35y=4.702.35y = 4.70
  • k3=17\frac{k}{3} = 17
  • 55x=11155x = 111
  • 8=a58 = \frac{a}{5}

On the other hand, the equation that cannot be solved using the division property of equality is:

  • 4=10w4 = 10w

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

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

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 and a constant, and you want to isolate the variable. The constant must be non-zero, and you must be able to divide both sides of the equation by the constant.

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

A: To apply the division property of equality, follow these steps:

  1. Write down the equation you want to solve.
  2. Identify the variable you want to isolate.
  3. Identify the constant you want to divide by.
  4. Divide both sides of the equation by the constant.
  5. Simplify the equation to find the value of the variable.

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:

  • 2.35y=4.702.35y = 4.70
  • k3=17\frac{k}{3} = 17
  • 55x=11155x = 111
  • 8=a58 = \frac{a}{5}

Q: What are some examples of equations that cannot be solved using the division property of equality?

A: Some examples of equations that cannot be solved using the division property of equality include:

  • 4=10w4 = 10w (because the constant is zero)
  • 0=5x0 = 5x (because the constant is zero)

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

A: Yes, you can use the division property of equality with fractions. For example, if you have the equation:

a2=3\frac{a}{2} = 3

You can divide both sides of the equation by 2 to get:

a=6a = 6

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

A: Yes, you can use the division property of equality with decimals. For example, if you have the equation:

2.5x=52.5x = 5

You can divide both sides of the equation by 2.5 to get:

x=2x = 2

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 by zero
  • Not simplifying the equation after dividing
  • Not checking if the constant is non-zero before dividing

Conclusion

In conclusion, the division property of equality is a powerful tool in solving equations. By understanding this property, we can isolate variables in equations and find their values. Remember to follow the steps outlined above and avoid common mistakes when using the division property of equality.