Question

Simplify the following expression.
\[25+14~\div \left( 5-3 \right)\]

Answer 1

Hint: To solve this question, we need to recollect the concept of order of operations of algebraic equations. First of all, we will define the order of expressions and see in what conditions it is applied. We will go step by step applying the operations to finally get an answer.

Complete step-by-step answer:
The order of operations is a set of rules for how to evaluate or simplify an algebraic expression. It is a standard form and hence everyone who simplifies the expression gets the same answer.
The first priority is always given to parentheses. In simple language, they are known as round brackets. This means whenever an expression has more than one kind of operations, we need to perform the operations inside the parentheses.
Next is exponents. Exponents means the powers of a number. For example, ${{2}^{2}}$ is an exponent. They are given second priority.
This is followed by multiplication and division. Once operations inside parentheses are executed and exponents are solved, we execute multiplication and division. Both of these have priority and can be solved simultaneously.
At last, we execute addition and subtraction.
The expression given to us is as follows: \[25+14~\div \left( 5-3 \right)\]
There is a parenthesis in this expression. Therefore, we will carry out the operation inside the parenthesis.
The operation inside the parenthesis is subtraction of 3 from 5, which yields 2.
The expression modifies as follows: \[25+14~\div 2\]
Now, there are no exponents, so will go down to multiplication and division. In our expression, we have a division. Thus, we will divide 14 by 2, which gives the quotient as 7.
The expression now is \[25+7\]
Now, only addition is left. We need to add 7 to 25. This will yield 32.
Therefore, \[25+14~\div \left( 5-3 \right)=32\].

Note: If the expression has the same operation more than once, then we must solve the expression from left to right. Students can memorize this order as PEMDAS (pronounced as it is spelled).