74/7 as a Decimal and Mixed Number

74/7 as a decimal and mixed number expansion provides the detailed information about what is 74/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

74/7 as a Decimal Expansion
74/7 = 10.5714
Hence,
74/7 as a decimal equals to 10.5714
where,
74/7 is a given fraction,
The decimal expansion of 74/7 is 10.5714

74/7 as a Mixed Number
74/7 = (70 + 4)/7
= 70/7 + 4/7
= 10 + 4/7
= 10 4/7
74/7 = 10 4/7

Hence,
74/7 as a mixed number is 10 ⁴/₇
where,
74/7 is a given fraction,
10 ⁴/₇ is the mixed number representation of 74/7.

The below work with steps provide the detailed information about how to convert fraction 74/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 74/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 74/7.

step 2 The numerator is greater than the denominator of the fraction 74/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 74/7
= 70 + 4/7
= (10 x 7) + 4/7

step 3 Make the above expression as individual fractions:
= (10 x 7)/7 + 4/7

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


step 5 Find the decimal equivalent for the fractional part 4/7 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 4/7. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 4/7.
= 10 + (4/7 x 10/10)

step 6 Simplify the above expression further:
= 10 + (40/7 x 1/10)
= 10 + (35 + 5/7 x 1/10)
= 10 + [(35/7 + 5/7 ) x 1/10]
= 10 + [(5 + 5/7) x 1/10]

step 7 Repeat the step 5 to find the decimal equivalent for the fraction 5/7 in the above expression:
= 10 + [(5 + 5/7) x 1/10]
= 10 + [(5 + 0.71) x 1/10]
= 10 + (5.71 x 1/10)
= 10 + 5.71/10
= 10 + 0.571

step 8 Find the sum of above expression:
= 10 + 0.571
= 10.571
74/7 = 10.571

Hence,
74/7 as a decimal is 10.571
74/7 as a mixed number is 10 ⁴/₇