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What Is 7/22 as a Decimal + Solution With Free Steps

The fraction 7/22 as a decimal is equal to 0.318.

Fractions of the form p/q represent the operation of division ($\div$), where p (numerator) and q (denominator) are any two numbers representing the dividend and divisor respectively. Here, p and q are both integers (7 and 22), and since 7 < 22, 7/22 is a proper fraction. If the numerator > denominator, we have an improper fraction.

Here, we are interested more in the types of division that results 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 22 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 7/22.

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 seen done as follows:

Dividend = 7

Divisor = 22

Now, we introduce the most important quantity in our process of division, this is 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 $\div$ 22

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

7/22 Long Division Method

Figure 1

7/22 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 22 we can see how 7 is Smaller than 22, and to solve this division we require that 7 be Bigger than 22.

This is done by multiplying the dividend by 10 and checking whether it is bigger than the divisor or not. If it is then we calculate the Multiple of the divisor which is 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 22, this can be seen done as follows:

 70 $\div$ 22 $\approx$ 3

Where:

22 x 3 = 66

We add 3 to our quotient. This will lead to the generation of a remainder equal to 70 – 66 = 4, now this means we have to repeat the process by Converting the 4 into 40 (4 times 10) and solving for that:

40 $\div$ 22 $\approx$ 1 

Where:

22 x 1 = 22

We add 1 to our quotient. This, therefore, produces another remainder which is equal to 40 – 22 = 18. Now we must solve this problem to Third Decimal Place for accuracy, so we repeat the process with dividend 180.

180 $\div$ 22 $\approx$ 8 

Where:

22 x8 = 176

Finally, we add to our quotient and combine all the pieces to get the final Quotient of 0.318, with a final remainder equal to 4.

7 by 22 Quotient and Remainder

Images/mathematical drawings are created with GeoGebra.

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