Dividing integers involves applying the rules of signs alongside standard division. The core of integer division relies on understanding how positive and negative signs interact.
Rules for Dividing Integers
The sign of the quotient (the result of division) depends on the signs of the dividend (the number being divided) and the divisor (the number doing the dividing). Here's a summary:
| Dividend Sign | Divisor Sign | Quotient Sign | Example |
|---|---|---|---|
| Positive | Positive | Positive | 10 / 2 = 5 |
| Negative | Negative | Positive | -10 / -2 = 5 |
| Positive | Negative | Negative | 10 / -2 = -5 |
| Negative | Positive | Negative | -10 / 2 = -5 |
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Same Signs, Positive Result: When both the dividend and the divisor have the same sign (both positive or both negative), the quotient is always positive.
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Example: -10 / -2 = 5
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Different Signs, Negative Result: When the dividend and divisor have different signs (one positive and one negative), the quotient is always negative.
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Example: -10 / 2 = -5 or 10 / -2 = -5
Practical Examples:
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Scenario 1: You have a debt of $15, which you decide to split equally between 3 friends. Each friend will owe you a portion of that debt which is shown as -15 / 3 = -5. Each friend owes you $5.
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Scenario 2: If you have a $20 gift card and want to buy some $5 items, the division would be 20 / 5 = 4, you will be able to buy 4 items.
Key takeaway from reference:
As explained in the referenced YouTube video, when dividing a negative number by a positive number (or a positive number by a negative number), you will get a negative result: "So we have negative divided by a positive. So different signs equals negative quotient." Therefore, if you divide -10 by 2, the result will be -5.
In summary, the key to dividing integers lies in dividing the absolute values of the numbers and then applying the rules for signs to determine the final quotient's sign.
