Understanding the Three Steps to Solve an Expression

Oct 13, 2025 by talynt.org 22 views

Understanding the Three Steps to Solve an Expression

In mathematics, solving expressions is a crucial skill that requires a step-by-step approach. The three steps outlined below are used to find the value of a given expression. In this practice quiz, we will focus on understanding these steps and applying them to solve a specific expression.

Step 1: Simplifying the Expression Inside the Parentheses

The first step in solving the expression $$[(-10+2)-1]+(2+3)$$ is to simplify the expression inside the parentheses. This involves performing the operations inside the parentheses first, which in this case is the subtraction of 10 and 2, followed by the subtraction of 1.

Simplifying the Expression Inside the Parentheses

To simplify the expression inside the parentheses, we need to follow the order of operations (PEMDAS):

Subtract 10 and 2: $$-10+2=-8$$
Subtract 1 from the result: $$-8-1=-9$$

Therefore, the simplified expression inside the parentheses is $$-9$$.

Step 2: Adding the Result to the Expression Outside the Parentheses

The second step is to add the result from the first step to the expression outside the parentheses. In this case, we need to add $$-9$$ to $$2+3$$.

Adding the Result to the Expression Outside the Parentheses

To add the result to the expression outside the parentheses, we need to follow the order of operations (PEMDAS):

Add 2 and 3: $$2+3=5$$
Add $$-9$$ to the result: $$-9+5=-4$$

Therefore, the result of the second step is $$-4$$.

Step 3: Simplifying the Final Expression

The third step is to simplify the final expression by performing any remaining operations. In this case, we need to add $$-7$$ and $$3$$.

Simplifying the Final Expression

To simplify the final expression, we need to follow the order of operations (PEMDAS):

Add $$-7$$ and $$3$$: $$-7+3=-4$$

Therefore, the final result of the expression is $$-4$$.

Conclusion

In conclusion, the three steps outlined above are used to find the value of a given expression. By following these steps, we can simplify the expression inside the parentheses, add the result to the expression outside the parentheses, and finally simplify the final expression to get the final result.

Practice Problems

To practice solving expressions using the three steps outlined above, try the following problems:

Solve the expression $$[(-5+3)-2]+(4+1)$$ using the three steps.
Solve the expression $$[(-8+4)-3]+(2+5)$$ using the three steps.
Solve the expression $$[(-2+1)-4]+(3+6)$$ using the three steps.

Answer Key

$-2+9=7$
$-7+7=0$
$-5+9=4$

Tips and Tricks

When solving expressions using the three steps outlined above, remember to:

Simplify the expression inside the parentheses first
Add the result to the expression outside the parentheses
Simplify the final expression to get the final result
Follow the order of operations (PEMDAS) to ensure accuracy

Q&A: Frequently Asked Questions

In this section, we will address some of the most frequently asked questions related to solving expressions using the three steps outlined above.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first
Exponents: Evaluate any exponential expressions next
Multiplication and Division: Evaluate any multiplication and division operations from left to right
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right

Q: Why is it important to simplify the expression inside the parentheses first?

A: Simplifying the expression inside the parentheses first is important because it allows you to evaluate the expression correctly. If you don't simplify the expression inside the parentheses first, you may end up with an incorrect result.

Q: What if I have multiple sets of parentheses in an expression?

A: If you have multiple sets of parentheses in an expression, you should simplify the innermost set of parentheses first, then work your way outwards.

Q: Can I use a calculator to solve expressions?

A: Yes, you can use a calculator to solve expressions. However, it's always a good idea to double-check your work by following the three steps outlined above.

Q: What if I get a different result when using a calculator versus following the three steps?

A: If you get a different result when using a calculator versus following the three steps, it's likely because you made a mistake in one of the steps. Go back and recheck your work to ensure that you followed the correct order of operations.

Q: Can I use the three steps to solve inequalities?

A: Yes, you can use the three steps to solve inequalities. However, you should be aware that inequalities have different rules and properties than equations.

Q: What if I'm unsure about how to solve an expression?

A: If you're unsure about how to solve an expression, try breaking it down into smaller parts and solving each part separately. You can also ask a teacher or tutor for help.