Question

Solve: $5 - 3\dfrac{3}{4}$

Answer 1

Hint: Given question is a Subtraction of two rational numbers using LCM method. LCM stands for Least Common Multiple. In this problem we will be using LCM as following way,
$ \Rightarrow \dfrac{a}{b} \pm \dfrac{c}{d} = \dfrac{{a \times d \pm c \times b}}{{b \times d}}$_ _ _ _ _ _ _ _ _$\left( 1 \right)$

Complete step-by-step answer:
Given problem is $5 - 3\dfrac{3}{4}$,
We can write $3\dfrac{3}{4}$as $\dfrac{{12 + 3}}{4} \Rightarrow \dfrac{{15}}{4}$because,
$\left[ {a\dfrac{b}{c}} \right] = \dfrac{{(a \times c) + b}}{c}$.
So, that becomes,
$ \Rightarrow 5 - \dfrac{{15}}{4}$
By using $\left( 1 \right)$,
$ \Rightarrow \dfrac{{20 - 15}}{4}$
$ \Rightarrow \dfrac{5}{4}$.
Therefore, by using the LCM method the solution is$ \Rightarrow \dfrac{5}{4}$.

Note: The Difference between any two Rational Numbers always results in a Rational Number. Let $\dfrac{a}{b},\dfrac{c}{d}$ be two Rational Numbers then $\left( {\dfrac{a}{b} - \dfrac{c}{d}} \right)$ will also result in a Rational Number.
$ \Rightarrow $Subtraction of Two Rational Numbers doesn’t obey Commutative Property. Let us consider$\dfrac{a}{b},\dfrac{c}{d}$ be two rational numbers then $\dfrac{a}{b} - \dfrac{c}{d} \ne \dfrac{c}{d} - \dfrac{a}{b}$.Have a look at the Example stated below and verify whether the commutative property is applicable or not.
$ \Rightarrow $Subtraction of Rational Numbers is not Associative. Let us consider$\dfrac{a}{b},\dfrac{c}{d}$$,\dfrac{e}{f}$ three Rational Numbers then $\left[ {\dfrac{a}{b} - \left( {\dfrac{c}{d} - \dfrac{e}{f}} \right)} \right]$$ \ne \left( {\dfrac{a}{b} - \dfrac{c}{d}} \right) - \dfrac{e}{f}.$