Question

Roy lives $1\frac{5}{12}$ miles away from the Museum. Philip lives $2\frac{3}{20}$ miles away from the Museum. How much closer does Roy live to Philip

• A. $\frac{11}{15}$
• B. $\frac{13}{30}$
• C. $\frac{23}{30}$
• D. $\frac{17}{30}$

Answer 1

The correct option is A $\frac{11}{15}$

Convert each mixed fraction into the improper fractions as follows

$1\frac{5}{12}=\frac{12\times 1+5}{12}=\frac{17}{12}$

$2\frac{3}{20}=\frac{20\times 2+3}{20}=\frac{43}{20}$

As these are unlike fractions, convert them into the like fractions as follows

Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 20: 20, 40, 60, 80, ...
LCM(12, 20) = 60

Now rewrite the denominators in each fractions as 60 (LCM of 12 and 20)

$\frac{17}{12}=\frac{17\times 5}{12\times 5}=\frac{85}{60}$
$\frac{43}{20}=\frac{43\times 3}{20\times 3}=\frac{129}{60}$

Difference of distances $=\frac{129}{60}-\frac{85}{60}$
$=\frac{129-85}{60}$
$=\frac{44}{60}$
$=\frac{2\times 2\times 11}{2\times 2\times 3\times 5}$
$=\frac{11}{15}$