309/4 as a Decimal and Mixed Number

309/4 as a decimal and mixed number expansion provides the detailed information about what is 309/4 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

309/4 as a Decimal
309/4 = 77.25
Hence,
309/4 as a decimal equals to 77.25
where,
309/4 is a given fraction,
The decimal expansion of 309/4 is 77.25

309/4 as a Mixed Number
309/4 = (308 + 1)/4
= 308/4 + 1/4
= 77 + 1/4
= 77 1/4
309/4 = 77 1/4

Hence,
309/4 as a mixed number is 77 ¹/₄
where,
309/4 is a given fraction,
77 ¹/₄ is the mixed number representation of 309/4.

The below work with steps provide the detailed information about how to convert fraction 309/4 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 309/4

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 309/4.

step 2 The numerator is greater than the denominator of the fraction 309/4, so write the given fraction in the expression form in terms of denominator as like the below:
= 309/4
= 308 + 1/4
= (77 x 4) + 1/4

step 3 Make the above expression as individual fractions:
= (77 x 4)/4 + 1/4

step 4 Simplify the above expression:
= 77 x 4/4 + 1/4
= 77 + 1/4
77 + 1/4 can be written as a mixed number 77 ¹/₄.


step 5 Find the decimal equivalent for the fractional part 1/4 in the above expression:
Multiply both numerator and denominator by 25 to make the denominator as powers of 10:
= 77 + (1/4 x 25/25)
= 77 + 25/100

step 6 Simplify the above expression further:
= 77 + 0.25
= 77.25
309/4 = 77.25

Hence,
309/4 as a decimal is 77.25
309/4 as a mixed number is 77 ¹/₄