Problem 15
Question
Simplify the given expression. $$ 5+(6+4)-11 $$
Step-by-Step Solution
Verified Answer
The simplified expression is 4.
1Step 1: Identify the Expression
The expression given is: \(5 + (6 + 4) - 11\). We need to simplify this.
2Step 2: Simplify the Parentheses
First, address the operation inside the parentheses. Calculate \(6 + 4\), which equals 10. Now our expression is \(5 + 10 - 11\).
3Step 3: Addition
Add 5 and 10 together. So, \(5 + 10 = 15\). The expression now becomes \(15 - 11\).
4Step 4: Subtract
Finally, subtract 11 from 15. Calculate \(15 - 11\) to get 4.
Key Concepts
Order of OperationsArithmetic OperationsExpression Simplification
Order of Operations
When faced with any mathematical expression, knowing the order of operations is crucial. The commonly used acronym PEMDAS helps us remember this order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In our given exercise, we must first look for and simplify the contents within any parentheses.
In the context of our exercise, we first simplify inside the parentheses, which is \(6 + 4\). By following PEMDAS, we ensure expressions are consistently and correctly simplified.
- Parentheses: Calculate the expression inside the parentheses first.
- Exponents: Solve any exponents next if present.
- Multiplication/Division: Perform all multiplication and division operations as they appear from left to right.
- Addition/Subtraction: Execute all addition and subtraction from left to right.
In the context of our exercise, we first simplify inside the parentheses, which is \(6 + 4\). By following PEMDAS, we ensure expressions are consistently and correctly simplified.
Arithmetic Operations
Arithmetic operations include the basic mathematical processes of addition, subtraction, multiplication, and division. In our problem, we mainly deal with addition and subtraction, the simplest yet fundamental operations.
Understanding and accurately performing these operations is a key step in math problem-solving, ensuring you achieve the correct results in expression simplification.
- Addition: Involves combining numbers to get their total. For instance, in \(5 + 10\), you take 5 and add 10 to it, resulting in 15.
- Subtraction: This is the process of removing a number from another. So, when you see an operation like \(15 - 11\), it involves subtracting 11 from 15 to get 4.
Understanding and accurately performing these operations is a key step in math problem-solving, ensuring you achieve the correct results in expression simplification.
Expression Simplification
Expression simplification aims to make a complex expression more understandable by reducing it to its simplest form. This not only makes the expression easier to work with but also reveals essential insights into the relationships between variables or components involved.
When simplifying, follow the order of operations and perform each arithmetic operation methodically. In our example, starting with \(5 + (6 + 4) - 11\), we first addressed the parentheses creating \(5 + 10 - 11\). Then, by adding to get \(15\) and subtracting \(11\), the expression was simplified to its lowest term, \(4\).
Expression simplification is crucial in various mathematical contexts, optimizing calculations and making complex ideas more accessible.
When simplifying, follow the order of operations and perform each arithmetic operation methodically. In our example, starting with \(5 + (6 + 4) - 11\), we first addressed the parentheses creating \(5 + 10 - 11\). Then, by adding to get \(15\) and subtracting \(11\), the expression was simplified to its lowest term, \(4\).
Expression simplification is crucial in various mathematical contexts, optimizing calculations and making complex ideas more accessible.
Other exercises in this chapter
Problem 15
For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. $$ 4^{2} \cdot 4^{3} \div
View solution Problem 15
For the following exercises, simplify the given expression. $$ 5+(6+4)-11 $$
View solution Problem 16
For the following exercises, factor the polynomial. $$ 7 x^{2}+48 x-7 $$
View solution Problem 16
For the following exercises, multiply the rational expressions and express the product in simplest form. $$ \frac{2 d^{2}+9 d-35}{d^{2}+10 d+21} \cdot \frac{3 d
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