Question

How do write in simplest form given \[\dfrac{5}{{16}} - \dfrac{4}{{16}}?\]

Answer 1

Hint: In the given problem first we take L.C.M of denominators then we divide the L.C.M with both the denominator one by one and multiply the resultant with both the numerator one by one. After that, we subtract the one numerator from others and then finally divide the numerator with the denominator to get the final value that will be in the simplest form. By keeping the above steps in mind now we can proceed to solve the above problem.

Complete step-by-step solution:
First write the above expression as follows,
\[ = \dfrac{5}{{16}} - \dfrac{4}{{16}}\]
Now taking L.C.M of denominators, which will equal to 16 then we divide the 16 with both the denominators one by one and multiply the resultant with both the numerator one by one. Therefore, writing it as following,
\[ = \dfrac{{5 \times 1 - 4 \times 1}}{{16}}\]
Multiplying numerator part and writing it as following,
\[ = \dfrac{{5 - 4}}{{16}}\]
Now, subtracting numerator and writing it as,
\[ = \dfrac{1}{{16}}\]
So, we got the required simplest form. It can also be written in the decimal form as following,
Dividing numerator by denominator to get the decimal form,
\[ = 0.0625\]
Second method:
As denominator are same, we can directly subtract the numerator and write it as following to get the required simplest form,
\[ = \dfrac{{5 - 4}}{{16}}\]
\[ = \dfrac{1}{{16}}\]

Note: When fraction addition or fraction subtraction is asked in the problem then first, we should try to concentrate on denominators, if both the denominators are same then we can directly subtract the numerator part to get the required simplest form. If both the denominators are not the same then we have to follow all the above steps to solve the given problem.