Problem 90 - Prealgebra

Question

Simplify. $$16-4+8$$

Step-by-Step Solution

Answer

The simplified expression is 20.

Step 1: Identify the Operation Sequence

The expression to simplify is \(16 - 4 + 8\). Notice it involves subtraction and addition. According to the order of operations, perform these operations from left to right as they appear, since they are of the same precedence level.

Step 2: Subtract First

Start by calculating the subtraction part of the expression. Subtract 4 from 16:\[16 - 4 = 12\]

Step 3: Add to the Result

Now use the result from the subtraction step. Take the number 12 and add 8 to it:\[12 + 8 = 20\]

Step 4: Conclusion: Simplified Expression

The simplified value of the expression \(16 - 4 + 8\) is 20.

Key Concepts

Addition and Subtraction

In mathematics, addition and subtraction are two of the fundamental operations. These operations are used to combine numbers or quantities in various ways. Let's break down some key points.

• **Addition** is bringing two or more numbers (or things) together to make a new total. For example, adding 3 and 4 gives us 7 because we combine the quantities.
• **Subtraction** is the process of taking one quantity away from another. For instance, subtracting 4 from 16 gives us 12, as we remove parts from the whole.

For our example, the expression 16 - 4 + 8 involves both operations.
According to the order of operations, which dictates Calculation Rules, subtraction and addition should be performed from left to right.

By subtracting 4 from 16, we get 12. Next, adding 8 to 12 yields 20. Using these operations properly ensures accuracy in calculations.

Simplifying Expressions

Simplifying expressions is all about making them as concise and straightforward as possible. This involves combining like terms and performing basic operations until you reach a simplified form.

Here's how you simplify the expression 16 - 4 + 8:

• First, **identify the sequence** of operations that need to be completed. Since addition and subtraction are on the same level of precedence, perform these operations from left to right.
• **Break down each step**: Start with the subtraction, 16 minus 4, which equals 12.
• Then, **add the remaining numbers**: Take 12 and add 8, resulting in 20.

This approach reduces the expression to its simplest form efficiently. Simplifying allows us to understand and work with expressions quickly.

Mathematical Operations

Mathematics relies on operations such as addition, subtraction, multiplication, and division to solve problems.
These operations follow a specific set of rules called the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

For the given problem 16 - 4 + 8:

• **Identify the operations**: Recognize that the expression is a combination of subtraction and addition.
• **Apply the rules**: Since addition and subtraction have equal priority, perform them as they appear from left to right.

By applying these principles, you ensure calculations are carried out correctly and efficiently. Each operation adheres to a specific method which, when applied in sequence, leads to finding an accurate solution.