47/6 as a Decimal and Mixed Number

47/6 as a decimal and mixed number expansion provides the detailed information about what is 47/6 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

47/6 as a Decimal Expansion
47/6 = 7.8333
Hence,
47/6 as a decimal equals to 7.8333
where,
47/6 is a given fraction,
The decimal expansion of 47/6 is 7.8333

47/6 as a Mixed Number
47/6 = (42 + 5)/6
= 42/6 + 5/6
= 7 + 5/6
= 7 5/6
47/6 = 7 5/6

Hence,
47/6 as a mixed number is 7 ⁵/₆
where,
47/6 is a given fraction,
7 ⁵/₆ is the mixed number representation of 47/6.

The below work with steps provide the detailed information about how to convert fraction 47/6 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 47/6

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 47/6.

step 2 The numerator is greater than the denominator of the fraction 47/6, so write the given fraction in the expression form in terms of denominator as like the below:
= 47/6
= 42 + 5/6
= (7 x 6) + 5/6

step 3 Make the above expression as individual fractions:
= (7 x 6)/6 + 5/6

step 4 Simplify the above expression:
= 7 x 6/6 + 5/6
= 7 + 5/6
7 + 5/6 can be written as a mixed number 7 ⁵/₆.


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

step 6 Simplify the above expression further:
= 7 + (50/6 x 1/10)
= 7 + (48 + 2/6 x 1/10)
= 7 + [(48/6 + 2/6 ) x 1/10]
= 7 + [(8 + 2/6) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 2/6 in the above expression:
= 7 + [(8 + 2/6) x 1/10]
= 7 + [(8 + 0.33) x 1/10]
= 7 + (8.33 x 1/10)
= 7 + 8.33/10
= 7 + 0.833

step 8 Find the sum of above expression:
= 7 + 0.833
= 7.833
47/6 = 7.833

Hence,
47/6 as a decimal is 7.833
47/6 as a mixed number is 7 ⁵/₆