76/7 as a Decimal and Mixed Number

76/7 as a decimal and mixed number expansion provides the detailed information about what is 76/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

76/7 as a Decimal Expansion
76/7 = 10.8571
Hence,
76/7 as a decimal equals to 10.8571
where,
76/7 is a given fraction,
The decimal expansion of 76/7 is 10.8571

76/7 as a Mixed Number
76/7 = (70 + 6)/7
= 70/7 + 6/7
= 10 + 6/7
= 10 6/7
76/7 = 10 6/7

Hence,
76/7 as a mixed number is 10 ⁶/₇
where,
76/7 is a given fraction,
10 ⁶/₇ is the mixed number representation of 76/7.

The below work with steps provide the detailed information about how to convert fraction 76/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 76/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 76/7.

step 2 The numerator is greater than the denominator of the fraction 76/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 76/7
= 70 + 6/7
= (10 x 7) + 6/7

step 3 Make the above expression as individual fractions:
= (10 x 7)/7 + 6/7

step 4 Simplify the above expression:
= 10 x 7/7 + 6/7
= 10 + 6/7
10 + 6/7 can be written as a mixed number 10 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.
= 10 + (6/7 x 10/10)

step 6 Simplify the above expression further:
= 10 + (60/7 x 1/10)
= 10 + (56 + 4/7 x 1/10)
= 10 + [(56/7 + 4/7 ) x 1/10]
= 10 + [(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:
= 10 + [(8 + 4/7) x 1/10]
= 10 + [(8 + 0.57) x 1/10]
= 10 + (8.57 x 1/10)
= 10 + 8.57/10
= 10 + 0.857

step 8 Find the sum of above expression:
= 10 + 0.857
= 10.857
76/7 = 10.857

Hence,
76/7 as a decimal is 10.857
76/7 as a mixed number is 10 ⁶/₇