Question

1. steven multiplies all the integers from -99 to -90, including -99 and -90. should his answer be positive or negative? explain your thinking.

Explanation:

Step1: Count number of negative integers

Integers from -99 to -90: calculate the number of terms. The formula for the number of terms in an arithmetic sequence is $n = b - a + 1$, where $a=-99$, $b = -90$. So $n=-90-(-99)+1=-90 + 99+1 = 10$. So there are 10 negative integers.

Step2: Determine sign of product

The rule for multiplying negative numbers: when multiplying an even number of negative numbers, the product is positive; when multiplying an odd number of negative numbers, the product is negative. Since we have 10 (an even number) negative integers, their product will be positive.

Answer:

His answer should be positive.