What Is 7/31 as a Decimal + Solution With Free Steps

The fraction 7/31 as a decimal is equal to 0.225.

One of the fundamental operations in mathematics is called Division, which can also be expressed as a fractional mathematical expression. This alternative representation can sometimes help solve or simplify complex mathematical expressions. A fraction is represented by the symbol a/b, where the top entity (a) is the Numerator, and the bottom one (b) is the Denominator.

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.

7 31 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 7/31. Figure 1 shows the long division process:

7/31 Long Division Method

Figure 1


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 = 7

Divisor = 31

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 = 7 $\div$ 31

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

7/31 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 7 and 31, we can see how 7 is Smaller than 31, and to solve this division, we require that 7 be Bigger than 31.

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 7, which after getting multiplied by 10 becomes 70.

We take this 70 and divide it by 31; this can be done as follows:

 70 $\div$ 31 $\approx$ 2


31 x 2 = 62

This will lead to the generation of a Remainder equal to 70 – 62 = 8. Now this means we have to repeat the process by Converting the 8 into 80 and solving for that:

80 $\div$ 31 $\approx$ 2 


31 x 2 = 62

This, therefore, produces another Remainder which is equal to 80 – 62 = 18. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 180.

180 $\div$ 37 $\approx$ 5 


37 x 5 = 155

Finally, we have a Quotient generated after combining the three pieces of it as 0.225=z, with a Remainder equal to 25.

7 by 31 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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