Question

How do you express $7\dfrac{3}{5}+-4.8$, as a simplified fraction?

Answer 1

Hint: In this question we have to simplify the expression in the form of a simplified fraction. To do this we will first consider the first term which is $7\dfrac{3}{5}$ which is a mixed fraction which we will convert into an improper fraction. Then we will convert the decimal term $-4.8$ into a simplified fraction. We will then add both the fractions and solve them by taking the lowest common multiple and simplifying the terms to get the required solution.

Complete step-by-step solution:
We have the expression given to us as:
$\Rightarrow 7\dfrac{3}{5}+-4.8\to (1)$
Consider the first term in the expression:
$\Rightarrow 7\dfrac{3}{5}$
The term is in the format of a mixed fraction therefore, we have to convert it into a simplified fraction. The method over here is that we have to keep the denominator as it is, there will be changes in the numerator only while converting.
We have to multiply the denominator of the fraction with the whole number and add whatever there is in the numerator, it can be written as:
$\Rightarrow \dfrac{\left( 5\times 7 \right)+3}{5}$
On simplifying the brackets, we get:
$\Rightarrow \dfrac{35+3}{5}$
On simplifying the numerator, we get:
$\Rightarrow \dfrac{38}{5}\to (2)$
Consider the second term in the expression:
$\Rightarrow -4.8$
Now the term can be written as:
$\Rightarrow -\left( 4+0.8 \right)$
Now since the term $0.8$ is a decimal term, we will multiply and divide it by $10$ so that the decimal can be removed. On substituting, we get:
$\Rightarrow -\left( 4+0.8\times \dfrac{10}{10} \right)$
On simplifying, we get:
$\Rightarrow -\left( 4+\dfrac{8}{10} \right)$
On taking the lowest common multiple, we get:
$\Rightarrow -\left( \dfrac{4\times 10+8}{10} \right)$
On simplifying the numerator, we get:
$\Rightarrow -\dfrac{48}{10}\to (2)$
Now on substituting equation $(2)$ and $(3)$ in equation $(1)$, we get:
$\Rightarrow \dfrac{38}{5}+\left(-\dfrac{48}{10} \right) $
On simplifying the sign, we get:
$\Rightarrow \dfrac{38}{5}-\dfrac{48}{10}$
On taking the lowest common multiple, we get:
$\Rightarrow \dfrac{76-48}{10}$
On simplifying, we get:
$\Rightarrow \dfrac{28}{10} = 2\dfrac{4}{5} $, which is the required solution.

Note: In the answer we can see that the numerator which is $28$, which is greater than the denominator which is $10$ therefore, it satisfies the condition of being an improper fraction.
There is also a type of fraction called a proper fraction in which the numerator is lesser than the denominator for example:
$\dfrac{3}{7}$ and $\dfrac{8}{13}$.