Question

How much longer is $1$ inch button than an ${\displaystyle \frac{3}{8}}$ inch button?

Answer 1

Hint: Firstly, take both the quantities and compare which is larger. Then write them in a subtraction equation and evaluate using the LCM method or else by cross-multiplying the fractions and then subtracting the second number from the first to get the numerator part and multiply the denominators to get a common denominator.

Complete step-by-step answer:
Given quantities are, $1$ inch and ${\displaystyle \frac{3}{8}}$ inch.
       

By comparing the quantities, we can say that $1>{\displaystyle \frac{3}{8}}$
Since we must find how much is left of the first quantity after removing the second quantity, we shall write a subtraction equation.
$\Rightarrow 1-{\displaystyle \frac{3}{8}}$
We can write $1$ in fraction form as ${\displaystyle \frac{1}{1}}$,we can rewrite the equation as,
$\Rightarrow {\displaystyle \frac{1}{1}}-{\displaystyle \frac{3}{8}}$
Now cross-multiply the fractions and then subtract the numerators and then multiply the denominators to get a common denominator.
$\Rightarrow {\displaystyle \frac{(1\times 8)-(3\times 1)}{(1\times 8)}}$
On further evaluation,
$\Rightarrow {\displaystyle \frac{8-3}{8}}$
Which is equal to,
$\Rightarrow {\displaystyle \frac{5}{8}}$

$\therefore$$1$ inch button is ${\displaystyle \frac{5}{8}}$ times longer than ${\displaystyle \frac{3}{8}}$ inch buttons.

Additional Information: Whenever there are different denominators in a subtraction equation, the first step must be to convert it in such a way to get the same denominators. Then only we should proceed to the subtraction operation. The quantity which is given in the question is an Inch which is a unit of length.$1$ inch$=2.54$ centimeters.
Note:
The above question can also be solved using LCM (least common multiples) method.
Firstly, write both the quantities in fraction form.
$\Rightarrow {\displaystyle \frac{1}{1}};{\displaystyle \frac{3}{8}}$
Now, write the subtraction equation for the both quantities.
$\Rightarrow {\displaystyle \frac{1}{1}}-{\displaystyle \frac{3}{8}}$
Now, find the multiples for the denominators
For $1$ the multiples are $1$,
For $8$ the multiples are $1,2,4,8,$
On comparing both the multiples, the LCM of $1$ and $8$ is $8$.
$\Rightarrow$${\displaystyle \frac{1}{1}}={\displaystyle \frac{(1\times 8)}{(1\times 8)}}={\displaystyle \frac{8}{8}}$, (because ${\displaystyle \frac{8}{1}}=8$)
$\Rightarrow$${\displaystyle \frac{3}{8}}={\displaystyle \frac{(3\times 1)}{(8\times 1)}}={\displaystyle \frac{3}{8}}$, (because ${\displaystyle \frac{8}{8}}=1$)
Therefore,
$\Rightarrow {\displaystyle \frac{8}{8}}-{\displaystyle \frac{3}{8}}$
On further evaluation,
$\Rightarrow {\displaystyle \frac{5}{8}}$