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Chapter 1: Problem 19

Fill in the blanks. To subtract a number, we _____ its ______.

Short Answer

Expert verified
To subtract a number, we add its opposite.

Step by step solution

01

Understanding the Subtracting Rule

To subtract a number, what we actually do is adding its negative (or its opposite). So, in this context, 'add' takes the place of the first blank, and 'opposite' takes the place of the second blank.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Operations with Integers
Performing operations with integers is a fundamental skill in algebra. Integers include negative numbers, positive numbers, and zero. To perform operations efficiently, it's important to understand each operation's nature.
  • Addition: Combine the values of the integers. If both integers are positive, their sum is positive, while if both are negative, their sum is negative.
  • Subtraction: Instead of subtracting a number directly, you can add its opposite. This concept is crucial, especially when working with negative numbers.
  • Multiplication: Multiply the absolute values of the numbers. If the signs are different, the result is negative, otherwise, it's positive.
  • Division: Similarly to multiplication, divide the absolute values and apply the rule of signs: different signs yield a negative, same signs yield a positive.
Understanding these operations simplifies calculations and helps you avoid common pitfalls, such as sign errors. Breaking down operations into clear steps and recognizing the role of each element are key strategies in mastering integers.
Subtraction
Subtraction might seem tricky, especially with integers, but it can be simplified by thinking of it in terms of addition. The principle for subtracting a number is to add its opposite. In practical terms:
  • Identify the number you want to subtract. For instance, if you have 8 - 3, think of this as 8 + (-3).
  • Replace subtraction with addition by changing the sign of the number being subtracted from positive to negative, or vice versa.
  • Continue with the addition. In our example, 8 + (-3) results in 5.
This method leverages your existing understanding of addition, making subtraction with integers more intuitive. It reduces errors by maintaining consistency in sign operations.
Negative Numbers
Negative numbers might initially seem confusing, but they are just numbers less than zero. Understanding how to work with them is crucial for solving algebra problems.
  • Understanding Negative Numbers: They represent values below zero and are typically used to depict debts or losses.
  • Adding Negative Numbers: Adding a negative number is the same as moving left on the number line. For instance, 5 + (-3) will move you 3 spaces left, landing on 2.
  • Subtracting Negative Numbers: Subtracting a negative number involves converting it into addition. For example, 5 - (-3) is equivalent to 5 + 3, resulting in 8. Essentially, subtracting negatives leads to higher values, as two negatives make a positive.
Once the concept of negative numbers clicks, integrating them into operations can become as straightforward as working solely with positive numbers.

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Most popular questions from this chapter

Subtract vertically. SEE EXAMPLE \(6 .\) (OB]ECTIVE 3 ) $$\begin{array}{r}-13 \\\\-\quad 5 \\\\\hline\end{array}$$

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