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Chapter 1: Problem 51

Simplify each of the numerical expressions. $$ 16+9-4-2+8-1 $$

Short Answer

Expert verified
The simplified expression is 26.

Step by step solution

01

Addition

First, let's add all the positive numbers together. We have 16, 9, and 8. Let's add these numbers: 16 + 9 = 25, 25 + 8 = 33.
02

Subtraction

Now, subtract the negative numbers sequentially from the sum we found. The numbers to subtract are 4, 2, and 1. 33 - 4 = 29, 29 - 2 = 27, 27 - 1 = 26.

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Key Concepts

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

Addition and Subtraction
When tackling numerical expressions involving both addition and subtraction, it's crucial to understand how these operations interact. Addition means combining numbers to form a larger total, while subtraction involves taking away amounts from a larger number to make it smaller.

To simplify expressions like the one given, start with addition first, combining all positive numbers. After obtaining a sum, proceed with subtraction by sequentially removing the negative numbers.

This two-step method ensures clarity and accuracy, as it helps keep track of changes to the total.
Numerical Expressions
Numerical expressions consist of numbers and operations like addition or subtraction. They are mathematical phrases that represent a specific value. For example, the expression you are simplifying, \(16+9-4-2+8-1\), is a sequence of numbers combined through operations.

The goal of simplifying numerical expressions is to find the simplest form or single value for the expression. By systematically applying operations, the numerical value of such expressions is determined.

Understanding each element of the expression and its role is key to accurate simplification.
Step-by-Step Problem Solving
Solving a numerical problem step-by-step helps ensure that each part of the expression is carefully evaluated. This methodical approach guards against mistakes that might arise from attempting all operations at once.

Begin by identifying and summing all positive numbers, as seen in the given problem's first step. Next, address each subtraction individually, updating the result at each stage.

This systematic approach not only makes the process easier to follow, but it also reduces the likelihood of errors, and aids in a better understanding of the underlying mathematical principles.

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Most popular questions from this chapter

Evaluate the algebraic expressions for the given values of the variables. $$ -2(x+4)-(2 x-1), \quad x=-3 $$

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