Multiplying & Dividing Rational Numbers - Pre Algebra

1. What is $(-2)(-3)(-1)$?

   $-6$. There are three negative factors, an odd number, so the product is negative.

2. What is $(-1.5)(4)$?

   $-6$. The signs differ, and $1.5 \times 4 = 6$.

3. What is $-6 \times 4$?

   $-24$. The signs differ, so the product is negative.

4. What is $45 \div (-5)$?

   $-9$. The signs differ, so the quotient is negative.

5. Which two of these equal $\frac{-3}{4}$: $\frac{3}{-4}$, $-\frac{3}{4}$, $\frac{-3}{-4}$?

   $\frac{3}{-4}$ and $-\frac{3}{4}$. One negative sign makes the quotient negative, while $\frac{-3}{-4} = \frac{3}{4}$.

6. What is $-8 \times (-5)$?

   $40$. The signs are the same, so the product is positive.

7. What is the sign of a product of five negative numbers?

   Negative. A product with an odd number of negative factors is negative.

8. What is $-\frac{1}{2} \div \left(-\frac{1}{4}\right)$?

   $2$. Compute $-\frac{1}{2} \cdot (-4) = 2$.

9. What is the sign of the product or quotient of two numbers with different signs?

   Negative. For example, $(-4)(2) = -8$ and $8 \div (-2) = -4$.

10. What is $-\frac{2}{3} \times \frac{3}{4}$?

    $-\frac{1}{2}$. Compute $\frac{6}{12}$ and make it negative.

11. What is $-36 \div (-9)$?

    $4$. The signs are the same, so the quotient is positive.

12. What is the sign of the product or quotient of two numbers with the same sign?

    Positive. For example, $(-4)(-2) = 8$ and $(-8) \div (-2) = 4$.

Study these flashcards