Question

If a and b are integers and the expression ab is positive, what do you know about the signs of a and b?

Short answer

The signs of a and b will be same. Either both are positive or negative.

Step-by-step solution

Step-1 – Apply the concept of product

In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. The numbers that are being multiplied are called the factors and the product of two numbers is the result you get when you multiply them together.

Step-2 – Rule and examples of multiplication of integers 

Multiplication of Integers

RULE 1: The product of a positive integer and a negative integer is negative.

RULE 2: The product of two positive integers is positive.

RULE 3: The product of two negative integers is positive.

Type of Numbers	Result	Example
Positive × Positive	Positive	1 × 5 = 5
Negative × Negative	Positive	(-1) × (-5) = 5
Positive × Negative	Negative	1 × (-5) = -5
Negative × Positive	Negative	(-1) × 5 = -5

Step-3 – If a and b are integers and their product is positive ab, what do you know about the signs of a and b?

RULE 1: The product of a positive integer and a negative integer is negative.

The product of two integers with the same signs is positive.

Product of two positive integers is positive.

Example: Find the product: $6 · 8$

6 and 8 both are positive, their product is also positive.

Example: Find the product: – 6 (– 8)

6 is negative and 8 is also negative, so the answer will be positive.

– 6 (– 8) = + 48

The integers both a and b are either positive or negative.