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Chapter 1: Problem 69

Subtract. $$ -7-14 $$

Short Answer

Expert verified
-21

Step by step solution

01

Understand the Problem

The task is to subtract 14 from -7. This can be written as -7 - 14.
02

Rewrite the Expression

When you subtract a number, it's the same as adding a negative number. So, -7 - 14 is the same as -7 + (-14).
03

Combine the Numbers

Add the two negative numbers together. -7 + (-14) = -21. When you add two negative numbers, you get a more negative number.

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Key Concepts

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

Negative Numbers
Negative numbers are simply numbers that are less than zero. They are often used to represent losses or decreases. For example, -5 can represent a 5-unit drop below zero. You can recognize a negative number by the minus sign (-) placed in front of it.
Negative numbers have some unique properties:
  • They are located to the left of zero on the number line.
  • When you add more negative numbers, the value becomes more negative.
  • Negative numbers are used in various real-life situations, like measuring temperature, accounting, or describing downward motion.
Understanding how to work with negative numbers is crucial for mastering other math concepts, including integer operations.
Subtracting Integers
Subtracting integers can be thought of as adding the opposite. For instance, subtracting 14 from -7 is the same as adding -14 to -7, written as -7 - 14 = -7 + (-14).
Here are some key points when subtracting integers:
  • Convert the subtraction into an addition of the opposite number, making it easier to handle.
  • Align the signs properly to understand the operation clearly.
    • Combining the numbers when both are negative means you are adding two negative values together.
Subtracting integers can at first seem tricky, but once you think of it as adding a negative, it becomes much easier to handle.
This method can simplify many math problems, leading to quicker and more accurate solutions.
Addition of Negatives
When you add negative numbers together, the result is always more negative. This is because you're accumulating more negative value. For example, in our exercise, we added -7 and -14:
-7 + (-14) = -21
This results in -21 since you are adding two negative values which deepen the negative value.
Here鈥檚 what to keep in mind when adding negatives:
  • Negative numbers further from zero have larger absolute values. So, more negatives mean a greater negative.
  • Using the number line can help visualize this process. Moving left from -7 by another 14 spaces ends at -21.
    • Understanding how to add negative numbers is essential for solving a wide range of math problems. Once you get the hang of this concept, other related arithmetic operations will become a lot simpler.

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