Problem 64 - Prealgebra

Question

Find the sum of \(-4,17,\) and \(-6\).

Step-by-Step Solution

Answer

The sum of -4, 17, and -6 is 7.

Step 1: Understanding the problem

The problem asks us to find the sum of three numbers: -4, 17, and -6. Sum means we need to add these numbers together to find their total.

Step 2: Adding the first two numbers

First, add the first number, -4, to the second number, 17. Calculate: \(-4 + 17 = 13\). This gives us a temporary sum of 13.

Step 3: Adding the third number

Now, take the result from Step 2, which is 13, and add the third number, -6.Calculate:\(13 + (-6) = 7\).This gives us the final sum of all three numbers.

Step 4: Verify the calculation

Check the calculation by ensuring the arithmetic was done correctly. We first got 13 from adding -4 and 17, and then added -6 to get 7. Everything checks out.

Key Concepts

Understanding Negative Numbers

Negative numbers can initially be a bit puzzling, but once you understand them, they become quite simple. In our everyday lives, we often think about numbers above zero, like 3, 4, 5, etc. These are positive numbers. Negative numbers are simply the ones below zero, on the opposite side of the number line. If you think of zero as a starting point, negative numbers, such as -1, -2, or -6, move to the left of zero.

Negative numbers typically come into play in various scenarios, such as temperatures below freezing, reductions in bank balances, or even decreases in any measured quantity. It's useful to remember that:

• A negative number plus another negative number results in a more negative number.
• When a positive number is added to a negative number, it's like moving in opposite directions on a number line.

Grasping the fundamental concept of negative numbers helps simplify how we handle arithmetic operations with them.

Basic Arithmetic Operations

Arithmetic operations are the building blocks of mathematics, allowing us to calculate and solve problems. The most basic operations include addition, subtraction, multiplication, and division. When performing these operations with negative numbers, there are a few key rules to bear in mind:

• Adding a negative number is like subtracting a positive one.
• Subtracting a negative number is equivalent to adding a positive one. This is because two negatives make a positive.

For example, the arithmetic operation in our exercise showed adding -4 to 17, giving us 13. Then, the key operation was adding -6 to this temporary sum, which made it crucial to understand that -6 means we take away 6 from 13. Thus, understanding these basic operations is vital for tackling problems involving both positive and negative numbers.

Effective Problem-Solving Steps

Successful problem-solving in math involves a series of logical steps, especially when dealing with negative numbers and various operations. Here are some strategies:

• **Read and Understand the Problem:** Clearly define what is being asked. In our case, the problem is about finding the total sum of the given numbers.
• **Organize the Calculation:** Break down the problem into manageable parts. We first added -4 to 17, followed by adding -6.
• **Perform Calculations Carefully:** Execute each step, considering the rules of adding and subtracting negative numbers.
• **Verify Your Result:** Double-check your calculations to ensure accuracy. Verification helps catch any errors promptly.

By following these steps, you can systematically approach math problems with confidence, ensuring you understand each part thoroughly and reach the correct solution.