Problem 5
Question
For the following problems, simplify the expressions. $$ \frac{(4+17+1)+4}{14-1} $$
Step-by-Step Solution
Verified Answer
Question: Simplify the given expression by following the order of operations (PEMDAS):
$$
\frac{(4+17+1)+4}{14-1}
$$
Answer: __2__
1Step 1: Perform operations inside parentheses
First, we must add the numbers inside the parentheses:
$$
(4+17+1) = 22
$$
Now our expression looks like this:
$$
\frac{22+4}{14-1}
$$
2Step 2: Perform addition and subtraction
Next, we must perform the addition and subtraction operations on both the numerator and denominator.
In the numerator, we must add 22 and 4:
$$
22+4 = 26
$$
In the denominator, we must subtract 1 from 14:
$$
14-1 = 13
$$
Now our expression looks like this:
$$
\frac{26}{13}
$$
3Step 3: Perform division
Finally, we must perform the division operation, which consists of dividing 26 by 13:
$$
\frac{26}{13} = 2
$$
So, the simplified expression is:
$$
2
$$
Key Concepts
Order of OperationsArithmetic OperationsPerforming Division
Order of Operations
Understanding the order of operations is crucial when simplifying algebraic expressions. It provides a consistent method to solve math problems that contain more than one arithmetic operation. This rule is commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
In the given exercise, we start by solving the operations inside the parentheses, which is the first P in our PEMDAS guideline. Only after completing this step do we move to perform addition or subtraction in the expression. This systematic approach prevents mistakes and ensures that anyone simplifying the expression will arrive at the same result. For example, adding the numbers inside the parentheses gave us 22, setting the stage for further operations.
In the given exercise, we start by solving the operations inside the parentheses, which is the first P in our PEMDAS guideline. Only after completing this step do we move to perform addition or subtraction in the expression. This systematic approach prevents mistakes and ensures that anyone simplifying the expression will arrive at the same result. For example, adding the numbers inside the parentheses gave us 22, setting the stage for further operations.
Arithmetic Operations
Arithmetic operations are the foundation of algebra and include addition, subtraction, multiplication, and division. When simplifying expressions, it is important to perform these operations accurately and in the correct order (as guided by the order of operations).
Once the operations inside the parentheses are completed, as they were in our example, the next step involves dealing with addition or subtraction in the expression. In this case, the operation was addition in the numerator and subtraction in the denominator. Accurately performing these operations is essential, as it simplifies the expression and prepares it for the final operation, which in this problem was division.
Once the operations inside the parentheses are completed, as they were in our example, the next step involves dealing with addition or subtraction in the expression. In this case, the operation was addition in the numerator and subtraction in the denominator. Accurately performing these operations is essential, as it simplifies the expression and prepares it for the final operation, which in this problem was division.
Performing Division
Performing division is a fundamental arithmetic operation which is often the final step in simplifying an expression. It involves finding how many times the divisor fits into the dividend. In the context of algebraic expressions, it helps to reduce fractions or expressions to their simplest form.
In our example, after performing addition and subtraction, the last step was to divide the numerator by the denominator. The division of 26 by 13 led to the final simplified answer of 2. It is important to note that division by zero is undefined, so always ensure that the denominator in any expression is not zero before performing division.
In our example, after performing addition and subtraction, the last step was to divide the numerator by the denominator. The division of 26 by 13 led to the final simplified answer of 2. It is important to note that division by zero is undefined, so always ensure that the denominator in any expression is not zero before performing division.
Other exercises in this chapter
Problem 4
Is every rational number a real number?
View solution Problem 4
Use the grouping symbols to help perform the following operations. $$6\\{2[2(10-9)]\\}$$
View solution Problem 5
Find each product. $$ (x+2)^{3} \cdot(x+2)^{5} $$
View solution Problem 5
Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ [4 t(s-5)]^{3} $$
View solution