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Chapter 1: Problem 66

Perform each indicated operation. $$ (-9-4)(-2)+10 $$

Short Answer

Expert verified
36

Step by step solution

01

- Simplify inside the parentheses

First, simplify the expression inside the parentheses (-9 - 4). -9 - 4 = -13
02

- Multiply next

Next, multiply the simplified value with -2 (-13)(-2) = 26.
03

- Add the remaining value

Finally, add the product to 10 26 + 10 = 36.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

parentheses simplification
When dealing with a math problem, it's important to simplify any expressions inside parentheses first. This helps to make the problem easier to solve step by step. In the given problem \((-9 - 4)\), we need to combine \(-9\) and \(-4\) into a single number.

Since both are negative numbers, we add their absolute values (9 and 4) and stick the negative sign back onto the result.
\[ -9 - 4 = -13 \]
By combining these, we transform our original equation into a simpler form. Always remember to address the expressions inside parentheses first before moving on to other operations!
multiplication with negatives
Multiplying negative numbers can be confusing at first, but it follows a clear set of rules. When you multiply two negative numbers, the product is positive. Conversely, if you multiply a positive number with a negative number, the product will be negative.

In our problem, we simplified the parentheses to get \(-13\). Next, we need to multiply this by \(-2\). Using the rule that a negative times a negative equals a positive:
\[ (-13) \times (-2) = 26 \]
This is because the two negatives cancel each other out. Remember to keep track of your signs to avoid mistakes during multiplication!
addition of integers
Adding integers, especially when involving both positive and negative values, is a fundamental skill. Here, after simplifying the multiplication step, we have \ 26 \ on hand. The final part involves adding this positive result to \ 10 \.

Whenever you add two positive numbers, you simply combine their values.

In our case:
\[ 26 + 10 = 36 \]
Addition becomes straightforward once you understand the nature of the numbers involved. Keep positive and negative integers distinct to avoid errors. This concept wraps up our exercise neatly!

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