Question

How do you solve $\dfrac{4}{9} = \dfrac{x}{{25}}?$

Answer 1

Hint: Here the given expression is in the form of one fraction equal to the other fraction. Here we will use the cross multiplication and will simplify the equation to get the value of the unknown term “x”.

Complete step-by-step solution:
Take the given expression:
$\dfrac{4}{9} = \dfrac{x}{{25}}$
Perform cross multiplication in the above equation, where numerator of one side is multiplied with the denominator of the opposite side.
$4(25) = x(9)$
Simplify the above equation.
$100 = 9x$
The above equation can be re-written as:
$9x = 100$
When the term multiplicative on one side is moved to the opposite side, then it goes to the denominator. Observe that the term is multiplication of one constant and one variable, so move constant on the opposite side.
$x = \dfrac{{100}}{9}$
Simplify the above fraction, fraction is the number expressed as the numerator upon the denominator. Here the numerator is greater than the denominator we will get the resultant fraction can be expressed as the mixed fraction.
$x = 11\dfrac{1}{9}$
This is the required solution.

Additional Information: Be careful about the sign while doing simplification remember the golden rules- when the term multiplicative on one side is moved to the opposite then it goes to the denominator and when term is in the division on one side is moved to the opposite side then it is multiplied.

Note: Be careful while doing simplification of the equations. Constants are the terms with fixed value such as the numbers it can be positive or negative whereas the variables are terms which are denoted by small alphabets such as x, y, z, a, b, etc. Be careful while moving any term from one side to another.