ISEE Upper Level Mathematics Achievement Flashcards: Integer Operations

What this deck covers

This deck focuses on Integer Operations, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer: 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Flashcard 17: What is the value of $0 imes(-19)$?

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

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

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

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

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

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

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

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

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

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

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

Flashcard 23: What is the value of $-11-7$?

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

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

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

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

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