Translate The Phrase; Then Simplify.Find The Sum Of { -47$}$, { -11$}$, And ${ 40\$} .The Phrase Translates To The Expression { \square$}$. (Do Not Simplify.)The Sum Is { \square$}$. (Simplify Your Answer.)
Understanding the Problem
When we are given a phrase that translates to an expression, we need to find the sum of the numbers involved. In this case, the phrase is "Find the sum of {-47$}$, {-11$}$, and ${40\$}." The first step is to translate the phrase into an expression, which is {\square$}$. This means we need to add the three numbers together.
Translating the Phrase into an Expression
To translate the phrase into an expression, we need to replace the words with mathematical symbols. The phrase "Find the sum of" can be translated to the addition symbol (+). The numbers {-47$}$, {-11$}$, and ${40\$} can be represented as -47, -11, and 40, respectively.
Writing the Expression
Now that we have translated the phrase into an expression, we can write it as:
-47 + (-11) + 40
Evaluating the Expression
To evaluate the expression, we need to follow the order of operations (PEMDAS):
- Parentheses: None
- Exponents: None
- Multiplication and Division: None
- Addition and Subtraction: Perform from left to right
Adding the Numbers
Now that we have evaluated the expression, we can add the numbers together:
-47 + (-11) = -58 -58 + 40 = -18
Simplifying the Answer
The final answer is -18. However, we are asked to simplify our answer. In this case, the answer is already simplified, as it is a single number.
Conclusion
In conclusion, we have successfully translated the phrase "Find the sum of {-47$}$, {-11$}$, and ${40\$}" into an expression, evaluated the expression, and simplified the answer. The final answer is -18.
Key Takeaways
- Translating a phrase into an expression involves replacing words with mathematical symbols.
- Evaluating an expression involves following the order of operations (PEMDAS).
- Simplifying an answer involves expressing it in its simplest form.
Real-World Applications
This problem has real-world applications in finance, accounting, and science. For example, in finance, you may need to calculate the total cost of a project by adding the costs of different components. In accounting, you may need to calculate the total revenue of a company by adding the revenues from different sources. In science, you may need to calculate the total distance traveled by an object by adding the distances traveled in different segments.
Common Mistakes
- Failing to translate the phrase into an expression correctly.
- Failing to evaluate the expression correctly.
- Failing to simplify the answer correctly.
Tips and Tricks
- Make sure to translate the phrase into an expression correctly.
- Make sure to evaluate the expression correctly.
- Make sure to simplify the answer correctly.
Practice Problems
- Find the sum of ${23\$}, ${17\$}, and {-12$}$.
- Find the sum of {-25$}$, {-30$}$, and ${15\$}.
- Find the sum of ${40\$}, {-20$}$, and {-10$}$.
Conclusion
In conclusion, we have learned how to translate a phrase into an expression, evaluate the expression, and simplify the answer. We have also discussed real-world applications, common mistakes, and tips and tricks. Finally, we have provided practice problems for you to try.
Q: What is the first step in solving the problem "Find the sum of {-47$}$, {-11$}$, and ${40\$}?"
A: The first step is to translate the phrase into an expression. This involves replacing the words with mathematical symbols. In this case, the phrase "Find the sum of" can be translated to the addition symbol (+), and the numbers {-47$}$, {-11$}$, and ${40\$} can be represented as -47, -11, and 40, respectively.
Q: How do I evaluate the expression -47 + (-11) + 40?
A: To evaluate the expression, you need to follow the order of operations (PEMDAS):
- Parentheses: None
- Exponents: None
- Multiplication and Division: None
- Addition and Subtraction: Perform from left to right
In this case, you need to add the numbers together:
-47 + (-11) = -58 -58 + 40 = -18
Q: What is the final answer to the problem "Find the sum of {-47$}$, {-11$}$, and ${40\$}?"
A: The final answer is -18.
Q: Can I simplify the answer further?
A: In this case, the answer is already simplified, as it is a single number. However, if the answer were a fraction or a decimal, you may need to simplify it further.
Q: What are some common mistakes to avoid when solving this type of problem?
A: Some common mistakes to avoid include:
- Failing to translate the phrase into an expression correctly
- Failing to evaluate the expression correctly
- Failing to simplify the answer correctly
Q: What are some real-world applications of this type of problem?
A: This type of problem has real-world applications in finance, accounting, and science. For example, in finance, you may need to calculate the total cost of a project by adding the costs of different components. In accounting, you may need to calculate the total revenue of a company by adding the revenues from different sources. In science, you may need to calculate the total distance traveled by an object by adding the distances traveled in different segments.
Q: How can I practice solving this type of problem?
A: You can practice solving this type of problem by trying the following exercises:
- Find the sum of ${23\$}, ${17\$}, and {-12$}$.
- Find the sum of {-25$}$, {-30$}$, and ${15\$}.
- Find the sum of ${40\$}, {-20$}$, and {-10$}$.
Q: What are some tips and tricks for solving this type of problem?
A: Some tips and tricks for solving this type of problem include:
- Make sure to translate the phrase into an expression correctly
- Make sure to evaluate the expression correctly
- Make sure to simplify the answer correctly
Q: Can I use a calculator to solve this type of problem?
A: Yes, you can use a calculator to this type of problem. However, it's always a good idea to check your work by hand to make sure you're getting the correct answer.
Q: How can I check my work to make sure I'm getting the correct answer?
A: You can check your work by plugging the numbers into a calculator and making sure the answer matches the one you got by hand. You can also use a calculator to check your work by evaluating the expression step by step.
Q: What if I get a different answer than the one in the book or online?
A: If you get a different answer than the one in the book or online, it's possible that the answer in the book or online is incorrect. You can try checking your work again or asking a teacher or tutor for help.