Problem 62 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. \(32 \cdot 4+8\)

Step-by-Step Solution

Answer

The evaluated result of the expression \(32 \cdot 4+8\) is 136.

Step 1: Execute the multiplication operation

According to the rules of BODMAS/BIDMAS/PEDMAS, multiplication is conducted before addition in arithmetic operations. Therefore, first multiply 32 with 4, which equals 128

Step 2: Execute the addition operation

After the multiplication operation, the next operation left to execute is addition. So, add the result from Step 1 with 8. Hence, 128 + 8 results into 136

Key Concepts

BODMAS

In arithmetic, BODMAS is an acronym that stands for Brackets, Orders (i.e., powers and square roots, etc.), Division, Multiplication, Addition, and Subtraction. It is a sequence that determines the order in which operations should be performed to accurately solve mathematical expressions. When you look at an expression like \(32 \cdot 4 + 8\), BODMAS acts like a set of rules that dictate that operations inside Brackets come first, followed by Orders, then Division and Multiplication (which are equal in precedence and resolved from left to right). Finally, Addition and Subtraction are handled last, also resolved from left to right. This sequence helps prevent confusion and ensures everyone solves the problem consistently and correctly. When evaluating our expression, multiplication is carried out before addition according to these principles.

Multiplication

Multiplication is one of the fundamental arithmetic operations, often visualized as repeated addition. It involves two numbers known as the 'multiplicand' and the 'multiplier'. For example, in the expression \(32 \cdot 4\), 32 is the multiplicand, and 4 is the multiplier. The operation produces a product, making 128 in this case since \(32 + 32 + 32 + 32 = 128\).
Whenever you perform multiplication, you are essentially scaling the multiplicand by the number represented by the multiplier. This operation's positioning in the BODMAS rules often requires it to be performed before addition to maintain computational integrity. Thus, when you see an expression like in our exercise, you always solve the multiplication portion first.

Addition

Addition is a basic yet vital arithmetic operation that involves combining two or more numbers to find their total sum. In the context of our exercise, after performing the multiplication part \(32 \cdot 4\), we end up with 128. The next step is to add the remaining part, which is 8. This gives us \(128 + 8\) resulting in 136.
Addition is typically one of the last operations to be performed in an arithmetic sequence according to BODMAS. It is relatively straightforward since it can be thought of as 'combining'. Despite its simplicity, obeying the correct sequence ensures no computational errors, supporting mathematical clarity. So, even in complex expressions, always watch for additions last unless directed otherwise by the presence of brackets or an order power.