What Is 12/45 as a Decimal + Solution With Free Steps

The fraction 12/45 as a decimal is equal to 0.266.

Rational numbers can be expressed in form of fractional notation. In the fraction 12/45, 12 is the numerator and 45 is the denominator. As the numerator is less than the denominator, it is a proper 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.

12 45 as a decimal

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 12/45.


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 = 12

Divisor = 45

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 = 12 $\div$ 45

This is when we go through the Long Division solution to our problem. The following figure shows the solution for fraction 12/45.

12/45 Long Division Method

Figure 1

12/45 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 12 and 45, we can see how 12 is Smaller than 45, and to solve this division, we require that 12 be Bigger than 45.

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 12, which after getting multiplied by 10 becomes 120.

We take this 120 and divide it by 45; this can be done as follows:

 120 $\div$ 45 $\approx$ 2


45 x 2 = 90

This will lead to the generation of a Remainder equal to 120 – 90 = 30. Now this means we have to repeat the process by Converting the 30 into 300 and solving for that:

300 $\div$ 45 $\approx$ 6 


45 x 6 = 270

This, therefore, produces another Remainder which is equal to 300 – 270 = 30. Now this means we have to repeat the process by Converting the 30 into 300 and solving for that:

300 $\div$ 45 $\approx$ 6 


45 x 6 = 270

Finally, we have a Quotient generated after combining the three pieces of it as 0.266, with a Remainder equal to 30.

12_45 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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