Question

How do you simplify \[21 + 6 + 9\]?

Answer 1

Hint: In the given question, we have been asked to solve the given question by using the operation addition. In order to proceed with the following question we need to be aware of the Associative property. Associative property says that we can add or multiply in any order i.e. any group of numbers can be added or multiplied before others; it does not lead to change in value of sum. Grouping basically means putting brackets to group numbers. The numbers grouped in a bracket are counted as one unit. For example:
 $ a + (b + c) = (a + b) + c = m $
 $ a,b,c $ are called addends.
After associative property, we have to make use of the BODMAS rule. BODMAS is an acronym for the terms Brackets, Orders, Division, Multiplication, Addition and Subtraction. This rule states that if an expression contains brackets then solve the brackets in order, then division, multiplication, addition and subtraction.

Complete step by step solution:
Given,\[21 + 6 + 9\]
 $ \Rightarrow (21 + 6) + 9 $
,as stated in BODMAS rule.
 $
   \Rightarrow 27 + 9 \\
   \Rightarrow 36 \;
  $
Alternate method: Changing of group while adding does not change the value of sum.
 $ \Rightarrow 21 + (6 + 9) $
First we’ll solve the brackets, as stated in BODMAS rule.
 $
   \Rightarrow 21 + 15 \\
   \Rightarrow 36 \;
  $
This is the required answer.
So, the correct answer is “36”.

Note: Associative property can be applied only if there or 3 or more numbers. Also it can only be applied while multiplication or division. It cannot be applied to subtraction or division, since order becomes an important part of those operations. The order of brackets should be (), {}, []. Parentheses is another word for brackets. There are two more properties which form the backbone of mathematics- Commutative property and Distributive property.