40/7 as a Decimal and Mixed Number
40/7 as a decimal and mixed number expansion provides the detailed information about what is 40/7 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
40/7 as a Decimal Expansion
40/7 = 5.7143
Hence,
40/7 as a decimal equals to 5.7143
where,
40/7 is a given fraction,
The decimal expansion of 40/7 is 5.7143
40/7 as a Mixed Number
40/7 = (35 + 5)/7
= 35/7 + 5/7
= 5 + 5/7
= 5 5/7
40/7 = 5 5/7
Hence,
40/7 as a mixed number is 5 5/7
where,
40/7 is a given fraction,
5 5/7 is the mixed number representation of 40/7.
How-to: 40/7 as a Decimal
The below work with steps provide the detailed information about how to convert fraction 40/7 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 40/7
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 40/7.
step 2 The numerator is greater than the denominator of the fraction 40/7, so write the given fraction in the expression form in terms of denominator as like the below:
= 40/7
= 35 + 5/7
= (5 x 7) + 5/7
step 3 Make the above expression as individual fractions:
= (5 x 7)/7 + 5/7
step 4 Simplify the above expression:
= 5 x 7/7 + 5/7
= 5 + 5/7
5 + 5/7 can be written as a mixed number 5 5/7.
step 5 Find the decimal equivalent for the fractional part 5/7 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 5/7. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 5/7.
= 5 + (5/7 x 10/10)
step 6 Simplify the above expression further:
= 5 + (50/7 x 1/10)
= 5 + (49 + 1/7 x 1/10)
= 5 + [(49/7 + 1/7 ) x 1/10]
= 5 + [(7 + 1/7) x 1/10]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 1/7 in the above expression:
= 5 + [(7 + 1/7) x 1/10]
= 5 + [(7 + 0.14) x 1/10]
= 5 + (7.14 x 1/10)
= 5 + 7.14/10
= 5 + 0.714
step 8 Find the sum of above expression:
= 5 + 0.714
= 5.714
40/7 = 5.714
Hence,
40/7 as a decimal is 5.714
40/7 as a mixed number is 5 5/7