47/12 as a decimal and mixed number expansion provides the detailed information about what is 47/12 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
47/12 as a Decimal Expansion
47/12 = 3.9167
Hence,
47/12 as a decimal equals to 3.9167
where,
47/12 is a given fraction,
The decimal expansion of 47/12 is 3.9167
47/12 as a Mixed Number
47/12 = (36 + 11)/12
= 36/12 + 11/12
= 3 + 11/12
= 3 11/12
47/12 = 3 11/12
Hence,
47/12 as a mixed number is 3 11/12
where,
47/12 is a given fraction,
3 11/12 is the mixed number representation of 47/12.
The below work with steps provide the detailed information about how to convert fraction 47/12 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 47/12
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 47/12.
step 2 The numerator is greater than the denominator of the fraction 47/12, so write the given fraction in the expression form in terms of denominator as like the below:
= 47/12
= 36 + 11/12
= (3 x 12) + 11/12
step 3 Make the above expression as individual fractions:
= (3 x 12)/12 + 11/12
step 4 Simplify the above expression:
= 3 x 12/12 + 11/12
= 3 + 11/12
3 + 11/12 can be written as a mixed number 3 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.
= 3 + (11/12 x 10/10)
step 6 Simplify the above expression further:
= 3 + (110/12 x 1/10)
= 3 + (108 + 2/12 x 1/10)
= 3 + [(108/12 + 2/12 ) x 1/10]
= 3 + [(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:
= 3 + [(9 + 2/12) x 1/10]
= 3 + [(9 + 0.17) x 1/10]
= 3 + (9.17 x 1/10)
= 3 + 9.17/10
= 3 + 0.917
step 8 Find the sum of above expression:
= 3 + 0.917
= 3.917
47/12 = 3.917
Hence,
47/12 as a decimal is 3.917
47/12 as a mixed number is 3 11/12