Question

Solve the following:
(a) $( - 13) \div [( - 30) + ( - 1)]$
(b) $[( - 6) + 5] \div [( - 2) + 1]$

Answer 1

Hint: We need to know the BODMAS rule to solve this question. The full form of BODMAS is Brackets (Parts of a calculation inside the bracket always come first), Precedence of brackets are : $\text{[{(  )}]}$, Orders (powers and square roots), Division, Multiplication, Addition and Subtraction.
If an expression involves two or more similar operators that appear in succession, then the precedence is from left to right. By using BODMAS, we can evaluate an expression in the correct order of precedence.

Complete step by step solution:
a) Now, we will solve the equation $( - 13) \div [( - 30) + ( - 1)]$ using BODMAS
$ ( - 13) \div [( - 30) + ( - 1)]$
We have removed brackets () and simplified the equation as we know that the product of minus and plus sign gives us minus.
$ \Rightarrow ( - 31) \div [ - 30 - 1]$
$ \Rightarrow ( - 31) \div [ - 31]$
We know that when a number is divided by itself, we get 1
$\Rightarrow 1$
$\therefore ( - 13) \div [( - 30) + ( - 1)] = 1$

b) We will now solve the equation $[( - 6) + 5] \div [( - 2) + 1]$ using BODMAS
$ [( - 6) + 5] \div [( - 2) + 1]$
We have simplified the equations inside the brackets,
$ \Rightarrow [ - 1] \div [ - 1]$
We know that when a number is divided by itself, we get 1
$\Rightarrow 1$
$\therefore [( - 6) + 5] \div [( - 2) + 1] = 1$

Note:
> While solving these types of problems, we should always follow the rule of BODMAS. We have to take care of the order of preference of brackets as it may also create confusion.
> There is another rule named PEDMAS. PEDMAS stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.