Evaluate Each Expression:a. \[$-1 \cdot 2 \cdot 3 =\$\] B. \[$-1 \cdot (-2) \cdot 3 =\$\] C. \[$-1 \cdot (-2) \cdot (-3) =\$\]

Feb 26, 2025 by ADMIN 131 views

**Evaluating Expressions with Negative Numbers**

Introduction

In mathematics, understanding how to evaluate expressions with negative numbers is crucial for solving various mathematical problems. Negative numbers can be challenging to work with, especially when it comes to multiplication and division. In this article, we will evaluate three expressions that involve negative numbers and explore the rules of multiplication with negative numbers.

Expression a: $-1 \cdot 2 \cdot 3$

To evaluate this expression, we need to follow the order of operations (PEMDAS):

Multiply $-1$ and $2$ : $-1 \cdot 2 = -2$
Multiply $-2$ and $3$ : $-2 \cdot 3 = -6$

Therefore, the value of the expression $-1 \cdot 2 \cdot 3$ is $-6$ .

Expression b: $-1 \cdot (-2) \cdot 3$

When we have two or more negative numbers multiplied together, we need to remember that a negative number multiplied by another negative number results in a positive number. Therefore, we can rewrite the expression as:

$-1 \cdot (-2) \cdot 3 = 1 \cdot 2 \cdot 3$

Now, we can evaluate the expression:

Multiply $1$ and $2$ : $1 \cdot 2 = 2$
Multiply $2$ and $3$ : $2 \cdot 3 = 6$

Therefore, the value of the expression $-1 \cdot (-2) \cdot 3$ is $6$ .

Expression c: $-1 \cdot (-2) \cdot (-3)$

As mentioned earlier, a negative number multiplied by another negative number results in a positive number. Therefore, we can rewrite the expression as:

$-1 \cdot (-2) \cdot (-3) = 1 \cdot 2 \cdot 3$

Now, we can evaluate the expression:

Multiply $1$ and $2$ : $1 \cdot 2 = 2$
Multiply $2$ and $3$ : $2 \cdot 3 = 6$

Therefore, the value of the expression $-1 \cdot (-2) \cdot (-3)$ is $6$ .

Rules of Multiplication with Negative Numbers

When multiplying two or more negative numbers, we need to remember the following rules:

A negative number multiplied by another negative number results in a positive number.
A negative number multiplied by a positive number results in a negative number.
A positive number multiplied by another positive number results in a positive number.

Example Problems

Here are some example problems that involve multiplying negative numbers:

$-2 \cdot (-3) = ?$
$-4 \cdot 2 = ?$
$-5 \cdot (-6) = ?$

To solve these problems, we need to apply the rules of multiplication with negative numbers:

$-2 \cdot (-3) = 6$
$-4 \cdot 2 = -8$
$-5 \cdot (-6) = 30$

Conclusion

Evaluating expressions with negative numbers requires a good understanding of the rules of multiplication with negative numbers. By following the order of operations and applying the rules of multiplication with negative numbers, we can solve various mathematical problems involving negative numbers. In this article, we evaluated three expressions that involved negative numbers and explored the rules of multiplication with negative numbers. We also provided example problems to help readers practice their skills.

Frequently Asked Questions

Here are some frequently asked questions about evaluating expressions with negative numbers:

Q: What is the rule for multiplying two negative numbers? A: A negative number multiplied by another negative number results in a positive number.
Q: What is the rule for multiplying a negative number and a positive number? A: A negative number multiplied by a positive number results in a negative number.
Q: What is the rule for multiplying two positive numbers? A: A positive number multiplied by another positive number results in a positive number.

References

Here are some references that provide more information about evaluating expressions with negative numbers:

Introduction

In our previous article, we evaluated three expressions that involved negative numbers and explored the rules of multiplication with negative numbers. In this article, we will answer some frequently asked questions about evaluating expressions with negative numbers.

Q: What is the rule for multiplying two negative numbers?

A: A negative number multiplied by another negative number results in a positive number.

Q: What is the rule for multiplying a negative number and a positive number?

A: A negative number multiplied by a positive number results in a negative number.

Q: What is the rule for multiplying two positive numbers?

A: A positive number multiplied by another positive number results in a positive number.

Q: How do I evaluate an expression with multiple negative numbers?

A: To evaluate an expression with multiple negative numbers, you need to follow the order of operations (PEMDAS) and apply the rules of multiplication with negative numbers. For example, if you have the expression $-2 \cdot (-3) \cdot 4$ , you would first multiply $-2$ and $-3$ to get $6$ , and then multiply $6$ by $4$ to get $24$ .

Q: What is the difference between a negative number and a positive number?

A: A negative number is a number that is less than zero, while a positive number is a number that is greater than zero. For example, $-5$ is a negative number, while $5$ is a positive number.

Q: Can I simplify an expression with negative numbers?

A: Yes, you can simplify an expression with negative numbers by applying the rules of multiplication with negative numbers. For example, if you have the expression $-2 \cdot (-3)$ , you can simplify it to $6$ by applying the rule that a negative number multiplied by another negative number results in a positive number.

Q: How do I evaluate an expression with a negative number and a fraction?

A: To evaluate an expression with a negative number and a fraction, you need to follow the order of operations (PEMDAS) and apply the rules of multiplication with negative numbers. For example, if you have the expression $-2 \cdot \frac{1}{3}$ , you would first multiply $-2$ by $1$ to get $-2$ , and then divide $-2$ by $3$ to get $-\frac{2}{3}$ .

Q: Can I use a calculator to evaluate an expression with negative numbers?

A: Yes, you can use a calculator to evaluate an expression with negative numbers. However, it's always a good idea to check your work by hand to make sure you understand the rules of multiplication with negative numbers.

Q: How do I write a negative number in exponential form?

A: To write a negative number in exponential form, you need to use the negative sign in front of the base number. For example, $-2^3$ is equal to $-8$ .

Q: Can I use a negative number as an exponent?

A: Yes, you can use a negative number as an exponent. For example, $2^{-3}$ is equal to $\frac{1}{2^3}$ , which is equal to $\frac{1}{8}$ .

Conclusion

Evaluating expressions with negative numbers requires a good understanding of the rules of multiplication with negative numbers. By following the order of operations (PEMDAS) and applying the rules of multiplication with negative numbers, you can solve various mathematical problems involving negative numbers. In this article, we answered some frequently asked questions about evaluating expressions with negative numbers and provided examples to help readers practice their skills.

Frequently Asked Questions

Here are some frequently asked questions about evaluating expressions with negative numbers:

Q: What is the rule for multiplying two negative numbers? A: A negative number multiplied by another negative number results in a positive number.
Q: What is the rule for multiplying a negative number and a positive number? A: A negative number multiplied by a positive number results in a negative number.
Q: What is the rule for multiplying two positive numbers? A: A positive number multiplied by another positive number results in a positive number.
Q: How do I evaluate an expression with multiple negative numbers? A: To evaluate an expression with multiple negative numbers, you need to follow the order of operations (PEMDAS) and apply the rules of multiplication with negative numbers.

References

Here are some references that provide more information about evaluating expressions with negative numbers:

Introduction

Expression a: −1⋅2⋅3-1 \cdot 2 \cdot 3−1⋅2⋅3

Expression b: −1⋅(−2)⋅3-1 \cdot (-2) \cdot 3−1⋅(−2)⋅3

Expression c: −1⋅(−2)⋅(−3)-1 \cdot (-2) \cdot (-3)−1⋅(−2)⋅(−3)

Rules of Multiplication with Negative Numbers

Example Problems

Conclusion

Frequently Asked Questions

References

Introduction

Q: What is the rule for multiplying two negative numbers?

Q: What is the rule for multiplying a negative number and a positive number?

Q: What is the rule for multiplying two positive numbers?

Q: How do I evaluate an expression with multiple negative numbers?

Q: What is the difference between a negative number and a positive number?

Q: Can I simplify an expression with negative numbers?

Q: How do I evaluate an expression with a negative number and a fraction?

Q: Can I use a calculator to evaluate an expression with negative numbers?

Q: How do I write a negative number in exponential form?

Q: Can I use a negative number as an exponent?

Conclusion

Frequently Asked Questions

References

Expression a: $-1 \cdot 2 \cdot 3$

Expression b: $-1 \cdot (-2) \cdot 3$

Expression c: $-1 \cdot (-2) \cdot (-3)$