312/40 as a Decimal and Mixed Number

312/40 as a decimal and mixed number expansion provides the detailed information about what is 312/40 in decimal and mixed number form, and the answer with steps help students to easily understand how it is being calculated.

312/40 as a Decimal
312/40 = 7.8
Hence,
312/40 as a decimal equals to 7.8
where,
312/40 is a given fraction,
The decimal expansion of 312/40 is 7.8

312/40 as a Mixed Number
312/40 = (280 + 32)/40
= 280/40 + 32/40
= 7 + 32/40
= 7 32/40
312/40 = 7 32/40

Hence,
312/40 as a mixed number is 7 ³²/₄₀
where,
312/40 is a given fraction,
7 ³²/₄₀ is the mixed number representation of 312/40.

The below work with steps provide the detailed information about how to convert fraction 312/40 as a decimal equivalent.
step 1 Address the input parameters and observe what to be found:
Input values:
The fraction = 312/40

What to be found:
Find the equivalent decimal expansion and mixed number for fraction 312/40.

step 2 The numerator is greater than the denominator of the fraction 312/40, so write the given fraction in the expression form in terms of denominator as like the below:
= 312/40
= 280 + 32/40
= (7 x 40) + 32/40

step 3 Make the above expression as individual fractions:
= (7 x 40)/40 + 32/40

step 4 Simplify the above expression:
= 7 x 40/40 + 32/40
= 7 + 32/40
= 7 + 4 x 8/5 x 8
= 7 + 4/5
7 + 4/5 can be written as a mixed number 7 ⁴/₅.


step 5 Find the decimal equivalent for the fractional part 4/5 in the above expression:
Multiply both numerator and denominator by 2 to make the denominator as powers of 10:
= 7 + (4/5 x 2/2)
= 7 + 8/10

step 6 Simplify the above expression further:
= 7 + 0.8
= 7.8
312/40 = 7.8

Hence,
312/40 as a decimal is 7.8
312/40 as a mixed number is 7 ⁴/₅