Problem 22 - Prealgebra

Question

Subtract. $$-50-60$$

Step-by-Step Solution

Answer

The result of \(-50 - 60\) is \(-110\).

Step 1: Understanding the Problem

We need to subtract two numbers: \(-50\) and \(60\). This involves combining the terms with their signs taken into account.

Step 2: Rewriting the Expression

Rewriting the expression with the second number as a negative gives us: \(-50 + (-60)\). Subtracting \(60\) is the same as adding \(-60\).

Step 3: Adding Negative Numbers

To solve \(-50 + (-60)\), we combine the negative numbers. Adding two negative numbers results in a negative sum.

Step 4: Calculating the Sum

Combine the numbers by adding their absolute values and keeping the negative sign: \(-50 - 60 = -(50 + 60) = -110\).

Key Concepts

Understanding Negative Numbers

Negative numbers can be a bit tricky at first, but they are simply numbers with a minus sign in front of them. In math, they are used to represent values below zero. You can think of them as representing the concept of going backwards or losing something.
For example, if you say you owe someone $50, you might think of that amount as 50$. This means you're essentially 50 units below zero because you haven't paid back the money yet.

Understanding how negative numbers work is essential, especially when it comes to calculating things like temperature differences or altitude changes. An easy way to grasp negative numbers is to imagine a number line.

• Positive numbers are to the right of zero.
• Negative numbers are to the left of zero.

To subtract negative numbers correctly, it's crucial to remember that the further left a number is on the number line, the smaller (or more negative) it is. This will help you avoid errors when dealing with them. By mastering negative numbers, you will also find integer operations easier to handle.

Mastering Integer Addition

Adding integers goes hand in hand with understanding negative numbers. Integers include zero, positive numbers (like 1, 2, 3), and negative numbers (like -1, -2, -3).
Let's break it down with some steps:

• If the signs are the same (both positive or both negative), you add their absolute values, and the sum takes the common sign.
• If the signs are different, subtract their absolute values, and give the result the sign of the larger absolute value.

For example, adding -50 and -60 means you look at the absolute values, 50 and 60. You then add these numbers to get 110. Since both starting numbers were negative, the result is also negative, giving you -110.

Remember, like charges, negatives and positives can cancel each other out. For instance, if you add +8 and -8, you end up with zero. Practicing with these rules regularly will make integer addition second nature.

Exploring Arithmetical Operations

Arithmetical operations include the basic functions of addition, subtraction, multiplication, and division. Understanding how they work, especially with different types of numbers, is key to succeeding in math.
Let's dive into subtraction and its intricacies:

• Subtraction traditionally means taking away, but with negative numbers, it gets interesting.
• Subtracting a positive number from a negative number is the same as adding the corresponding negative number.

For instance, in the problem 50 - 60, subtracting 60 is treated as adding -60. This translates to a problem of addition where you add two negative numbers, resulting in a larger negative number.

A subtle yet powerful concept: subtracting a negative number is like adding a positive. (For example, -5 - (-3) becomes -5 + 3). This unique property emphasizes the importance of combining different operations to solve complex math challenges efficiently. By regularly practicing different scenarios and learning these operations' rules, you will grow confident in tackling any arithmetic problem.