Problem 36 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 9+2 \cdot 0 $$

Step-by-Step Solution

Answer

9

Step 1: Identify the operations

First, identify the operations in the expression. Here we have addition and multiplication: $$9 + 2 \times 0$$

Step 2: Apply the order of operations (PEMDAS)

According to the order of operations (Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right)), we should first perform the multiplication: $$2 \times 0$$

Step 3: Perform the multiplication

Multiply 2 by 0: $$2 \times 0 = 0$$

Step 4: Add the results

Now, add the result of the multiplication to 9: $$9 + 0 = 9$$

Key Concepts

Understanding PEMDAS

PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (left to right), Addition, and Subtraction (left to right). This rule helps us to determine the order in which we solve mathematical expressions. By following the PEMDAS rule, we ensure that we get the correct answer. Let's break it down further:

• P - Parentheses: Solve expressions inside parentheses first.
• E - Exponents: Next, solve the exponents (powers and roots, etc.).
• M and D - Multiplication and Division: Solve these operations from left to right. They are on the same level, so do them in the order they appear.
• A and S - Addition and Subtraction: Finally, do these last from left to right. They are also on the same level, so follow the order they appear.

For example, in the expression $$9 + 2 \times 0$$, we first perform the multiplication because it comes before addition in PEMDAS. This ensures our calculations are accurate and follow the mathematical conventions.

Understanding Multiplication

Multiplication is one of the basic arithmetic operations. It involves combining groups of equal size. In the context of the given exercise, we are asked to multiply two numbers. The concept of multiplication here is represented by the symbol \times. When we see the expression $$2 \times 0$$, we interpret this as two groups of zero.
The result of any number multiplied by zero is zero. This is because if we have zero groups of any number, or any number of zero groups, we end up with nothing—zero. Mathematically, it's expressed as:
$$a \times 0 = 0$$. In our specific problem, $$2 \times 0 = 0$$ because there are two groups of zero items, which results in zero. This concept is crucial to correctly solving our initial expression $$9 + 2 \times 0$$.

Understanding Addition

Addition is another fundamental arithmetic operation. It involves combining the values of numbers to find their total. The operation of addition is denoted by the symbol \(+\). In the context of our problem, once we have calculated the multiplication part, we proceed with the addition:
$$9 + 0$$. Here, we simply add 0 to 9, which does not change its value. Therefore,
$$9 + 0 = 9$$.

Remember, addition involves these simple steps:

• Align the numbers by their place values (units, tens, etc.).
• Start from the rightmost value (units) and move to the left, adding each corresponding digit.
• If digits add up to more than 9, carry over the extra value to the next left place value.

In this problem, there are no carry-overs and the result is straightforward. Thus, the final answer to the problem $$9 + 2 \times 0$$ is 9.