Problem 65 - Elementary Algebra

Question

\(18-4(9)\)

Step-by-Step Solution

Answer

-18

Step 1: Understand the Expression

The given expression is: \(18 - 4(9)\). We need to simplify this expression using basic arithmetic operations.

Step 2: Perform Multiplication

First, perform the multiplication part of the expression. Multiply 4 by 9: \[4 \times 9 = 36\]

Step 3: Substitute the Result

Now, substitute the result of the multiplication back into the expression. The expression becomes: \[18 - 36\]

Step 4: Perform Subtraction

Finally, perform the subtraction part of the expression: \[18 - 36 = -18\]

Key Concepts

arithmetic operations

In this exercise, we are dealing with arithmetic operations, which are the foundation of mathematics. Arithmetic operations include addition, subtraction, multiplication, and division. When performing these operations, it is essential to follow the **order of operations** to achieve the correct result. For this exercise, our main focus is on multiplication and subtraction.
The priority or order of operations can be remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
In the given expression, we first have to handle the multiplication before moving on to the subtraction.

multiplication

Multiplication is one of the four elementary arithmetic operations, represented by the symbol '×' or '*'. It essentially means adding a number to itself a certain number of times.
In our exercise, the multiplication involves the numbers 4 and 9. The expression given is:
\( 18 - 4(9) \).
According to the order of operations, we perform the multiplication part of the expression first:
\( 4 \times 9 = 36 \).
Now that we've got the result of the multiplication, we replace 4(9) with 36 in the expression, making it 18 - 36.

subtraction

Subtraction is another primary arithmetic operation. It represents the process of taking one quantity away from another and is symbolized by the minus sign '-'.
After handling the multiplication in our exercise, we are left with the expression: \( 18 - 36 \).
To subtract 36 from 18, you can think of it as moving 36 units to the left on a number line starting from 18. This operation results in:
\( 18 - 36 = -18 \).
Thus, after performing both arithmetic operations, we find that the simplified value of the expression 18 - 4(9) is -18.