Question

A man is $66{\displaystyle \frac{5}{12}}$ inches tall and his son is $58{\displaystyle \frac{8}{9}}$ inches tall. How much taller is the man?

Answer 1

Hint: First of all convert the given mixed fraction in the form of the simple fraction and then will find the difference between the two fractions and simplify for the resultant required value.

Complete step by step answer:
Mixed number is the combination of a whole number and the fraction. Fraction is the number expressed in the form of the numerator and the denominator.
Convert the given fraction $66{\displaystyle \frac{5}{12}}$in the form of the simple fraction.
$\Rightarrow 66{\displaystyle \frac{5}{12}}={\displaystyle \frac{797}{12}}$ …. (A)
Similarly, convert the given fraction $58{\displaystyle \frac{8}{9}}$in the form of the simple fraction.
$\Rightarrow 58{\displaystyle \frac{8}{9}}={\displaystyle \frac{530}{9}}$ …. (B)
Find the difference between the equations (A) and (B)
$\Rightarrow {\displaystyle \frac{797}{12}}-{\displaystyle \frac{530}{9}}$ ….. (C)
When denominators are different, we cannot simplify the numerator. And so, take LCM ((Least common multiple) of the terms in the denominator.
$$\begin{gathered} 12=3\times 4 \\ \Rightarrow 9=3\times 3 \end{gathered}$$
So, the LCM is $=3\times 3\times 4=36$
Take the equation (C)
${\displaystyle \frac{797}{12}}-{\displaystyle \frac{530}{9}}$
Place, LCM value in the above expression
$={\displaystyle \frac{797}{12}}\times {\displaystyle \frac{3}{3}}-{\displaystyle \frac{530}{9}}\times {\displaystyle \frac{4}{4}}$
Simplify the above expression
$\Rightarrow {\displaystyle \frac{2391}{36}}-{\displaystyle \frac{2120}{36}}$
When denominators are same, numerators are subtracted.
$\Rightarrow {\displaystyle \frac{2391-2120}{36}}$
Simplify the above expression finding the subtraction
$\Rightarrow {\displaystyle \frac{271}{36}}$
Convert the above fraction in the form of the mixed fraction,
$=7{\displaystyle \frac{19}{36}}$

Hence, man is $7{\displaystyle \frac{19}{36}}$ taller than his son.

Additional Information:
Fractions are the part of the whole. Generally, it represents any number of equal parts and it describes the part from the certain size and it is the number expressed in the form of numerator upon the denominator. Know the difference between the fraction and the percentage and apply accordingly.

Note: Read the given word statements and understand it properly and then frame the equations accordingly and use division or multiplication for the required value. Always frame the mathematical expression properly since the solution depends on it only. Be good in finding the factors of the terms and remember multiples till twenty.