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Chapter 1: Problem 21

Find each sum. $$ 4+[13+(-5)] $$

Short Answer

Expert verified
The sum is 12.

Step by step solution

01

Evaluate the inner parentheses

First, solve the expression inside the parentheses: Starting with +(-5)$. Since adding a negative number is the same as subtracting, this becomes: 13 - 5 = 8. Now we have 4 + 8.
02

Add the results

Next, perform the addition: 4 + 8. When you add these two numbers together, the result is 12.

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Key Concepts

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

Addition
Addition is one of the basic arithmetic operations where you combine two or more numbers to get a sum. For example, when you have 4 and you add 8 to it, you write it as 4 + 8. This means you are combining the value of 4 and 8 together to get the total, which is 12.
Adding works regardless of the order of numbers, due to the commutative property. So, 4 + 8 and 8 + 4 both give you the same result. Always start by aligning numbers properly when adding them, especially with larger or decimal numbers.
Subtraction
Subtraction is another fundamental arithmetic operation. It involves taking one number away from another. For instance, if you have 13 and you subtract 5 from it (written as 13 - 5), you get 8. This concept is useful in situations where you need to find the difference between two quantities.
Unlike addition, the order in subtraction matters. For example, 13 - 5 is not the same as 5 - 13. In our case, after evaluating the inner parentheses, we performed subtraction because we encountered a negative number inside the parentheses.
Remember, when subtracting large numbers, align the digits correctly for accurate results.
Order of Operations
The order of operations is a set of rules that defines the sequence in which calculations should be performed to ensure accurate results. In mathematics, this is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
In our example, we started by evaluating the expression inside the parentheses first: (13 + -5). This gave us 8, which we then added to 4 outside the parentheses. Following the correct order of operations is crucial for solving mathematical expressions accurately.
Negative Numbers
Negative numbers are numbers less than zero, represented with a minus (-) sign. They play a crucial role in arithmetic operations. When adding a negative number, it is similar to subtraction. For example, in the expression 13 + (-5), adding -5 is the same as subtracting 5 from 13, resulting in 8.
Negative numbers can sometimes be confusing, but remembering a few rules can help make calculations easier:
  • Adding a negative number: similar to subtracting its positive counterpart.
  • Subtracting a negative number: similar to adding its positive counterpart.
Practice with negative numbers helps improve your arithmetic skills.

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Most popular questions from this chapter

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Find each difference. $$ -6.4-3.5 $$

Perform each indicated operation. $$ \left(-\frac{3}{2}-0.75\right)-\left(0.5-\frac{1}{2}\right) $$

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Perform each indicated operation. $$ -7.6247-[(-3.9928+1.42773)-(-2.80981)] $$
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