Problem 71 - Elementary and Intermediate Algebra

Question

Add. $$ 19.35+(-20.21)+1.53 $$

Step-by-Step Solution

Answer

0.67

Step 1: Simplify the Problem Statement

The exercise requires adding three numbers together: 19.35, -20.21, and 1.53. Our task is to perform the arithmetic operations correctly.

Step 2: Combine the First Two Numbers

First, add 19.35 and -20.21. Since -20.21 is negative, this operation is equivalent to subtraction: \( 19.35 + (-20.21) = 19.35 - 20.21 = -0.86 \).

Step 3: Add the Result to the Third Number

Next, take the result from Step 2, which is -0.86, and add the third number, 1.53: \( -0.86 + 1.53 = 0.67 \).

Key Concepts

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. When dealing with numbers, operations such as addition, subtraction, multiplication, and division are essential. In this exercise, we're focusing on addition, but it's also important to realize that adding a negative number is like a subtraction.

• Addition: Adding numbers means combining their values. For example, 3 + 2 equals 5.
• Subtraction: Subtracting one number from another reduces the total value. For example, 5 - 2 yields 3.
• Multiplication: Represents adding a number to itself multiple times. For instance, 3 multiplied by 2 equals 6.
• Division: Splits a number into specified equal parts. Dividing 6 by 2 results in 3.

Understanding how these operations interact is crucial, especially when combining them in complex expressions.

Negative Numbers

Negative numbers can seem tricky at first, but once grasped, they become just like any other part of arithmetic.

• They are numbers less than zero, represented by the negative sign (-).
• In a sense, they denote a deficit or something that's taken away.
• Handling negative numbers often requires a mindset shift: subtracting a negative is like adding, while adding a negative is akin to subtracting.

When you see an expression like 19.35 + (-20.21), you actually need to subtract 20.21 from 19.35, which gives a negative result because 20.21 is larger than 19.35.

Addition

Addition is the act of bringing two numbers together to form a new, larger number. It might seem simple, but it's the cornerstone of more complex mathematical operations. Here’s a brief overview of what to keep in mind when performing addition:

• Order Doesn't Matter: Addition is commutative, which means changing the order of the numbers doesn’t affect the result. For instance, 1 + 2 equals the same as 2 + 1.
• Associative Property: This property states that how you group the numbers you're adding doesn't change the sum. For example, (3 + 2) + 1 is the same as 3 + (2 + 1).
• Combination of Positives and Negatives: When adding a series of positive and negative numbers, treat the positive numbers first, then the negatives, or vice versa.

In problems involving both positive and negative numbers, it’s usually helpful to think of movement along a number line, moving right for positive and left for negative.