Evaluate within parentheses

Oct 13, 2025 by thesweetdesigns.com 114 views

Introduction

The order of operations is a set of rules that helps us to simplify complex mathematical expressions by following a specific order. It is a crucial concept in mathematics that helps us to avoid confusion and ensure that we are performing calculations correctly. In this article, we will simplify a numerical expression using the order of operations.

The Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

Evaluate within parentheses: This means that we need to evaluate any expressions that are inside parentheses first.
Evaluate exponents: This means that we need to evaluate any exponents (such as squaring or cubing) next.
Multiply and divide from left to right: This means that we need to perform any multiplication and division operations from left to right.
Add and subtract from left to right: This means that we need to perform any addition and subtraction operations from left to right.

Simplifying the Numerical Expression

Now that we have reviewed the order of operations, let's simplify the numerical expression:

$5.75-\frac{1}{2}(20+2.5)+2+6$

Step 1: Evaluate within Parentheses

The first step is to evaluate the expression inside the parentheses:

$20+2.5 = 22.5$

So, the expression becomes:

$5.75-\frac{1}{2}(22.5)+2+6$

Step 2: Evaluate Exponents

There are no exponents in this expression, so we can move on to the next step.

Step 3: Multiply and Divide from Left to Right

The next step is to perform any multiplication and division operations from left to right. In this expression, we have a fraction that needs to be multiplied by a number:

$\frac{1}{2}(22.5) = 11.25$

So, the expression becomes:

$5.75-11.25+2+6$

Step 4: Add and Subtract from Left to Right

The final step is to perform any addition and subtraction operations from left to right. In this expression, we have a subtraction operation that needs to be performed first:

$5.75-11.25 = -5.5$

Then, we have an addition operation that needs to be performed next:

$-5.5+2 = -3.5$

Finally, we have another addition operation that needs to be performed:

$-3.5+6 = 2.5$

Conclusion

In this article, we simplified a numerical expression using the order of operations. We reviewed the order of operations and then applied it to the expression step by step. We evaluated expressions within parentheses, evaluated exponents, performed multiplication and division operations from left to right, and finally performed addition and subtraction operations from left to right. The final answer is $2.5$ .

Common Mistakes to Avoid

When simplifying numerical expressions using the order of operations, there are several common mistakes to avoid:

Not evaluating expressions within parentheses first: This can lead to incorrect answers.
Not performing multiplication and division operations from left to right: This can lead to incorrect answers.
Not performing addition and subtraction operations from left to right: This can lead to incorrect answers.

Practice Problems

To practice simplifying numerical expressions using the order of operations, try the following problems:

$3(2+1)-4+2$
$5-\frac{1}{3}(9+2)+3$
$2(4-1)+6-3$

Conclusion

Introduction

The order of operations is a set of rules that helps us to simplify complex mathematical expressions by following a specific order. In our previous article, we reviewed the order of operations and applied it to a numerical expression step by step. In this article, we will answer some frequently asked questions about the order of operations.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

Evaluate within parentheses
Evaluate exponents
Multiply and divide from left to right
Add and subtract from left to right

Q: Why is the order of operations important?

A: The order of operations is important because it helps us to avoid confusion and ensure that we are performing calculations correctly. Without the order of operations, we might perform operations in the wrong order, leading to incorrect answers.

Q: What happens if I forget to evaluate expressions within parentheses first?

A: If you forget to evaluate expressions within parentheses first, you might perform operations in the wrong order, leading to incorrect answers. For example, consider the expression:

$3(2+1)-4+2$

If you forget to evaluate the expression within the parentheses first, you might perform the multiplication and subtraction operations in the wrong order, leading to an incorrect answer.

Q: What happens if I forget to perform multiplication and division operations from left to right?

A: If you forget to perform multiplication and division operations from left to right, you might perform operations in the wrong order, leading to incorrect answers. For example, consider the expression:

$5-\frac{1}{3}(9+2)+3$

If you forget to perform the multiplication and division operations from left to right, you might perform the addition and subtraction operations in the wrong order, leading to an incorrect answer.

Q: Can I use the order of operations to simplify expressions with fractions?

A: Yes, you can use the order of operations to simplify expressions with fractions. When simplifying expressions with fractions, you need to follow the order of operations and perform the operations in the correct order.

Q: Can I use the order of operations to simplify expressions with decimals?

A: Yes, you can use the order of operations to simplify expressions with decimals. When simplifying expressions with decimals, you need to follow the order of operations and perform the operations in the correct order.

Q: What are some common mistakes to avoid when using the order of operations?

A: Some common mistakes to avoid when using the order of operations include:

Not evaluating expressions within parentheses first
Not performing multiplication and division operations from left to right
Not performing addition and subtraction operations from left to right
Not following the order of operations when simplifying expressions with fractions or decimals

Q: How can I practice using the order of operations?

A: You can practice using the order of operations by working on problems that involve multiple operations. Try simplifying expressions with parentheses, exponents, multiplication and division, and addition and subtraction. You can also try working on problems that involve fractions and decimals.

Conclusion

In conclusion, the order of operations is a crucial concept in mathematics that helps us to simplify complex numerical expressions. By following the order of operations, we can ensure that we are performing calculations correctly and avoid common mistakes. In this article, we answered some frequently asked questions about the order of operations and provided tips for practicing using this concept.

Practice Problems

To practice using the order of operations, try the following problems:

$3(2+1)-4+2$
$5-\frac{1}{3}(9+2)+3$
$2(4-1)+6-3$
$\frac{1}{2}(10+5)-3+2$
$4(3-2)+5-1$

Answer Key

$3(2+1)-4+2 = 3(3)-4+2 = 9-4+2 = 7$
$5-\frac{1}{3}(9+2)+3 = 5-\frac{1}{3}(11)+3 = 5-3.67+3 = 4.33$
$2(4-1)+6-3 = 2(3)+6-3 = 6+6-3 = 9$
$\frac{1}{2}(10+5)-3+2 = \frac{1}{2}(15)-3+2 = 7.5-3+2 = 6.5$
$4(3-2)+5-1 = 4(1)+5-1 = 4+5-1 = 8$