Question

If q is inversely proportional to p, and q $= {3}{2}$ when $p = 72$ how do you write the equation?

Answer 1

Hint : Here first of all read the given question twice and frame the mathematical equation from the given word statement and place the given values and find the value of the constant and the required equation.

Complete Step By Step Answer:
First of all frame the given word statement in the form of mathematical expression.
Given that “q” is inversely proportional to “p”
$\Rightarrow q\alpha {1}{p}$
Convert the above expression in the form of an equation multiplying with “k”.
$\Rightarrow q = k \times {1}{p}$ ….. (A)
Place the given values in the above expression –
$\Rightarrow {3}{2} = k \times {1}{{72}}$
Make the required value of “k” as the subject –
$\Rightarrow {3}{2} \times 72 = k$
The term in the division if moved to the opposite side then goes to the numerator and multiplied.
Common multiple from the numerator and the denominator cancel each other.
$\Rightarrow 3 \times 36 = k$
Simplify the above expression finding the product of the terms on the left hand side of the equation.
$\Rightarrow 108 = k$
By placing the above value in the equation (A)
$\Rightarrow q = {{108}}{p}$
This is the required solution.

Additional Information:
Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $1$ and which are not the product of any two smaller natural numbers. For Example: $2,{\text{ 3, 5, 7,}}......$

Note :
Always remember that when any term in the denominator is moved to the opposite side then it goes to the numerator and vice-versa. Be good in multiples and remember multiples till twenty numbers. Always convert the given number in the prime numbers and then find the common factors in the numerator and the denominator and then remove them.