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Chapter 1: Problem 38

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

Short Answer

Expert verified
The sum is 5.

Step by step solution

01

- Simplify the Inner Parentheses

First, solve the expression inside the parentheses: ewline ewline ewline ewline -3 + (-4).
02

- Perform the Addition Inside the Parentheses

Add the numbers inside the parentheses: ewline ewline -3 + (-4) = -7.
03

- Substitute and Simplify

Replace the parentheses with the result from Step 2: ewline ewline12 + (-7).
04

- Final Addition

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

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Key Concepts

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

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.

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Most popular questions from this chapter

Solve each problem. Linda owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00\). She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?

Write a numerical expression for each phrase, and simplify the expression. The sum of 12 and \(-7,\) decreased by 14

Write a numerical expression for each phrase, and simplify the expression. 14 added to the sum of -19 and -4

Write a numerical expression for each phrase, and simplify the expression. The difference of 4 and -8

Write a numerical expression for each phrase, and simplify the expression. 9 less than -13
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