Question

On a map, $1$ inch represents $150$km. What is the actual distance between the two cities, if they are $4\dfrac{1}{2}$inches apart?
A.$225$
B.$300$
C.$525$
D.$675$

Answer 1

Hint: Here we will convert the mixed fraction in the form of the simple fraction by using the combination of the multiplication and addition and then will find the correlation between the two given data and find the required resultant value.

Complete step-by-step answer:
First of all convert the mixed fraction in the form of the simple fraction.
$4\dfrac{1}{2}$inches $ = \dfrac{9}{2}$inches
Given that: $1$ inch $ = 150$km.
$\dfrac{9}{2}$Inches $ = ?$
Perform cross multiplication, where the term on the left side of the first equation is multiplied with the right side of the second equation and vice-versa.
$ = \dfrac{{150 \times \dfrac{9}{2}}}{1}$
Numerator’s denominator goes to the denominator in the above expression.
$ = \dfrac{{150 \times 9}}{2}$
Find factors of the term on the numerator –
$ = \dfrac{{75 \times 2 \times 9}}{2}$
Common factors from the numerator and the denominator cancel each other.
$ = 75 \times 9$
Simplify finding the product of the terms in the above expression –
$ = 675$km
Hence, from the given multiple choices – the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Remember that the numerator's denominator goes to the denominator and the denominator’s denominator goes to the numerator. Always remember while simplifying the expression, split the number finding the factors and remove common factors from the numerator and the denominator and then multiply or divide accordingly.