Mathematics - Class ...

Key Points

Product of a positive integer and a negative integer without using number line

Steps

      1.   Multiply them as whole numbers.

      2.   Put a minus sign (–) before the product.

 

Product of two negative integers without using number line

Steps

       1.   Multiply the two negative integers as whole numbers.

       2.   Put the positive sign before the product because product of two negative integers is a positive integer.

 

Product of three or more Negative Integers

If the number of negative integers in a product is even, then the product is a positive integer; if the number of negative integers in a product is odd, then the product is a negative integer.

This means,

(a) The product of two negative integers is a positive integer.

(b) The product of three negative integers is a negative integer.

(c) Product of four negative integers is a positive integer.

 

Properties of Multiplication

      1.   Closure property under multiplication states the product of two integers will always be an integer.

      2.   Commutative property of multiplication states that swapping of terms will not change the product.

      3.   Associative property of multiplication states that the way of grouping of numbers will not change the result.   

      4.   Distributive property of multiplication explains the distributing ability of an operation over another mathematical operation within a bracket. It can be either distributive property of multiplication over addition or distributive property of multiplication over subtraction.  

      5.   This property of multiplication states that the product of any integer (positive or negative) and zero is zero.

      6.   Multiplicative identity property states that when we multiply one to any integer, we will get the integer itself as the product. 

 

The product of two negative integers or two positive integers is a positive integer.

The product of a positive integer and a negative integer is negative.

 

If the signs are different the answer is negative.

 

If the signs are alike the answer is positive.