Problem 38 - Beginning and Intermediate Algebra

Question

Find each sum. $$ 12+[-3+(-4)] $$

Step-by-Step Solution

Answer

The sum is 5.

Step 1 - Simplify the Inner Parentheses

First, solve the expression inside the parentheses: ewline ewline ewline ewline -3 + (-4).

Step 2 - Perform the Addition Inside the Parentheses

Add the numbers inside the parentheses: ewline ewline -3 + (-4) = -7.

Step 3 - Substitute and Simplify

Replace the parentheses with the result from Step 2: ewline ewline12 + (-7).

Step 4 - Final Addition

Perform the final addition: ewline ewline 12 + (-7) = 5.ewline ewline ewline The sum is 5.

Key Concepts

Integer Addition

Adding integers involves combining both positive and negative numbers. For positive numbers, you simply add their absolute values. For example, 7 + 3 = 10.

Negative numbers, though, are a bit different. When adding two negative numbers, you add the absolute values and then attach a negative sign to the result. For example, ewline -3 + (-4) = -7.

If a positive and a negative number are added, subtract the smaller absolute value from the larger one, and attach the sign of the number with the larger absolute value to the result. For instance, 12 + (-7) = 5 because we essentially subtract 7 from 12.

Simplifying Expressions

Simplifying expressions means to make them simpler and easier to work with. One way to simplify is to combine like terms. In our example,

ewline 12 + [-3 + (-4)]

, we must first simplify the expression inside the brackets: -3 + (-4).

Combining these like terms gives us -7 since adding two negative numbers results in a more negative value.

Another method for simplifying is by using the rules for the order of operations. Follow BIDMAS/BODMAS rules: Brackets, Orders (i.e., powers and square roots, etc.), Division, Multiplication, Addition, and Subtraction.

Parentheses Operations

Parentheses indicate which operations should be completed first. Inside any equation, always start with the calculations inside the parentheses. In our problem, we have:

12 + [-3 + (-4)]

The addition within the parentheses should be resolved first. Separately calculating -3 + (-4) gives us -7.

After this, replace the parenthesis in the original expression with the result: 12 + (-7).

Now, you can complete the final addition step: 12 + (-7) = 5.