Problem 73 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ 48+(-16) $$

Step-by-Step Solution

Answer

32

Step 1: Identify the Operation

The exercise involves adding 48 and -16. Notice that adding a negative number is equivalent to subtraction.

Step 2: Convert to Subtraction

Rewrite the expression to simplify the operation. Instead of adding -16, we can subtract 16 from 48.

Step 3: Perform the Calculation

After rewriting, we have: \[ 48 - 16 \] Now, perform the subtraction to get the result.

Step 4: Write the Simplified Expression

After performing the subtraction, the result is \[ 48 - 16 = 32 \]. Therefore, the simplified expression is 32.

Key Concepts

Addition with Negative Numbers

Adding negative numbers can be confusing at first, but it becomes simple with practice. When you add a negative number to a positive number, the operation is essentially subtraction. For example, in the exercise given:

• The expression is 48 + (-16).
• Adding -16 is the same as subtracting 16.

So, instead of seeing it as addition, you can rewrite the expression as a subtraction: 48 - 16.

Subtraction

Subtraction is one of the basic operations in math, and understanding it is essential for simplifying expressions. When subtracting, you take away the value of one number from another. In the context of our exercise:

• You start with 48 and subtract 16 from it.
• This simplifies the problem and makes it easier to solve.

The subtraction operation is straightforward and results in:

Step-by-Step Solution:

1. Rewrite 48 + (-16) as 48 - 16.
2. Subtract 16 from 48 to get 32.

This step-by-step approach will help you consistently arrive at the correct answer.

Simplifying Expressions

Simplifying expressions means reducing them to their most basic form. It often involves performing arithmetic operations and combining like terms. In our example:

• We start with an expression involving addition of a negative number.
• We then rewrite it as a subtraction to simplify it.

Finally, after performing the subtraction, we combine the terms to find the simplified expression. Here,
The original expression 48 + (-16) simplifies to 32.
Always ensure that you perform each operation step by step to avoid mistakes and arrive at the simplest form of the expression.