What Is 5 1/4 as a Decimal + Solution With Free Steps

The fraction 5 1/4 as a decimal is equal to 5.2.

A Fraction can be employed to separate a smaller portion from a more extensive or complete object. For instance, the fraction 1/8 represents the eighth part of any item. These are also useful in estimating how many components of similar sizes can be combined to obtain a whole object.

According to the respective sizes of the numerator and denominator, the fraction might be either a Proper, Improper, or Mixed fraction. We refer to the combination of a proper fraction and a whole number as a mixed fraction. An example is 5 1/4 containing 5 as a whole number and 1/4 as a proper fraction.

Among the different methods to solve a fraction, one is the Long Division method. It gives us the decimal value and will be studied in detail here.


Since we have a mixed fraction to solve, we cannot solve it until it is transformed into an improper fraction. The equivalent improper fraction is determined as 21/4.

This fraction will now be solved by division. A division problem has three main elements: dividend, divisor, and quotient. Any number divided into smaller portions is called a Dividend, while the dividing number is termed a Divisor. However, the number obtained as an answer after dividing two numbers is called a Quotient.

The fraction of 21/4 has the following components.

Dividend = 21

Divisor = 4

Quotient = Dividend $\div$ Divisor = 21 $\div$ 4

Another term associated with the Division process is remainder. Sometimes, we have two numbers that cannot be divided evenly. These numbers give us certain left-over along with the quotient, which is referred to as Remainder.

Figure 1

5 1/4 Long Division Method

Long Division in mathematics is a methodology for breaking down complex division problems into a series of simpler and smaller steps. As an example, the solution of 21/4 is mentioned here.

21 $\div$ 4

A greater dividend than a divisor indicates that at this point, we can move forward without a Decimal Point. Thus, the division of 21 by 4 is mathematically stated as:

21 $\div$ 4 \approx 5

4 \times 5 = 20

1 is acquired as the value which is left behind.

21 – 20 = 1

This remaining value 1 is made 10, and a decimal point is gotten in the Quotient. Thus, the division is continued as follows.

10 $\div$ 4 \approx 2

4 \times 2 = 8

Deduction of 8 from 10 gives us 2 as the remaining value.

10 – 8 = 2

This 2 is changed to 20 and divided by 4.

20 $\div$ 4 = 5

4 \times 5 = 20

There is no remaining value in this step.

20 – 20 =0

Hence, we have 5.25 as the determined decimal value of 5 1/4.

Images/mathematical drawings are created with GeoGebra.

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