Problem 51
Question
Simplify each of the numerical expressions. $$ 16+9-4-2+8-1 $$
Step-by-Step Solution
Verified Answer
The simplified expression is 26.
1Step 1: 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.
2Step 2: 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.
Key Concepts
Addition and SubtractionNumerical ExpressionsStep-by-Step Problem Solving
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.
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.
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.
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.
Other exercises in this chapter
Problem 51
Simplify each of the numerical expressions. $$ 3\left(\frac{1}{2}\right)^{4}-2\left(\frac{1}{2}\right)^{3}+5\left(\frac{1}{2}\right)^{2}-4\left(\frac{1}{2}\righ
View solution Problem 51
Perform the following operations with real numbers. $$ \left(-\frac{3}{4}\right)\left(\frac{4}{5}\right) $$
View solution Problem 52
Evaluate the algebraic expressions for the given values of the variables. $$ -4(2 x-1)+7(3 x+4), \quad x=4 $$
View solution Problem 52
Simplify each of the numerical expressions. $$ 4(0.1)^{2}-6(0.1)+0.7 $$
View solution