Question

John lives $3\frac{4}{7}km$ from the school while George lives $4\frac{3}{10}km$ from the school.Who lives farther from the school and how much?

Answer 1

John's distance from the school $=3\frac{3}{4}=\frac{4x3+3}{4}=\frac{15}{4}km$

George's distance from the school $=4\frac{3}{10}=\frac{10x4+3}{10}=\frac{43}{10}km$

We know that if $\frac{a}{b},\frac{c}{d}$ are any two fraction

$\frac{a}{b}>\frac{c}{d}$ , if and only if $ad>bc$

And $\frac{a}{b}<\frac{c}{d}$, if and only if $ad<bc$.

$a=3,b=5,c=2,d=3$

Therefore , $$\begin{gathered} ad=15x10=150 \\ bc=4x43=172 \end{gathered}$$

Here, $ad<bc$

So, $\frac{15}{4}<\frac{43}{10}$. Which means George lives farther than the John.

Difference between John and George's from the school$=\frac{43}{10}-\frac{15}{4}$

$$\begin{gathered} =\frac{43x2-15x5}{20}LCMof4,10=20 \\ =\frac{86-75}{20} \\ =\frac{11}{20}km \end{gathered}$$

Hence George lives farther from the school by $\frac{11}{20}km$.