Problem 54 - Prealgebra and Introductory Algebra

Question

Evaluate the expression \(x+y\) for the given values of \(x\) and \(y .\) $$x=62.97, y=-43.85$$

Step-by-Step Solution

Answer

The result of the expression \(x+y\) for the given values of \(x=62.97, y=-43.85\) is \(19.12\).

Step 1: Substitution

Firstly, substitute the given values of \(x\) and \(y\) into the expression \(x + y\). After substituting: \(62.97 + (-43.85)\)

Step 2: Perform Addition

Since \(y\) is negative, this will turn into subtracting \(43.85\) from \(62.97\). The problem becomes \(62.97 - 43.85\).

Step 3: Calculate the Result

Perform the arithmetic operation to get the result. The result will be \(19.12\).

Key Concepts

Substitution

Substitution is the process of replacing variables in an expression with their actual numeric values. When you're given an expression like \(x + y\), and specific values for \(x\) and \(y\), such as \(x = 62.97\) and \(y = -43.85\), substitution lets you evaluate the expression by directly inserting these values into it.
Imagine you have a box that says "x," and by substituting, you simply open the box and use whatever is inside – in this case, the number 62.97. Similarly, for the variable "y," you substitute it with -43.85.
By doing so, the expression \(x + y\) becomes \(62.97 + (-43.85)\). It's as if you're exchanging the letters with the numbers so that you can perform further calculations.

Negative Numbers

Negative numbers are numbers less than zero and are represented with a minus sign (-). Understanding how to work with negative numbers is crucial in math, especially in operations like addition and subtraction.
When you encounter a negative number in an expression, it can change how you perform calculations. Take the expression \(62.97 + (-43.85)\). Here, the number \(-43.85\) is negative, meaning you're adding a negative value, which is the same as subtracting its positive equivalent.
Think of it like handling money: if you have \\(62.97 and spend \\)43.85, you're left with less money. This is why \(62.97 + (-43.85)\) simplifies to \(62.97 - 43.85\). Using practice and visualization can help make handling negative numbers become second nature.

Arithmetic Operations

Arithmetic operations are basic mathematical processes like addition, subtraction, multiplication, and division. These operations allow you to solve equations and perform calculations.
In this exercise, you're mainly dealing with addition and its special case when involved with negative numbers, which turns into subtraction. To find the value of the expression \(62.97 + (-43.85)\), you'll perform subtraction because you're adding a negative number – effectively subtracting the number's magnitude.
Breaking it down, start by setting the numbers for subtraction: \(62.97 - 43.85\).

• Align the decimal points for accuracy.
• Subtract the numbers starting from the rightmost side (the hundredths place) and move left.
• Continue each column's subtraction step by step, borrowing as necessary to maintain mathematical accuracy.
• The final result is \(19.12\).

This is a simple yet powerful process to ensure correct arithmetic results.