Question

Solve the following
(i) \[\left( -7 \right)\times \left( -3 \right)=\]
(ii) \[\dfrac{16}{\left( -8 \right)}=\]

Answer 1

Hint: First of all students must recall the BODMAS rule and different rules like \[\left( -a \right)\times \left( b \right)=-ab\] or \[\left( -a \right)\times \left( -b \right)=ab\] or \[\dfrac{a}{\left( -b \right)}=-\left( \dfrac{a}{b} \right)\]. Now use these rules to find the desired value of the given expression.

Complete step by step answer:
In this question, we have to find the value of
(i) \[\left( -7 \right)\times \left( -3 \right)=\]
(ii) \[\dfrac{16}{\left( -8 \right)}=\]
Before proceeding with this question, we must know some basic mathematical operations and BODMAS rules. The BODMAS rule tells us the order of operations like addition, division, multiplication, etc while solving any equation. BODMAS is an acronym for BRACKET, OF, DIVISION, MULTIPLICATION, ADDITION, and SUBTRACTION. According to the BODMAS rule, if any expression contains a bracket, we first have to solve or simplify the bracket followed by (powers of the roots, etc.), then division, multiplication, addition, and subtraction from left to right.
Also, in mathematics, if we have two positive numbers a and b, then there are certain rules while performing multiplication of these numbers that are,
\[\Rightarrow \left( -a \right)\times \left( -b \right)=+\left( a\times b \right)\]
\[\Rightarrow \left( -a \right)\times \left( b \right)=-\left( a\times b \right)\]
\[\Rightarrow \left( a \right)\times \left( -b \right)=-\left( a\times b \right)\]
\[\Rightarrow \left( a \right)\times \left( b \right)=+\left( a\times b \right)\]
Similar rules are valid for the division as well, they are,
\[\Rightarrow \dfrac{-a}{-b}=+\left( \dfrac{a}{b} \right)\]
\[\Rightarrow \dfrac{-a}{b}=-\left( \dfrac{a}{b} \right)\]
\[\Rightarrow \dfrac{a}{-b}=-\left( \dfrac{a}{b} \right)\]
\[\Rightarrow \dfrac{a}{b}=+\left( \dfrac{a}{b} \right)\]
Now, let us consider our question
(i) \[\left( -7 \right)\times \left( -3 \right)\]
We know that \[\left( -a \right)\times \left( -b \right)=+\left( a\times b \right)\]. By using this expression, we get,
\[\left( -7 \right)\times \left( -3 \right)=+\left( 7\times 3 \right)\]
By simplifying the RHS of the above equation, we get,
\[\left( -7 \right)\times \left( -3 \right)=+21=21\]
(ii) \[\dfrac{16}{\left( -8 \right)}\]
We know that \[\dfrac{a}{-b}=-\left( \dfrac{a}{b} \right)\]. By using this in the above expression, we get,
\[\dfrac{16}{\left( -8 \right)}=-\left( \dfrac{16}{8} \right)\]
By simplifying the RHS of the above equation, we get,
\[\dfrac{16}{-8}=-\left( 2 \right)=-2\]
So, we finally get,
(i) \[\left( -7 \right)\times \left( -3 \right)=21\]
(ii) \[\dfrac{16}{\left( -8 \right)}=-2\]

Note: In these types of questions, students get confused between – a – b and (– a) \[\times \] (– b). So, students must note that – a – b is equal to – (a + b) while (– a) \[\times \] (– b) is equal to ab. Some students make this mistake of writing – a – b as a + b by considering (–) \[\times \] (–) = (+) but they must note that this is valid for only multiplication and division and not for addition, subtraction, etc. Also, students must solve the question according to the BODMAS rule in order to get the correct answer.