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Chapter 1: Problem 46

Simplify the given expression. $$ 19-4+13 $$

Short Answer

Expert verified
The simplified expression is 28.

Step by step solution

01

Identify the Operations

The expression given is \(19 - 4 + 13\). It involves two operations鈥攕ubtraction and addition.
02

Perform Subtraction First

Begin by performing the subtraction from left to right: \(19 - 4\). This equals \(15\).
03

Perform Addition

Take the result from the subtraction, \(15\), and add \(13\) to it. This comes out to \(15 + 13 = 28\).

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Key Concepts

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

Subtraction
Subtraction is a mathematical operation that represents the process of taking away or removing items from a collection. In the context of our expression, we begin with the number 19 and subtract 4 from it. The number 19 is referred to as the minuend, and 4 is the subtrahend. The result of this subtraction, in this case, is 15.
Here's how it works:
  • The minus sign (-) is used to indicate that we are subtracting one number from another.
  • The calculation is performed from left to right when simplifying an expression involving a combination of operations.
After performing the subtraction of 19 - 4, you are left with a remainder, which in our example is 15. Understanding subtraction is crucial as it lays the groundwork for more complex mathematical concepts.
Addition
Addition is the process of combining two or more numbers together to get a new total. After performing the necessary subtraction, we continue by adding the remaining number to our new total. In our exercise, after subtracting and finding 15, we add 13 to it.
Here's a basic breakdown:
  • We have two numbers: 15 (the result from subtraction) and 13 (the number we need to add).
  • The plus sign (+) denotes that these numbers need to be summed.
  • When you add 15 and 13, you get 28, which is the final result of the expression.
Addition connects to everyday scenarios, such as adding up items in a shopping cart or calculating a total score. Mastery of addition is a basic but essential skill for both academic and real-world applications.
Order of Operations
Order of operations is a fundamental principle in mathematics that dictates the order in which operations should be performed to accurately solve expressions. In the expression 19 - 4 + 13, although there are no parentheses or exponents, there is a particular sequence we must follow.
The general rule to remember is the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). For simplicity, consider:
  • When both addition and subtraction are present, we process the operations from left to right.
  • In our expression, we handle the subtraction first (19 - 4), followed by the addition (15 + 13).
This order is vital as performing operations in the incorrect sequence can lead to wrong answers. Remembering the order of operations ensures clarity and accuracy when solving mathematical problems.

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