83/7 as a Decimal and Mixed Number

83/7 as a decimal and mixed number expansion provides the detailed information about what is 83/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

83/7 as a Decimal Expansion
83/7 = 11.8571
Hence,
83/7 as a decimal equals to 11.8571
where,
83/7 is a given fraction,
The decimal expansion of 83/7 is 11.8571

83/7 as a Mixed Number
83/7 = (77 + 6)/7
= 77/7 + 6/7
= 11 + 6/7
= 11 6/7
83/7 = 11 6/7

Hence,
83/7 as a mixed number is 11 ⁶/₇
where,
83/7 is a given fraction,
11 ⁶/₇ is the mixed number representation of 83/7.

The below work with steps provide the detailed information about how to convert fraction 83/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 83/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 83/7.

step 2 The numerator is greater than the denominator of the fraction 83/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 83/7
= 77 + 6/7
= (11 x 7) + 6/7

step 3 Make the above expression as individual fractions:
= (11 x 7)/7 + 6/7

step 4 Simplify the above expression:
= 11 x 7/7 + 6/7
= 11 + 6/7
11 + 6/7 can be written as a mixed number 11 ⁶/₇.


step 5 Find the decimal equivalent for the fractional part 6/7 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 6/7. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 6/7.
= 11 + (6/7 x 10/10)

step 6 Simplify the above expression further:
= 11 + (60/7 x 1/10)
= 11 + (56 + 4/7 x 1/10)
= 11 + [(56/7 + 4/7 ) x 1/10]
= 11 + [(8 + 4/7) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 4/7 in the above expression:
= 11 + [(8 + 4/7) x 1/10]
= 11 + [(8 + 0.57) x 1/10]
= 11 + (8.57 x 1/10)
= 11 + 8.57/10
= 11 + 0.857

step 8 Find the sum of above expression:
= 11 + 0.857
= 11.857
83/7 = 11.857

Hence,
83/7 as a decimal is 11.857
83/7 as a mixed number is 11 ⁶/₇