Question

How much bigger is a \[\dfrac{1}{4}\] inch button than a \[\dfrac{5}{8}\] inch button?

Answer 1

Hint: Here we will find the difference between the lengths of the two buttons. First, we will subtract the smaller value with the bigger value for that we will take the L.C.M of the two fractions. Then we will solve the value to get the difference between the two buttons.

Complete step-by-step answer:
It is given that
The length of bigger button is \[ = \dfrac{5}{8}\]
The length of smaller button is \[ = \dfrac{1}{4}\]
So, the difference between the two buttons is
Difference \[ = \dfrac{5}{8} - \dfrac{1}{4}\]
Now taking the L.C.M, we get
\[ \Rightarrow \] Difference \[ = \dfrac{{5 - \left( {1 \times 2} \right)}}{8}\]
\[ \Rightarrow \] Difference \[ = \dfrac{{5 - 2}}{8} = \dfrac{3}{8}\]

Therefore, we get that a \[\dfrac{5}{8}\] inch button is \[\dfrac{3}{8}\] times bigger than a \[\dfrac{1}{4}\] inch button.

Additional Information:
Fractions are the term which are in the form of \[\dfrac{p}{q}\] where \[q \ne 0\] and \[p\], \[q\] are the integers. Another way to find the bigger among the two fractions we subtract them and see whether we are getting value in positive or negative if the value is in the negative second term is bigger if the value is in the positive first term is bigger. We solve the fraction terms by using the L.C.M method as there denominator has to be made the same for them to get added or subtracted

Note: L.C.M (Least Common Multiple) is the smallest number which is a multiple of the given numbers. L.C.M contains all the factors irrespective of common or uncommon so the two of them combined have all the factors common in double and non-common in single. Thus, the product of two numbers is equal to the product of their least common multiple and highest common divisor.