Question

Subtract \[5 - 3\dfrac{1}{3}\] ?

Answer 1

Hint: To solve this question, we will first convert the mixed fraction to an improper fraction. Then we will take L.C.M and simply subtract the terms. And hence we will get the required difference of these fractions. And at the end we will again change the result into mixed fractions.
General form of a mixed fraction is \[x\dfrac{y}{z}\] and it can be converted into proper or improper fraction as \[x\dfrac{y}{z} = \dfrac{{x \times z + y}}{z}\]

Complete step-by-step answer:
We have to simplify \[5 - 3\dfrac{1}{3}\]
Let it be equation \[\left( i \right)\]
i.e., \[5 - 3\dfrac{1}{3}{\text{ }} - - - \left( i \right)\]
Firstly, convert the mixed fraction into a proper fraction by using the general formula i.e.,
\[x\dfrac{y}{z} = \dfrac{{x \times z + y}}{z}\]
Here, in equation \[\left( i \right)\] the mixed fraction is \[3\dfrac{1}{3}\]
So, on converting it, we get
\[3\dfrac{1}{3} = \dfrac{{3 \times 3 + 1}}{3}\]
Now multiply the terms in the numerator of the right-hand side
\[ \Rightarrow 3\dfrac{1}{3} = \dfrac{{9 + 1}}{3}\]
Now add the terms in the numerator of the right-hand side
\[ \Rightarrow 3\dfrac{1}{3} = \dfrac{{10}}{3}\]
Therefore, the mixed fraction \[3\dfrac{1}{3}\] becomes \[\dfrac{{10}}{3}\]
Now back substitute the value in the equation \[\left( i \right)\]
\[ \Rightarrow 5 - 3\dfrac{1}{3}{\text{ }} = {\text{ }}5 - \dfrac{{10}}{3}\]
Take L.C.M in the right-hand side of the above equation
\[ \Rightarrow 5 - 3\dfrac{1}{3}{\text{ }} = {\text{ }}\dfrac{{15 - 10}}{3}\]
Now subtract the terms in the numerator
\[ \Rightarrow 5 - 3\dfrac{1}{3}{\text{ }} = {\text{ }}\dfrac{5}{3}\]
Hence, the value of \[5 - 3\dfrac{1}{3}\] is \[\dfrac{5}{3}\]
Now change back it into mixed fraction, we get
\[ \Rightarrow \dfrac{5}{3} = 1\dfrac{2}{3}\]

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. So, keep in mind we multiply the whole number to number in denominator and then add the number in numerator which becomes our new numerator.
Also, after converting mixed fraction, we can also solve it as follows:
After converting mixed fraction to proper fraction, we get the expression as:
\[5 - \dfrac{{10}}{3}\]
Now rewrite \[5\] as \[\dfrac{{15}}{3}\] to get a common denominator
Therefore, we have
\[\dfrac{{15}}{3} - \dfrac{{10}}{3}\]
Since, we have the same denominator, so just subtract the numerators.
Therefore, we get
\[ \Rightarrow \dfrac{5}{3}\]
which is the required answer.