32/7 as a Decimal and Mixed Number

32/7 as a decimal and mixed number expansion provides the detailed information about what is 32/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

32/7 as a Decimal Expansion
32/7 = 4.5714
Hence,
32/7 as a decimal equals to 4.5714
where,
32/7 is a given fraction,
The decimal expansion of 32/7 is 4.5714

32/7 as a Mixed Number
32/7 = (28 + 4)/7
= 28/7 + 4/7
= 4 + 4/7
= 4 4/7
32/7 = 4 4/7

Hence,
32/7 as a mixed number is 4 ⁴/₇
where,
32/7 is a given fraction,
4 ⁴/₇ is the mixed number representation of 32/7.

The below work with steps provide the detailed information about how to convert fraction 32/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 32/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 32/7.

step 2 The numerator is greater than the denominator of the fraction 32/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 32/7
= 28 + 4/7
= (4 x 7) + 4/7

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

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

step 6 Simplify the above expression further:
= 4 + (40/7 x 1/10)
= 4 + (35 + 5/7 x 1/10)
= 4 + [(35/7 + 5/7 ) x 1/10]
= 4 + [(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:
= 4 + [(5 + 5/7) x 1/10]
= 4 + [(5 + 0.71) x 1/10]
= 4 + (5.71 x 1/10)
= 4 + 5.71/10
= 4 + 0.571

step 8 Find the sum of above expression:
= 4 + 0.571
= 4.571
32/7 = 4.571

Hence,
32/7 as a decimal is 4.571
32/7 as a mixed number is 4 ⁴/₇