Question

1. You are given a problem that involves multiplying a positive number and a negative number. Which of the following are reasonable answers? Select all that apply.
[] -2
[] 2
[] -5
[] 5


2. Which of the following are reasonable answers for the product of two negative numbers and a positive number? Select all that apply.

[] 20
[] 10
[] -20
[] -10

Answer 1

Answer:

1) -2, -5

2) 20, 10

Step-by-step explanation:

We are given the following information in the question:

The product of two integers can be done in the following manner:

Product of a positive number and a positive number is positive.

$(+)\times (+) = (+)$

Product of a positive number and a negative number is negative .

$(+)\times (-) = (-)$

Product of a negative  number and a positive number is negative .

$(-)\times (+) = (-)$

Product of a negative  number and a negative  number is positive.

$(-)\times (-) = (+)$

1) Multiplication of a positive number with a negative number

-2, -5

Because the product will be negative.

2) Multiplication of two negative numbers and positive number

20, 10

Because the product of two negative will be a positive and product of two positive number is positive.

Answer 2

The multiplication of numbers with opposite signs is negative, while the multiplication of numbers with the same sign is positive:

• $(+) \cdot (+) = (+)$
• $(+) \cdot (-) = (-)$
• $(-) \cdot (+) = (-)$
• $(-) \cdot (-) = (+)$

So, the multiplication of a positive number and a negative number must be negative, and the only feasible answers are -2 and -5.

Similarly, if you multiply two negative numbers and a positive number, the two negative numbers will give a positive number as a result, and then when you multiply it by a positive number, you still have a positive number:

$[\ (-) \cdot (-)\ ] \cdot (+) = (+) \cdot (+) = (+)$