Problem 5 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 4+9-1 $$

Step-by-Step Solution

Answer

The result of evaluating the expression \( 4+9-1 \) is 12.

Step 1: Perform the Addition

The first operation to be performed, based on the order from left to right, is addition. Thus, add 4 and 9 to get 13.

Step 2: Perform the Subtraction

Next, subtract 1 from the result of the addition operation (13). The result will be \( 13-1 = 12 \).

Key Concepts

Order of Operations

Understanding the order of operations is crucial in arithmetic as it tells you which calculations to perform first. In mathematical expressions, such as the one given: \[ 4 + 9 - 1 \]The operations must be performed from left to right. This is a straightforward example that only involves addition and subtraction. The general rule is to handle any calculations involving parentheses and exponents first, but in this case, they don't apply.

• Perform operations in parentheses.
• Calculate exponents.
• Perform multiplication and division from left to right.
• Carry out addition and subtraction from left to right.

In our example, since there are no parentheses, exponents, multiplication, or division, you simply move from left to right handling addition and subtraction.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. It's one of the fundamental operations in arithmetic. In our example, the first step is to add 4 and 9:

• Write the numbers vertically or horizontally, aligning the place values if necessary.
• Start adding from the rightmost digit and move left in case of larger numbers.

Here, adding 4 and 9 is simple: \[ 4 + 9 = 13 \]There is no carrying over involved in this addition. It results in a straightforward sum. Once you have your total from the addition, you move to the next operation in your expression.

Subtraction

Subtraction is the operation of finding the difference between two numbers or decreasing a number by another value. In the exercise, once you've handled the addition, subtraction is the next operation:

• Start by writing the numbers down, ensuring their alignment by place value if they are large numbers.
• Subtract the bottom number from the top number working from right to left.

In our given example, we subtract 1 from 13:\[ 13 - 1 = 12 \]No borrowing or further steps are necessary here. Subtraction in this instance is straightforward, resulting in a final answer of 12. Subtraction completes the sequence of operations you've applied to solve the expression.