76/45 as a decimal and mixed number expansion provides the detailed information about what is 76/45 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.
76/45 as a Decimal Expansion
76/45 = 1.6889
Hence,
76/45 as a decimal equals to 1.6889
where,
76/45 is a given fraction,
The decimal expansion of 76/45 is 1.6889
76/45 as a Mixed Number
76/45 = (45 + 31)/45
= 45/45 + 31/45
= 1 + 31/45
= 1 31/45
76/45 = 1 31/45
Hence,
76/45 as a mixed number is 1 31/45
where,
76/45 is a given fraction,
1 31/45 is the mixed number representation of 76/45.
The below work with steps provide the detailed information about how to convert fraction 76/45 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 76/45
What to be found:
Find the equivalent decimal expansion and mixed number for fraction 76/45.
step 2 The numerator is greater than the denominator of the fraction 76/45, so write the given fraction in the expression form in terms of denominator as like the below:
= 76/45
= 45 + 31/45
step 3 Make the above expression as individual fractions:
= 45/45 + 31/45
step 4 Simplify the above expression:
= 1 x 45/45 + 31/45
= 1 + 31/45
1 + 31/45 can be written as a mixed number 1 31/45.
step 5 Find the decimal equivalent for the fractional part 31/45 in the above expression:
Find how many 10s should be multiplied with both numerator and denominator of fractional part 31/45. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 31/45.
= 1 + (31/45 x 10/10)
step 6 Simplify the above expression further:
= 1 + (310/45 x 1/10)
= 1 + (270 + 40/45 x 1/10)
= 1 + [(270/45 + 40/45 ) x 1/10]
= 1 + [(6 + 40/45) x 1/10]
step 7 Repeat the step 5 to find the decimal equivalent for the fraction 40/45 in the above expression:
= 1 + [(6 + 40/45) x 1/10]
= 1 + [(6 + 0.89) x 1/10]
= 1 + (6.89 x 1/10)
= 1 + 6.89/10
= 1 + 0.689
step 8 Find the sum of above expression:
= 1 + 0.689
= 1.689
76/45 = 1.689
Hence,
76/45 as a decimal is 1.689
76/45 as a mixed number is 1 31/45