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Chapter 1: Problem 12

The sum of two negative numbers is a _____ number.

Short Answer

Expert verified
negative

Step by step solution

01

Understanding Negative Numbers

Negative numbers are less than zero. They are the opposite of positive numbers.
02

Rules of Addition for Negative Numbers

When two negative numbers are added together, the result is also a negative number. This follows from the fact that when you move left on the number line (which symbolizes adding a negative number), you're getting further away from zero and thus adding more negativity.
03

Applying Rule to Solve the Question

Based on the rule, the sum of two negative numbers will always be a negative number.

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Key Concepts

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

Addition Rules for Negative Numbers
When dealing with the addition of negative numbers, there are specific rules to follow. Negative numbers lie below zero on the number line and represent values less than zero. Thus, when adding two negative numbers, you are essentially adding their magnitudes while keeping the sign negative.

Suppose you have two numbers, \(-3\) and \(-4\). If you add these by the rules of addition, you'll first add their absolute values. So, \(3 + 4 = 7\). Since both numbers are negative, the result remains negative. This means \(-3 + (-4) = -7\).

To sum it up:
  • When adding two negative numbers, add their absolute values.
  • The result will always be negative.
Mastering this rule will help you handle negative number operations more effectively.
Using the Number Line for Understanding
A number line is a straightforward tool that can help visualize the process of adding negative numbers. On a number line, you move left when dealing with negative numbers because you're moving further away from zero.

Consider adding \(-2\) and \(-3\):
  • Start at \(0\) on the number line.
  • Move 2 spaces to the left to represent \(-2\).
  • Next, move 3 more spaces to the left for \(-3\).
  • You will land on \(-5\).
The number line effectively demonstrates why the sum of two negative numbers is a larger negative number. This visual movement showcases how you accumulate more negativity by moving further left.
Understanding Integer Operations
Integer operations encompass various arithmetic actions involving whole numbers, both positive and negative. Adding negative numbers is a part of these operations and builds a foundation for understanding more complex math concepts.

Here are some key points about integer operations:
  • Integers include positive numbers, negative numbers, and zero.
  • Addition of integers follows specific rules, particularly when negatives are involved.
  • Subtracting a negative is equivalent to adding its positive counterpart.
Developing a solid grasp of integer operations helps in solving algebraic expressions and troubleshooting potential math hurdles. Always remember, practicing these operations will make them more intuitive and natural over time.

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