13/4 as a Decimal and Mixed Number

The below work with steps provide the detailed information about how to convert fraction 13/4 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 13/4

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 13/4.

step 2 The numerator is greater than the denominator of the fraction 13/4, so write the given fraction in the expression form in terms of denominator as like the below:
= 13/4
= 12 + 1/4
= (3 x 4) + 1/4

step 3 Make the above expression as individual fractions:
= (3 x 4)/4 + 1/4

step 4 Simplify the above expression:
= 3 x 4/4 + 1/4
= 3 + 1/4
3 + 1/4 can be written as a mixed number 3 ¹/₄.


step 5 Find the decimal equivalent for the fractional part 1/4 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/4. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/4.
= 3 + (1/4 x 10/10)

step 6 Simplify the above expression further:
= 3 + (10/4 x 1/10)
= 3 + (8 + 2/4 x 1/10)
= 3 + [(8/4 + 2/4 ) x 1/10]
= 3 + [(2 + 2/4) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/4 in the above expression:
= 3 + [(2 + 2/4) x 1/10]
= 3 + [(2 + 0.5) x 1/10]
= 3 + (2.5 x 1/10)
= 3 + 2.5/10
= 3 + 0.25

step 8 Find the sum of above expression:
= 3 + 0.25
= 3.25
13/4 = 3.25

Hence,
13/4 as a decimal is 3.25
13/4 as a mixed number is 3 ¹/₄