 # What Is 55/75 as a Decimal + Solution With Free Steps

The fraction 55/75 as a decimal is equal to 0.733.

A fractional number is converted into a decimal number for clarity in understanding the meaning of the value. This is done through a long division process. The number of steps in the long division process depends on how many decimal places are required for the final result. Here, we are more interested in the division types that result in a Decimal value, as this can be expressed as a Fraction. We see fractions as a way of showing two numbers having the operation of Division between them that result in a value that lies between two Integers.

Now, we introduce the method used to solve said fraction to decimal conversion, called Long Division, which we will discuss in detail moving forward. So, let’s go through the Solution of fraction 55/75.

## Solution

First, we convert the fraction components, i.e., the numerator and the denominator, and transform them into the division constituents, i.e., the Dividend and the Divisor, respectively.

This can be done as follows:

Dividend = 55

Divisor = 75

Now, we introduce the most important quantity in our division process: the Quotient. The value represents the Solution to our division and can be expressed as having the following relationship with the Division constituents:

Quotient = Dividend $\div$ Divisor = 55 $\div$ 75

This is when we go through the Long Division solution to our problem.  Given is the long division process in Figure 1: Figure 1

## 55/75 Long Division Method

We start solving a problem using the Long Division Method by first taking apart the division’s components and comparing them. As we have 55 and 75, we can see how 55 is Smaller than 75, and to solve this division, we require that 55 be Bigger than 75.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. If so, we calculate the Multiple of the divisor closest to the dividend and subtract it from the Dividend. This produces the Remainder, which we then use as the dividend later.

Now, we begin solving for our dividend 55, which after getting multiplied by 10 becomes 550.

We take this 550 and divide it by 75; this can be done as follows:

550 $\div$ 75 $\approx$ 7

Where:

75 x 7 = 525

This will lead to the generation of a Remainder equal to 550 – 525 = 25. Now this means we have to repeat the process by Converting the 25 into 250 and solving for that:

250 $\div$ 75 $\approx$ 3

Where:

75 x 3 = 225

This, therefore, produces another Remainder which is equal to 250 – 225 = 25. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 250.

250 $\div$ 75 $\approx$ 3

Where:

75 x 3 = 225

Finally, we have a Quotient generated after combining the three pieces of it as 0.733, with a Remainder equal to 25. Images/mathematical drawings are created with GeoGebra.