# What Is 31/60 as a Decimal + Solution With Free Steps

**The fraction 31/60 as a decimal is equal to 0.516.**

**Long division** in arithmetic is such kind of division that is used to divide large numbers into numerous smaller parts. A** Dividend** is divided by a divisor, while the quotient shows the possible groups that can be made, and the remainder depicts how many numbers will be left undivided.

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** 31/60.**

## 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 = 31**

**Divisor = 60**

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 = 31 $\div$ 60**

This is when we go through the **Long Division** solution to our problem.

## 31/60 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** 31** and **60, **we can see how** 31** is **Smaller** than **60,** and to solve this division, we require that 31 be **Bigger** than 60.

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 **31,** which after getting multiplied by **10** becomes **310.**

*We take this 310 and divide it by 60; this can be done as follows:*

** 310 $\div$ 60 $\approx$ 5**

Where:

**60 x 5 = 300**

This will lead to the generation of a **Remainder** equal to** 310 – 300 = 10**. Now this means we have to repeat the process by **Converting** the** 10** into **100** and solving for that:

**100 $\div$ 60 $\approx$ 1**

Where:

**60 x 1 = 60**

This, therefore, produces another **Remainder** which is equal to **100 – 60 = 40.** Now we must solve this problem to **Third Decimal Place** for accuracy, so we repeat the process with dividend **400.**

**400 $\div$ 60 $\approx$ 6 **

Where:

**60 x 6 = 360**

Finally, we have a **Quotient** generated after combining the three pieces of it as **0.516=z**, with a **Remainder** equal to **40.**

*Images/mathematical drawings are created with GeoGebra.*