Ratio Problem Setup

Let's denote the first number as '$N_1$' and the second number as '$N_2$'. The problem states that a specific portion of the first number is equal to a specific fraction of the second number.

• The condition given is: 36% of the first number = four-sevenths of the second number.

Percentage to Fraction Conversion

To work with the given values, we convert the percentage into a fraction:

$ 36\% = \frac{36}{100} $

The problem also provides a fraction:

$ \frac{4}{7} $

Equation Derivation

Using the converted values, we can write the mathematical equation representing the problem statement:

$ \frac{36}{100} \times N_1 = \frac{4}{7} \times N_2 $

Ratio Calculation Steps

Our goal is to find the ratio '$N_1 : N_2$', which is the same as finding the value of the fraction $\frac{N_1}{N_2}$. We can rearrange the equation to solve for this ratio:

1. Begin with the equation:

   $ \frac{36}{100} \times N_1 = \frac{4}{7} \times N_2 $

2. To get the ratio $\frac{N_1}{N_2}$ on one side, we first divide both sides by $N_2$:

   $ \frac{36}{100} \times \frac{N_1}{N_2} = \frac{4}{7} $

3. Next, isolate $\frac{N_1}{N_2}$ by multiplying both sides by the reciprocal of $\frac{36}{100}$, which is $\frac{100}{36}$:

   $ \frac{N_1}{N_2} = \frac{4}{7} \times \frac{100}{36} $

4. Simplify the multiplication. Notice that 4 and 36 share a common factor of 4 ($\frac{4}{36} = \frac{1}{9}$):

   $ \frac{N_1}{N_2} = \frac{1}{7} \times \frac{100}{9} $

5. Perform the final multiplication:

   $ \frac{N_1}{N_2} = \frac{1 \times 100}{7 \times 9} = \frac{100}{63} $

The resulting fraction $\frac{100}{63}$ represents the ratio $N_1 : N_2$.

Final Ratio Answer

Therefore, the ratio of the first number to the second number is 100 : 63.