43/7 as a Decimal and Mixed Number

43/7 as a decimal and mixed number expansion provides the detailed information about what is 43/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

43/7 as a Decimal Expansion
43/7 = 6.1429
Hence,
43/7 as a decimal equals to 6.1429
where,
43/7 is a given fraction,
The decimal expansion of 43/7 is 6.1429

43/7 as a Mixed Number
43/7 = (42 + 1)/7
= 42/7 + 1/7
= 6 + 1/7
= 6 1/7
43/7 = 6 1/7

Hence,
43/7 as a mixed number is 6 ¹/₇
where,
43/7 is a given fraction,
6 ¹/₇ is the mixed number representation of 43/7.

The below work with steps provide the detailed information about how to convert fraction 43/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 43/7

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 43/7.

step 2 The numerator is greater than the denominator of the fraction 43/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 43/7
= 42 + 1/7
= (6 x 7) + 1/7

step 3 Make the above expression as individual fractions:
= (6 x 7)/7 + 1/7

step 4 Simplify the above expression:
= 6 x 7/7 + 1/7
= 6 + 1/7
6 + 1/7 can be written as a mixed number 6 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.
= 6 + (1/7 x 10/10)

step 6 Simplify the above expression further:
= 6 + (10/7 x 1/10)
= 6 + (7 + 3/7 x 1/10)
= 6 + [(7/7 + 3/7 ) x 1/10]
= 6 + [(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:
= 6 + [(1 + 3/7) x 1/10]
= 6 + [(1 + 0.43) x 1/10]
= 6 + (1.43 x 1/10)
= 6 + 1.43/10
= 6 + 0.143

step 8 Find the sum of above expression:
= 6 + 0.143
= 6.143
43/7 = 6.143

Hence,
43/7 as a decimal is 6.143
43/7 as a mixed number is 6 ¹/₇