Question

How do you subtract and simplify \[9 - 5\dfrac{1}{3}\] ?

Answer 1

Hint: We firstly convert the mixed fraction to a proper fraction. Simply subtract the second value that comes after the minus sign from the first value that comes before the minus sign. Take LCM in the end and solve the fraction.
 * Subtraction is an operation denoted by minus sign \[( - )\] . When we subtract one value from another we deduct or lessen the second value that comes after the minus sign from the value that comes before the minus sign. We can write ‘b’ is subtracted from ‘a’ as: \[a - b\]
* General form of a mixed fraction is \[a\dfrac{b}{c}\]and it can be converted into proper fraction as \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]

Complete step by step solution:
We have to simplify the term \[9 - 5\dfrac{1}{3}\] … (1)
Firstly we convert the mixed fraction in to a proper fraction using the general formula \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
Mixed fraction is \[5\dfrac{1}{3}\] … (2)
Use the formula of converting mixed fraction to proper fraction i.e. \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
We can write the mixed fraction in equation (2) as
\[ \Rightarrow 5\dfrac{1}{3} = \dfrac{{5 \times 3 + 1}}{3}\]
Multiply the terms in the numerator of RHS
\[ \Rightarrow 5\dfrac{1}{3} = \dfrac{{15 + 1}}{3}\]
Add the terms in the numerator of RHS
\[ \Rightarrow 5\dfrac{1}{3} = \dfrac{{16}}{3}\]
So, the mixed fraction in equation (1) becomes \[\dfrac{{16}}{3}\]
Now we substitute the value of \[5\dfrac{1}{3} = \dfrac{{16}}{3}\] back in equation (1)
\[ \Rightarrow 9 - 5\dfrac{1}{3} = 9 - \dfrac{{16}}{3}\]
Take LCM in right hand side of the equation
\[ \Rightarrow 9 - 5\dfrac{1}{3} = \dfrac{{9 \times 3 - 16}}{3}\]
Calculate the product in the numerator on right hand side of the equation
\[ \Rightarrow 9 - 5\dfrac{1}{3} = \dfrac{{27 - 16}}{3}\]
Subtract the terms in the numerator on right hand side of the equation
\[ \Rightarrow 9 - 5\dfrac{1}{3} = \dfrac{{11}}{3}\]
\[\therefore \] The value of \[9 - 5\dfrac{1}{3}\] on simplification is \[\dfrac{{11}}{3}\]

Note: Many students might make mistakes while converting mixed fraction to proper fraction as they tend to multiply the whole number with a numerator and then add the denominator. Keep in mind we multiply the whole number to number in denominator and then add the number in numerator which becomes our new numerator.