Question

Write the rules for determining the sign of the product when multiplying integers. Then, write the rules for determining the sign of the quotient when dividing integers. Use your own words and use complete sentences. Make sure you answer both questions presented in this problem. 

(I completed this, no need to answer unless it is for other people's sake)

Answer 1

Integers=[Positive Natural Numbers +Negative Natural Numbers +Zero]

={---------,-3,-2,-1,0,1,2,3,4,...........}

⇒Suppose A and B are two integers.

If any of the A and B are Negative , then the product of the two integers will be negative.

If Both A and B are Negative, or Both A and B are Positive,then Product will be positive.

`\rightarrow A * B=C\\\\\rightarrow -A * B=-C\\\\\rightarrow A * -B=-C\\\\\rightarrow -A * -B=C`

⇒For, Division ,same rule Applies,if any of the A and B is Negative, the division yields Negative Quotient While if both A and B are Negative or Both are Positive ,the Quotient will be positive.

`\rightarrow(-A)/(B)=-C\\\\\rightarrow(A)/(-B)=-C\\\\\rightarrow(-A)/(-B)=C\\\\\rightarrow(A)/(B)=C`

Answer 2

An integer is a number that comprises of natural numbers like 0,1,2,3,4... so on and negative whole numbers like -1,-2,-3 and so on.

Multiplication Rules:

1. Product of two positive integers is always POSITIVE.

Eg:
`8\ast 6=48`

2. Product of two negative integers is always POSITIVE.

Eg:
`-7\ast -3=21`

3. Product of a negative integer and a positive integer is always NEGATIVE.

Eg:
`5\ast -4=-20`

Quotient Rules:

1. Positive integer divided by a positive integer is always POSITIVE.

Eg:
`(64)/(8)=8`

2. Positive integer divided by negative integer or negative integer divided by a positive integer is always NEGATIVE.

Eg:
`(63)/(-3)=-21`

3. Negative integer divided by a negative integer is always POSITIVE.

Eg:
`(-20)/(-4)=5`