Problem 79 - Prealgebra

Question

Simplify the given expression. \(-11.15+(11.6-(-16.68))\)

Step-by-Step Solution

Answer

The simplified expression is 17.13.

Step 1: Simplify the Inner Expression

Focus on simplifying the expression inside the parentheses: \(11.6 - (-16.68)\). In mathematics, subtracting a negative number is the same as adding its positive counterpart.

Step 2: Add the Inner Expression

Change the subtraction of a negative to addition: \(11.6 + 16.68\). Now, calculate the sum: \(11.6 + 16.68 = 28.28\).

Step 3: Substitute Back into the Original Expression

Replace the inner expression in the original problem with the result you found: \(-11.15 + 28.28\).

Step 4: Perform the Addition

Now, add the numbers: \(-11.15 + 28.28 = 17.13\).

Key Concepts

Subtraction of Negative Numbers

Subtracting negative numbers can be confusing at first, but it becomes simple once you understand the rule. When you subtract a negative number, it's like removing a debt, which means you actually gain. This translates to adding the positive version of the number you're subtracting.

For example, look at the expression inside the parentheses:

• We have: \(11.6 - (-16.68)\)
• According to the rule, subtracting \(-16.68\) becomes the same as adding \(16.68\).

So, it changes to \(11.6 + 16.68\). Converting subtraction of negative numbers into addition makes it all much clearer.

Addition

When you add numbers, whether they are whole numbers, decimals, or fractions, you are simply combining their quantities. Addition is fundamental in math and is often the next step after you've simplified using rules like subtraction of negatives. In our case:

• After simplifying \(11.6 - (-16.68)\) into \(11.6 + 16.68\), we need to perform the addition.
• Computing the sum gives us \(11.6 + 16.68 = 28.28\).

It is helpful to remember to line up decimal points if you are doing the addition by hand. Also, double-checking your calculations can prevent simple mistakes and ensure accuracy.

Evaluating Expressions

Evaluating an expression means finding the value of the expression by following the math operations involved. In our exercise, once we've simplified internally by dealing with the negative number subtraction, we're on our way to evaluating. Here's how we do it:

• We replaced the simplified inner expression into the original one: \(-11.15 + 28.28\).
• Then, continue by performing the indicated addition: \(-11.15 + 28.28\).
• This calculates to \(17.13\).

Remember that each step in simplifying and evaluating helps break down complex expressions into smaller, more manageable parts.