Associative Law Definition

In mathematics, an associative law is defined as the law where a group of numbers associated in brackets is solved first. However, it doesn't matter what numbers we group because the resultant answer will be the same in every state.

For Instance, adding a number (10 + 5) + 5 is equivalent to adding 10 + (5 + 5) because in both term the answer we will get is 20.

An associative law implies the same for multiplication as like addition. For instance, multiplying (5 × 4) × 2 is equivalent to 5 × (4 × 2) as 20 × 2 = 5 ×8 = 40 In symbolical form, both law addition and multiplication associative law can be written as:

• a + (b + c) = (a + b) + c

• a . (b . c) = (a . b) . c

However, note that you cannot use this law for subtraction because the answer for grouping the same number can be different. For Instance, subtracting a number (10 - 5) - 5 = 5 - 5 = 0 Whereas 10 - (5 - 5) = 10 - 0 = 10, 10 is not equivalent to 0.