# What Is 20/75 as a Decimal + Solution With Free Steps

**The fraction 20/75 as a decimal is equal to 0.266.**

**Improper fractions** are those fractions that have a **numerator** value **greater than** the **denominator** value. These fractions are **greater** than **1** and are written into a more simplified expression called a **Mixed fraction.**

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,Â **which we will discuss in detail moving forward. So, letâ€™s go through the **Solution** of fraction **20/75**.

## 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 = 20**

**Divisor = 75**

Now, we introduce the most important quantity in our division process: theÂ **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 = 20 $\div$ 75**

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

## 20/75 Long Division Method

We start solving a problem using the **Long Division Method** by first taking apart the divisionâ€™s components and comparing them. As we have **20 **and **75,** we can see how **20 **is **Smaller** than **75**, and to solve this division, we require that 20 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 **20**, which after getting multiplied by **10** becomes **200**.

*We take this 200 and divide it by 75; this can be done as follows:*

**Â 200 $\div$ 75 $\approx$ 2**

Where:

**75 x 2 = 150**

This will lead to the generation of a **Remainder** equal to **200 â€“ 150 = 50**. Now this means we have to repeat the process by **Converting** the **50** into **500**Â and solving for that:

**500 $\div$ 75 $\approx$ 6**

Where:

**75 x 6 = 50**

This, therefore, produces another **Remainder** which is equal to **500 â€“ 450 = 50**. Now we must solve this problem to **Third Decimal Place** for accuracy, so we repeat the process with dividend **500**

**500 $\div$ 75 $\approx$ 6**

Where:

**75 x 6 = 50**

Finally, we have a **Quotient** generated after combining the three pieces of it as **0.266**, with a **Remainder** equal to **50**.

*Images/mathematical drawings are created with GeoGebra.*