The property that is illustrated by the equation ax + ay = a ( x + y ) is Distributive property of multiplication over addition
Different Properties with examples:
Commutative Property
a. Addition. When two numbers are added, the sum is the same regardless of the order in which the numbers are added. 3 + 5 = 8 or 5 + 3 = 8
b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied. 3 x 5 = 15 or 5 x 3 = 15
Associative Property
a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped. 6 + (4 + 3) = 13 or (6 + 4) + 3 = 13
b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped. 6 x (4 x 3) = 72 or (6 x 4) x 3 = 72
Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number.
5 x (7 + 2) = 45 or 5 x 7 + 5 x 2 = 45
Identity Property
a. Addition. The sum of any number and zero is that number. 12 + 0 = 12
b. Multiplication, The product of any number and one is that number. 18 x 1 = 18
