What Is The Value Of The Expression $-37-15-(-27$\]?A. $-79$ B. $-25$ C. $5$ D. $49$

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Understanding the Order of Operations

When evaluating mathematical expressions, it's essential to follow the order of operations, which is a set of rules that dictate the order in which operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

The Expression −37−15−(−27)-37-15-(-27)

In the given expression, we have three numbers being subtracted from each other: −37-37, −15-15, and −27-27. To evaluate this expression, we need to follow the order of operations and perform the subtractions from left to right.

Step 1: Subtract −37-37 from −15-15

When we subtract −37-37 from −15-15, we are essentially adding 3737 to −15-15. This is because subtracting a negative number is equivalent to adding its positive counterpart.

-15 - (-37) = -15 + 37 = 22

Step 2: Subtract −27-27 from 2222

Now, we need to subtract −27-27 from 2222. Again, we are adding 2727 to 2222.

22 - (-27) = 22 + 27 = 49

Conclusion

Based on the order of operations and the rules of subtraction, we can conclude that the value of the expression −37−15−(−27)-37-15-(-27) is 4949.

Answer

The correct answer is D. 4949.

Additional Examples

To reinforce our understanding of the order of operations and subtraction, let's consider a few additional examples.

Example 1: −25−10−(−15)-25-10-(-15)

-25 - 10 - (-15) = -25 - 10 + 15 = -20

Example 2: −30−20−(−10)-30-20-(-10)

-30 - 20 - (-10) = -30 - 20 + 10 = -40

Example 3: −40−30−(−20)-40-30-(-20)

-40 - 30 - (-20) = -40 - 30 + 20 = -50

Conclusion

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which operations should be performed when evaluating mathematical expressions. The acronym PEMDAS is often used to remember the order of operations, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

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

A: When we subtract a negative number, we are essentially adding its positive counterpart. For example, −a−(−b)=−a+b-a - (-b) = -a + b. This is because subtracting a negative number is equivalent to adding its positive counterpart.

Q: How do I evaluate an expression with multiple subtractions?

A: To evaluate an expression with multiple subtractions, we need to follow the order of operations and perform the subtractions from left to right. We can use the distributive property to simplify the expression and make it easier to evaluate.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to distribute a single operation to multiple terms. For example, a(b+c)=ab+aca(b + c) = ab + ac. This property can be used to simplify expressions and make them easier to evaluate.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, we need to identify the terms that are being added or subtracted and distribute the operation to each term. For example, −a−(−b)=−a+b-a - (-b) = -a + b.

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

A: A positive number is a number that is greater than zero, while a negative number is a number that is less than zero. When we add a positive number to a negative number, we need to consider the sign of the result.

Q: How do I evaluate an expression with multiple additions and subtractions?

A: To evaluate an expression with multiple additions and subtractions, we need to follow the order of operations and perform the operations from left to right. We can use the distributive property to simplify the expression and make it easier to evaluate.

Q: What is the final answer to the expression −37−15−(−27)-37-15-(-27)?

A: The final answer to the expression −37−15−(−27)-37-15-(-27) is 4949.

Q: Can you provide more examples of expressions with multiple subtractions?

A: Yes, here are a few more examples:

Example 1: −25−10−(−15)-25-10-(-15)

-25 - 10 - (-15) = -25 - 10 + 15 = -20

Example 2: −30−20−(−10)-30-20-(-10)

-30 - 20 - (-10) = -30 - 20 + 10 = -40

Example 3: −40−30−(−20)-40-30-(-20)

-40 - 30 - (-20) = -40 - 30 + 20 = -50

Conclusion

In conclusion, the order of operations and the rules of subtraction are essential tools for evaluating mathematical expressions. By following these rules, we can ensure that we perform operations in the correct order and obtain accurate results.