Integer Operations - ISEE Upper Level Mathematics Achievement

1. What is the value of $-7+12$?

   $5$. Adding a larger positive to a smaller negative yields a positive result after subtracting absolute values.

2. What is the sign of the sum when adding two negative integers, $-a$ and $-b$ where $a,b>0$?

   Negative. Adding two negative integers results in a negative sum because both decrease the value from zero.

3. What is the value of $-42\div 6$?

   $-7$. A negative dividend divided by a positive divisor results in a negative quotient.

4. What is the value of $9-(-4)$?

   $13$. Subtracting a negative is equivalent to adding the positive counterpart.

5. What is the sign of the quotient when dividing two integers with the same sign?

   Positive. Dividing integers with the same sign produces a positive quotient.

6. What is the value of $-2(7-10)$?

   $6$. Evaluate inside parentheses first, then multiply, with negative times negative yielding positive.

7. What is the rule for adding integers with different signs (for example, $a+(-b)$)?

   Subtract absolute values; keep the sign of the greater absolute value. When adding integers with opposite signs, subtract the absolute values and take the sign of the number with the larger absolute value.

8. What is the value of $(-3)(-7)(2)$?

   $42$. Even number of negatives in multiplication yields a positive product.

9. What is the sign of the product when multiplying two integers with the same sign?

   Positive. Multiplying integers with matching signs produces a positive result.

10. What is the sign of the sum when adding two positive integers, $a$ and $b$?

    Positive. The sum of two positive integers is always positive since both values increase the total from zero.

11. What is the value of $(-81)\div(-9)$?

    $9$. Dividing two negatives gives a positive quotient of their absolute values.

12. What is the value of $-15+(-6)$?

    $-21$. Summing two negatives combines their magnitudes with a negative sign.

13. What is the value of $-24\div 3 + 5$?

    $-3$. Perform division first per order of operations, then add the result.

14. What is the value of $18+(-23)$?

    $-5$. The larger absolute value of the negative determines the negative sign after subtraction.

15. What is the sign of the quotient when dividing two integers with different signs?

    Negative. Division of integers with opposite signs yields a negative quotient.

16. What is the value of $-5-(-16)$?

    $11$. Subtracting a negative from a negative adds the positive, potentially changing the sign.

17. What is the value of $0\times(-19)$?

    $0$. Multiplication by zero always results in zero regardless of the other factor.

18. What is the value of $56\div(-8)$?

    $-7$. A positive dividend divided by a negative divisor produces a negative quotient.

19. What is the sign of the product when multiplying two integers with different signs?

    Negative. The product of integers with opposite signs is always negative.

20. What is the rule for rewriting subtraction of integers, $a-b$, as addition?

    $a-b=a+(-b)$. Subtraction is redefined as adding the additive inverse of the subtrahend.

21. What is the additive inverse of an integer $n$?

    $-n$. The additive inverse is the opposite sign that sums to zero with the original integer.

22. What is the value of $(-6)(-4)$?

    $24$. Multiplying two negatives yields a positive product of their absolute values.

23. What is the value of $-11-7$?

    $-18$. Subtracting a positive from a negative is adding a negative, increasing the magnitude.

24. What is the value of $(-8)(5)$?

    $-40$. A negative multiplied by a positive results in a negative product.

25. What is the value of $n+(-n)$ for any integer $n$?

    $0$. An integer added to its additive inverse cancels out to zero.

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