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What Is 18/21 as a Decimal + Solution With Free Steps

The fraction 18/21 as a decimal is equal to 0.857.

The division of two numbers (say, p and q) answers the question “how much are p parts of q?” It is the inverse of multiplication, which instead answers “how much is p groups of q?” fractions are another way of representing division in the form of a numeral p/q, where p is the numerator and q 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.

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 18/21.

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 = 18

Divisor = 21

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 = 18 $\div$ 21

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

18/21 Long Division Method

Figure 1

18/21 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 18 and 21, we can see how 18 is Smaller than 21, and to solve this division, we require that 18 be Bigger than 21.

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 18, which after getting multiplied by 10 becomes 180.

We take this 180 and divide it by 21; this can be done as follows:

 180 $\div$ 21 $\approx$ 8

Where:

21 x 8 = 168

This will lead to the generation of a Remainder equal to 180 – 168 = 12. Now this means we have to repeat the process by Converting the 12 into 120 and solving for that:

120 $\div$ 21 $\approx$ 5 

Where:

21 x 5 = 105

This, therefore, produces another Remainder which is equal to 120 – 105 = 15. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 150.

150 $\div$ 21 $\approx$ 7 

Where:

21 x 7 = 147

Finally, we have a Quotient generated after combining the three pieces of it as 0.857, with a Remainder equal to 3.

Images/mathematical drawings are created with GeoGebra.

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