85/7 as a decimal and mixed number expansion provides the detailed information about what is 85/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
85/7 as a Decimal Expansion
85/7 = 12.1429
Hence,
85/7 as a decimal equals to 12.1429
where,
85/7 is a given fraction,
The decimal expansion of 85/7 is 12.1429
85/7 as a Mixed Number
85/7 = (84 + 1)/7
= 84/7 + 1/7
= 12 + 1/7
= 12 1/7
85/7 = 12 1/7
Hence,
85/7 as a mixed number is 12 1/7
where,
85/7 is a given fraction,
12 1/7 is the mixed number representation of 85/7.
The below work with steps provide the detailed information about how to convert fraction 85/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 85/7
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 85/7.
step 2 The numerator is greater than the denominator of the fraction 85/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 85/7
= 84 + 1/7
= (12 x 7) + 1/7
step 3 Make the above expression as individual fractions:
= (12 x 7)/7 + 1/7
step 4 Simplify the above expression:
= 12 x 7/7 + 1/7
= 12 + 1/7
12 + 1/7 can be written as a mixed number 12 1/7.
step 5 Find the decimal equivalent for the fractional part 1/7 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 1/7. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 1/7.
= 12 + (1/7 x 10/10)
step 6 Simplify the above expression further:
= 12 + (10/7 x 1/10)
= 12 + (7 + 3/7 x 1/10)
= 12 + [(7/7 + 3/7 ) x 1/10]
= 12 + [(1 + 3/7) x 1/10]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 3/7 in the above expression:
= 12 + [(1 + 3/7) x 1/10]
= 12 + [(1 + 0.43) x 1/10]
= 12 + (1.43 x 1/10)
= 12 + 1.43/10
= 12 + 0.143
step 8 Find the sum of above expression:
= 12 + 0.143
= 12.143
85/7 = 12.143
Hence,
85/7 as a decimal is 12.143
85/7 as a mixed number is 12 1/7