Positive numbers are greater than zero, while negative numbers are less than zero and indicated by a minus sign (e.g., -10). Let’s explore how to visualize, add, subtract, multiply, and divide them.
Visualizing Negative and Positive Numbers
- Number Line:
- A horizontal line helps visualize positive (right) and negative (left) numbers.
- Adding: Move right.
- Subtracting: Move left.
- Example:
- ( 10 - 25 = -15 ) (move 25 steps left from 10).
- ( -17 + 23 = 6 ) (move 23 steps right from -17).
Rules for Subtracting Negative Numbers
- Subtracting a Negative Equals Adding:
- ( -10 - (-10) = -10 + 10 = 0 ).
- Tip: Brackets clarify the operation ( -10 - (-10) ).
Multiplying and Dividing Positive and Negative Numbers
- Basic Rule:
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Ignore the signs initially. Multiply or divide the numbers as usual. Then, apply the sign rule:
- Same Signs: Positive result.
- ( (+) * (+) = (+) ), ( (-) * (-) = (+) ).
- Different Signs: Negative result.
- ( (+) * (-) = (-) ), ( (-) * (+) = (-) ).
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Extended Rule:
- Even Number of Negatives: Positive result.
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Odd Number of Negatives: Negative result.
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Examples:
- ( -5 * 25 = -125 ) (one negative).
- ( -50 \div -5 = 10 ) (two negatives).
- ( 10 * -2 * 3 = -60 ) (odd negatives).
Why Does ( (-) * (-) = (+) )?
- Using a Number Line:
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Facing negative direction and moving backwards results in moving towards positive numbers.
- Example: Facing left (negative) and stepping backward lands you in positive territory.
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Double Negatives Cancel Out:
- In speech:
- "Don't not do it" = "Do it!"
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In math: Two negatives combine to form a positive.
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Adding Signs Visually:
- Two negative signs can "flip" to create a positive. One negative and one positive leave a single negative.
Key Points to Remember
- Subtracting a negative is equivalent to adding.
- Multiplication/division: Same signs positive, different signs negative.
- Practice using a number line or visual aids to reinforce these concepts.
Understanding these rules makes working with negative numbers straightforward and intuitive!