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How do you simplify \[\dfrac{4}{5} - \dfrac{1}{2}\]

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Last updated date: 03rd Mar 2024
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IVSAT 2024
Answer
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Hint: Here in this question, we have - symbol which represents the subtraction and we have to subtract the two numbers. The numbers are in the form of fraction. by taking the LCM for the denominators and we are going to simplify the given numbers.

Complete step-by-step solution:
Here in this question, we have to subtract the numbers. As we know - sign indicates subtraction. The numbers are in the form of fraction. In fraction we have 3 types. They are proper fraction, improper fraction and mixed fraction.

In the fraction the numerator is less than the denominator then it is a proper fraction. The numerator is greater than the denominator then it is an improper fraction. The fraction is a combination of the whole number and fraction then it is a mixed fraction.

Here in this question both numbers are a proper fraction.
Now consider the given data
\[\dfrac{4}{5} - \dfrac{1}{2}\]
The values of denominator are not same so we take LCM for the denominator
The LCM of 5 and 2
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Therefore, the LCM of 5 and 2 we have \[5 \times 2 = 10\]
Now taking the LCM we have
\[ \Rightarrow \dfrac{{\dfrac{4}{5} \times 10 - \dfrac{1}{2} \times 10}}{{10}}\]
On the simplification we get
\[ \Rightarrow \dfrac{{4 \times 2 - 1 \times 5}}{{10}}\]
Using the multiplication, we get
\[ \Rightarrow \dfrac{{8 - 5}}{{10}}\]
On further simplification we get
\[ \Rightarrow \dfrac{3}{{10}}\]
This is also a proper fraction, where the numerator is less than the denominator.
We can’t simplify further. Therefore, we have \[\dfrac{4}{5} - \dfrac{1}{2} = \dfrac{3}{{10}}\]

Note: The improper fraction can be converted to the mixed fraction. the proper fraction cannot be converted into the mixed fraction. where in the improper fraction the numerator value is greater than the value of the denominator. So we can apply the division arithmetic operation but it is impossible to the proper fraction.
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