31/13 as a Decimal and Mixed Number

31/13 as a decimal and mixed number expansion provides the detailed information about what is 31/13 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

31/13 as a Decimal Expansion
31/13 = 2.3846
Hence,
31/13 as a decimal equals to 2.3846
where,
31/13 is a given fraction,
The decimal expansion of 31/13 is 2.3846

31/13 as a Mixed Number
31/13 = (26 + 5)/13
= 26/13 + 5/13
= 2 + 5/13
= 2 5/13
31/13 = 2 5/13

Hence,
31/13 as a mixed number is 2 ⁵/₁₃
where,
31/13 is a given fraction,
2 ⁵/₁₃ is the mixed number representation of 31/13.

The below work with steps provide the detailed information about how to convert fraction 31/13 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 31/13

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 31/13.

step 2 The numerator is greater than the denominator of the fraction 31/13, so write the given fraction in the expression form in terms of denominator as like the below:
= 31/13
= 26 + 5/13
= (2 x 13) + 5/13

step 3 Make the above expression as individual fractions:
= (2 x 13)/13 + 5/13

step 4 Simplify the above expression:
= 2 x 13/13 + 5/13
= 2 + 5/13
2 + 5/13 can be written as a mixed number 2 ⁵/₁₃.


step 5 Find the decimal equivalent for the fractional part 5/13 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 5/13. Since the denominator is having 1 more digit than the numerator, multiply 100 with both numerator and denominator of 5/13.
= 2 + (5/13 x 100/100)

step 6 Simplify the above expression further:
= 2 + (500/13 x 1/100)
= 2 + (494 + 6/13 x 1/100)
= 2 + [(494/13 + 6/13 ) x 1/100]
= 2 + [(38 + 6/13) x 1/100]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 6/13 in the above expression:
= 2 + [(38 + 6/13) x 1/100]
= 2 + [(38 + 0.46) x 1/100]
= 2 + (38.46 x 1/100)
= 2 + 38.46/100
= 2 + 0.3846

step 8 Find the sum of above expression:
= 2 + 0.3846
= 2.3846
31/13 = 2.3846

Hence,
31/13 as a decimal is 2.3846
31/13 as a mixed number is 2 ⁵/₁₃