What Is 46/60 as a Decimal + Solution With Free Steps

The fraction 46/60 as a decimal is equal to 0.766.

The division process is one of the basic parts of the mathematics world. It is essential to find the division result to ease our difficult mathematical problem. This is usually expressed in the form of a fraction a/b.

46 60 as a decimal

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 46/60.


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 = 46

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 = 46 $\div$ 60

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

46/60 Long Division Method

Figure 1

46/60 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 46 and 60, we can see how 46 is Smaller than 60, and to solve this division, we require that 46 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 46, which after getting multiplied by 10 becomes 460.

We take this 460 and divide it by 60; this can be done as follows:

 460 $\div$ 60 $\approx$ 7


60 x 7 = 420

This will lead to the generation of a Remainder equal to 460 – 420 = 40. Now this means we have to repeat the process by Converting the 40 into 400 and solving for that:

400 $\div$ 60 $\approx$ 6 


60 x 6 = 360

This, therefore, produces another Remainder which is equal to 400 – 360 = 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 


60 x 6 = 360

Finally, we have a Quotient generated after combining the three pieces of it as 0.766, with a Remainder equal to 40.Quotient and Remainder of 46 per 60

Images/mathematical drawings are created with GeoGebra.

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