83/12 as a Decimal and Mixed Number

83/12 as a decimal and mixed number expansion provides the detailed information about what is 83/12 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

83/12 as a Decimal Expansion
83/12 = 6.9167
Hence,
83/12 as a decimal equals to 6.9167
where,
83/12 is a given fraction,
The decimal expansion of 83/12 is 6.9167

83/12 as a Mixed Number
83/12 = (72 + 11)/12
= 72/12 + 11/12
= 6 + 11/12
= 6 11/12
83/12 = 6 11/12

Hence,
83/12 as a mixed number is 6 ¹¹/₁₂
where,
83/12 is a given fraction,
6 ¹¹/₁₂ is the mixed number representation of 83/12.

The below work with steps provide the detailed information about how to convert fraction 83/12 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 83/12

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 83/12.

step 2 The numerator is greater than the denominator of the fraction 83/12, so write the given fraction in the expression form in terms of denominator as like the below:
= 83/12
= 72 + 11/12
= (6 x 12) + 11/12

step 3 Make the above expression as individual fractions:
= (6 x 12)/12 + 11/12

step 4 Simplify the above expression:
= 6 x 12/12 + 11/12
= 6 + 11/12
6 + 11/12 can be written as a mixed number 6 ¹¹/₁₂.


step 5 Find the decimal equivalent for the fractional part 11/12 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 11/12. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 11/12.
= 6 + (11/12 x 10/10)

step 6 Simplify the above expression further:
= 6 + (110/12 x 1/10)
= 6 + (108 + 2/12 x 1/10)
= 6 + [(108/12 + 2/12 ) x 1/10]
= 6 + [(9 + 2/12) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/12 in the above expression:
= 6 + [(9 + 2/12) x 1/10]
= 6 + [(9 + 0.17) x 1/10]
= 6 + (9.17 x 1/10)
= 6 + 9.17/10
= 6 + 0.917

step 8 Find the sum of above expression:
= 6 + 0.917
= 6.917
83/12 = 6.917

Hence,
83/12 as a decimal is 6.917
83/12 as a mixed number is 6 ¹¹/₁₂