Select The Postulate That Is Illustrated For The Real Numbers.${2(x+3)=2x+6}$A. The Distributive Postulate B. Multiplication Identity C. The Commutative Postulate For Multiplication D. The Addition Inverse Postulate E. The Addition Of

Introduction

In mathematics, the distributive postulate is a fundamental property that allows us to expand expressions involving multiplication and addition. It is a crucial concept in algebra and is used extensively in various mathematical operations. In this article, we will explore the distributive postulate and its application to real numbers.

What is the Distributive Postulate?

The distributive postulate states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$$a(b + c) = ab + ac$$

This postulate allows us to distribute the multiplication operation over the addition operation. In other words, it enables us to expand expressions involving multiplication and addition.

Example: Distributive Postulate Illustrated

Let's consider the given equation:

$$2(x+3)=2x+6$$

To determine which postulate is illustrated, we need to examine the equation and identify the properties being used.

Step 1: Expand the Left-Hand Side

Using the distributive postulate, we can expand the left-hand side of the equation:

$$2(x+3) = 2x + 6$$

This expansion is a direct application of the distributive postulate.

Step 2: Compare with the Right-Hand Side

Now, let's compare the expanded left-hand side with the right-hand side of the equation:

$$2x + 6 = 2x + 6$$

As we can see, the two sides of the equation are identical.

Conclusion

Based on the above analysis, we can conclude that the given equation illustrates the distributive postulate. The distributive postulate allows us to expand expressions involving multiplication and addition, and it is a fundamental property of real numbers.

Comparison with Other Postulates

Let's compare the distributive postulate with other postulates to determine which one is illustrated:

• Multiplication Identity: The multiplication identity states that for any real number $a$, $a \cdot 1 = a$. This postulate is not illustrated in the given equation.
• Commutative Postulate for Multiplication: The commutative postulate for multiplication states that for any real numbers $a$ and $b$, $ab = ba$. This postulate is not illustrated in the given equation.
• Addition Inverse Postulate: The addition inverse postulate states that for any real number $a$, $a + (-a) = 0$. This postulate is not illustrated in the given equation.
• Addition of Zero: The addition of zero states that for any real number $a$, $a + 0 = a$. This postulate is not illustrated in the given equation.

Conclusion

In conclusion, the given equation illustrates the distributive postulate. The distributive postulate is a fundamental property of real numbers that allows us to expand expressions involving multiplication and addition.

Real-World Applications

The distributive postulate has numerous real-world applications in various fields, including:

• Algebra: The distributive postulate is used extensively in algebra to expand expressions involving multiplication and addition.
• Geometry: The distributive postulate is used in geometry to calculate the area and perimeter of shapes.
• Physics: The distributive postulate is used in physics to calculate the force and energy of objects.

Conclusion

In conclusion, the distributive postulate is a fundamental property of real numbers that allows us to expand expressions involving multiplication and addition. It has numerous real-world applications in various fields, including algebra, geometry, and physics.

Final Thoughts

In this article, we explored the distributive postulate and its application to real numbers. We examined the given equation and identified the properties being used. We also compared the distributive postulate with other postulates to determine which one is illustrated. The distributive postulate is a crucial concept in mathematics, and it has numerous real-world applications in various fields.

References

• [1] "Algebra" by Michael Artin
• [2] "Geometry" by Michael Spivak
• [3] "Physics" by Halliday, Resnick, and Walker

Glossary

• Distributive Postulate: A fundamental property of real numbers that allows us to expand expressions involving multiplication and addition.
• Multiplication Identity: A postulate that states that for any real number $a$, $a \cdot 1 = a$.
• Commutative Postulate for Multiplication: A postulate that states that for any real numbers $a$ and $b$, $ab = ba$.
• Addition Inverse Postulate: A postulate that states that for any real number $a$, $a + (-a) = 0$.
• Addition of Zero: A postulate that states that for any real number $a$, $a + 0 = a$.
  Distributive Postulate Q&A =============================

Frequently Asked Questions

Q: What is the distributive postulate?

A: The distributive postulate is a fundamental property of real numbers that allows us to expand expressions involving multiplication and addition.

Q: How is the distributive postulate used in algebra?

A: The distributive postulate is used extensively in algebra to expand expressions involving multiplication and addition. It is a crucial concept in algebra and is used to simplify complex expressions.

Q: What is the difference between the distributive postulate and the multiplication identity?

A: The multiplication identity states that for any real number $a$, $a \cdot 1 = a$. The distributive postulate, on the other hand, states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Q: Can the distributive postulate be used to simplify expressions involving fractions?

A: Yes, the distributive postulate can be used to simplify expressions involving fractions. For example, if we have the expression $\frac{2}{3}(x + 4)$, we can use the distributive postulate to expand it as $\frac{2}{3}x + \frac{8}{3}$.

Q: How is the distributive postulate used in geometry?

A: The distributive postulate is used in geometry to calculate the area and perimeter of shapes. For example, if we have a rectangle with a length of $x$ and a width of $y$, we can use the distributive postulate to calculate its area as $xy$.

Q: Can the distributive postulate be used to solve equations involving exponents?

A: Yes, the distributive postulate can be used to solve equations involving exponents. For example, if we have the equation $2^x + 2^y = 2^{x+y}$, we can use the distributive postulate to simplify it as $2^x(1 + 2^{y-x}) = 2^{x+y}$.

Q: What are some common mistakes to avoid when using the distributive postulate?

A: Some common mistakes to avoid when using the distributive postulate include:

• Forgetting to distribute the multiplication operation over the addition operation.
• Not using the distributive postulate correctly when expanding expressions involving fractions.
• Not simplifying expressions correctly using the distributive postulate.

Q: How can I practice using the distributive postulate?

A: You can practice using the distributive postulate by working through algebraic expressions and simplifying them using the distributive postulate. You can also try solving equations involving exponents and using the distributive postulate to simplify them.

Q: What are some real-world applications of the distributive postulate?

A: The distributive postulate has numerous real-world applications in various fields, including:

• Algebra: The distributive postulate is used extensively in algebra to simplify complex expressions.
• Geometry: The distributive postulate is used in geometry to calculate the area and perimeter of shapes.
• Physics: The distributive postulate is used in physics to calculate the force and energy of objects.

Conclusion

In conclusion, the distributive postulate is a fundamental property of real numbers that allows us to expand expressions involving multiplication and addition. It has numerous real-world applications in various fields, including algebra, geometry, and physics. By understanding and using the distributive postulate correctly, you can simplify complex expressions and solve equations involving exponents.

References

• [1] "Algebra" by Michael Artin
• [2] "Geometry" by Michael Spivak
• [3] "Physics" by Halliday, Resnick, and Walker

Glossary

• Distributive Postulate: A fundamental property of real numbers that allows us to expand expressions involving multiplication and addition.
• Multiplication Identity: A postulate that states that for any real number $a$, $a \cdot 1 = a$.
• Commutative Postulate for Multiplication: A postulate that states that for any real numbers $a$ and $b$, $ab = ba$.
• Addition Inverse Postulate: A postulate that states that for any real number $a$, $a + (-a) = 0$.
• Addition of Zero: A postulate that states that for any real number $a$, $a + 0 = a$.