What is the product of 1 2/3 and −3 1/2 ? a. −5 5/6 b.−3 1/3 c.3 1/3 d.5 5/6

Hi there! First off, let's transform the mixed numbers into improper fractions by multiplying the denominator and whole number together, then adding the numerator. So in this case, 1 2/3 is 5/3 as an improper fraction, because 3 * 1 is 3. 3 + 2 is 5. -3 ½ is -7/2 as an improper fraction, because 2 * 3 is 6 and 6 + 1 is 7. Keep in mind that even after those steps, you keep the denominator the same in the improper fraction. For negative mixed numbers, don't incorporate the negative symbol when multiplying.
Now, we multiply those fractions. To multiply fractions, all you have to do is multiply straight across. That means multiplying the numerators together and the denominators together. 5/3 * -7/2 is -35/6 or -5 5/6 in mixed number form. There. The product is -5 5/6. The answer is A: -5 5/6.

Note: Whenever you have a negative and a positive number in any occasion of multiplication and division, the answer will ALWAYS be negative. There are no exceptions to that rule. That automatically eliminated answer choices C and D.