Problem 89 - Prealgebra

Question

Simplify. $$16-8+4$$

Step-by-Step Solution

Answer

The simplified result is 12.

Step 1: Identify the Operations

In the expression \(16 - 8 + 4\), you need to perform subtraction and addition. According to the order of operations, we perform these from left to right.

Step 2: Perform the First Operation

Start with the first operation from left to right, which is subtraction: \(16 - 8 = 8\). This simplifies the expression to \(8 + 4\).

Step 3: Perform the Second Operation

Now, perform the second operation, which is addition: \(8 + 4 = 12\). This is the final simplified result.

Key Concepts

Addition and Subtraction

When tackling a math problem like the one in our exercise, it's essential to understand the roles of addition and subtraction. These are two of the fundamental arithmetic operations. When we have both operations in a single expression, it is crucial to follow the order of operations. This principle ensures we obtain the correct answer. Subtraction is about taking away some value from another. For example, in the expression \(16 - 8\), we are removing 8 from 16. Addition, on the other hand, means you are combining quantities. In the expression \(8 + 4\), you combine the two numbers to get a larger sum.Combining these operations within a single expression means approaching them systematically to avoid errors. Always remember, these operations are not performed based on their type first, but rather their position in the equation.

Simplification

Simplification in math refers to the process of making a mathematical expression simpler or easier to understand. For our specific problem \(16 - 8 + 4\), simplification means reducing the expression to a single number by performing the operations given. The process often involves:

• Combining like terms or numbers by executing arithmetic operations on them.
• Reducing complex expressions to simpler forms without changing their value.

In our example, we simplified the expression in two steps, first tackling the subtraction and then the addition. The result was ultimately \(12\), which is a single, easy-to-understand number compared to the original expression.

Left-to-Right Operations

The concept of left-to-right operations is central when dealing with expressions that include addition and subtraction. According to the order of operations, these two types of operations should be performed in the order they appear from left to right.This rule is crucial because if you don't follow it, you might end up with the wrong answer. For example, considering the expression \(16 - 8 + 4\), if you decide to perform the addition first, you'd add 8 and 4 to get 12, and then subtract from 16, ending up with 4, which is incorrect.Therefore, sticking to left-to-right execution in expressions ensures accuracy. Your steps should include identifying the operations in their sequence and executing them one at a time as they appear, avoiding mistakes and arriving at the correct solution.