Integers: The Complete Number System: 20 flashcards
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1. What is the set of integers?
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Whole numbers with negatives: $\{\dots, -2, -1, 0, 1, 2, \dots\}$ — no fractions or decimals.
2. Is zero positive, negative, or neither?
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Zero is an integer but is neither positive nor negative.
3. How does the number line order integers?
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Left to right: numbers further left are smaller, numbers further right are larger.
4. What is absolute value $|x|$?
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The distance of $x$ from $0$ on the number line; it is always non-negative.
5. What are opposites in integers?
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Two numbers the same distance from $0$ on opposite sides, e.g. $5$ and $-5$; they have equal absolute value.
6. Rule for adding two integers with the same sign?
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Add their absolute values and keep the common sign: $(-4)+(-6)=-10$.
7. Rule for adding two integers with different signs?
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Subtract the smaller absolute value from the larger, and take the sign of the number with the larger absolute value: $(-9)+4=-5$.
8. Rewrite subtraction as addition.
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$a - b = a + (-b)$ — subtracting is adding the opposite.
9. Simplify $7 - (-3)$.
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$7 + 3 = 10$ — two consecutive minus signs combine into a plus.
10. Sign of the product of two integers with the same sign?
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Positive: $(+)\times(+)=+$ and $(-)\times(-)=+$.
11. Sign of the product of two integers with different signs?
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Negative: $(+)\times(-)=- $ and $(-)\times(+)=-$.
12. Do division sign rules match multiplication?
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Yes — division follows the same sign rules: same signs give positive, different signs give negative.
13. What is $n \div 0$?
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Undefined — division by zero is not allowed.
14. What does multiplying by $-1$ do on the number line?
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It reverses direction — flips the number to its opposite.
15. Does BODMAS/PEMDAS change for integers?
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No — the order of operations is unchanged; signs only change the values.
16. Give three real-world uses of integers.
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Temperature above/below zero, bank balance (deposits/withdrawals), elevation above/below sea level (also profit/loss).
17. Is every natural number an integer? Is every integer a natural number?
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Every natural number is an integer, but not every integer is a natural number (negatives are not).
18. Why is every integer a rational number?
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Because $n = \frac{n}{1}$, so every integer can be written as a fraction of integers.
19. What is the sum of an integer and its opposite?
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Zero: $a + (-a) = 0$.
20. What is the product of any integer and zero?
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Zero.
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