Problem 15 - Prealgebra

Question

Subtract. $$-10-(-3)$$

Step-by-Step Solution

Answer

-7

Step 1: Understand the Problem

You need to subtract \(-3\) from \(-10\). This is a subtraction problem involving negative numbers.

Step 2: Subtraction Rule

Recall that subtracting a negative number is the same as adding its positive. So, \(-10 - (-3)\) is the same as \(-10 + 3\).

Step 3: Perform the Addition

Now, add \(-10\) and \(+3\). Calculating, \(-10 + 3 = -7\).

Step 4: Verify Your Answer

Check if \(-7\) is correct by considering the operations: Start at \(-10\); adding \(+3\) moves you towards zero, resulting in \(-7\), which confirms the answer.

Key Concepts

Subtraction

In mathematics, subtraction is one of the basic arithmetic operations. It involves finding the difference between two numbers or quantities. When dealing with negative numbers, subtraction might seem tricky at first because the rules adjust slightly. To make things simpler, imagine subtraction as removing or taking away. For instance, in the exercise, you started with

• -10

Subtracting a negative number like

• -3

from it. Now, it transforms into addition. Instead of removing something negative, think of it as gaining or moving forward. So, when you have a subtraction expression like

• -10 - (-3)

you actually add

• +3

to

• -10

. That is essentially how subtraction reacts when negatives are involved. Hence, always remember that subtracting negative is like adding a positive.

Integer Operations

Integer operations extend the basic arithmetic concepts to include negative numbers. Integers consist of positive numbers, negative numbers, and zero. When operating with integers, especially negative ones, understanding how to manage signs is crucial. Consider the expression

• -10 + 3

. Since

• -10

is negative, it represents a position 10 steps below zero. Add the positive

• 3

steps, which moves you back up three steps toward zero. Mathematically: \[-10 + 3 = -7\] It's helpful to visualize these operations on a number line. Visualizing gives a clear understanding of why you're getting

• -7

as the result. Always remember: Adding a positive number to a negative number reduces the negativity. Conversely, adding a negative number makes a total more negative.

Prealgebra Concepts

Prealgebra serves as a foundation to more advanced math concepts by introducing basic operations involving integers. It sets the stage for understanding how numbers interact together. In prealgebra, you often encounter operations involving negative integers which can cause confusion. Therefore, revisiting concepts such as the importance of understanding subtraction—not just as an operation, but as a way to adjust our numerical perspective—is key. Understanding the difference in

• -10 - (-3)

requires recognizing it as

• -10 + 3

under prealgebra principles. Grasping the relation between addition and subtraction helps solve seemingly complex problems by converting stories of debt (negative numbers) to gains. Thus, prealgebra aims to familiarize you with these fundamental operations which you will encounter in more complex algebraic equations. Whenever you're faced with problems involving different signs, always review the basic rules of integer operations to clear the pathway for solving them efficiently.