Answer

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**Hint**: Here in this question, we have to simplify the given terms. The question contains more than one arithmetic operation so we use BODMAS rule. It is abbreviated as Brackets Of Division Multiplication Addition Subtraction. By applying the rule, we obtain the result.

**Complete step by step solution:**

Generally, we have 4 types of arithmetic operations namely

Addition (+) which adds the numbers.

Subtraction (-) which subtracts the numbers.

Multiplication (\[ \times \]) which multiplies the numbers.

Division (\[ \div \]) which divides the numbers.

To solve the above question, we follow the BODMAS rule and it is abbreviated as Brackets Of Division Multiplication Addition Subtraction. Here “of” signifies the operation multiplication. If we have “of” in the question we have to multiply.

We have to know about the sign conventions

\[ + \,\, \times \,\, + \,\, = \,\, + \]

\[ - \,\, \times \,\, - \,\, = \,\, + \]

\[ + \,\, \times \,\, - \,\, = \,\, - \]

\[ - \,\, \times \,\, + \,\, = \,\, - \]

Now we consider the given question

\[( - 16) + 14 - ( - 13)\]

First we apply the sign conventions and it is written as

\[ \Rightarrow - 16 + 14 + 13\]

On adding the number 14 and 13 we have

\[ \Rightarrow - 16 + 27\]

Here one term is a negative term and the other term is a positive term. Therefore we have to apply the subtraction.

On subtracting the number 16 from 27 we have

\[ \Rightarrow 11\]

In the solution we include the sign of the greatest number sign. Here the greatest number is 27 and its sign is +.

Therefore \[( - 16) + 14 - ( - 13)\] equals to 11

The option c) is the correct one.

**So, the correct answer is “Option c”.**

**Note**: Candidates must know about the arithmetic operations and tables of multiplication plays an important role in solving these types of questions. BODMAS rule is applied where the question involves more than one arithmetic operation. If we simplify randomically we don’t obtain the correct solution.

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