Question

Find the value of the expression $2-\dfrac{3}{5}$.

Answer 1

Hint:A fraction represents a part of a whole or more generally, and mixed numerals. Here, we will follow the steps for the subtraction of two fractions and so we will find the values of the given expression.

Complete step-by-step answer:
A fraction represents a part of a whole or, more generally, any number of equal parts.
Types of fractions:
Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: $\dfrac{3}{4}$,$\dfrac{7}{11}$
Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: $\dfrac{7}{3}$,$\dfrac{11}{7}$
Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example $1\dfrac{2}{5}$ , $3\dfrac{5}{6}$.
Here in this question,
The numerator represents a number of equal parts and the denominator indicates how many of those parts make up a unit or a whole.
For the subtraction of fractions, we follow the given steps:
First of all we make the denominators of both the fractions equal. Then, we find the lowest common multiple and multiply the denominator with it so that the denominator of both becomes the same. Then, we subtract the numerators keeping the denominator the same. In the last step, we check if we can simplify our answer. So, we find the greatest common factor of the numerator and denominator and divide both the numbers by it. Sometimes, depending on the answer, we may not be able to simplify it.
Here, the expression given to us is:
$2-\dfrac{3}{5}$
$=\dfrac{2}{1}-\dfrac{3}{5}$
Least common multiple of 1 and 5 is = 5.
Therefore, $\dfrac{2}{1}-\dfrac{3}{5}=\dfrac{2\times 5-3}{5}=\dfrac{10-3}{5}=\dfrac{7}{5}$
We see that the greatest common factor of 7 and 5 is 1. So, we cannot further simplify it.
Hence, the answer is $\dfrac{7}{5}$.

Note: Students should note here that 2 can be written as $\dfrac{2}{1}$ , that is , in case if no denominator is given, we take 1 as a denominator.Here in final answer we can't simplify it further but we can convert it into mixed fraction i.e writing in form of $a\dfrac{b}{c}$ where a is quotient, b is remainder and c is divisor, so $\dfrac{7}{5}$ can be written by dividing 7 by 5 replace a in above general formula by substituting value of quotient and put the value of remainder in numerator keeping denominator value same we get $1\dfrac{2}{5}$.