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Mathematics · pattern A, Numeric fields

Mixed numbers to improper fractions and back.

Enter a whole part with a fraction to get the improper form, the decimal value and a check that the fractional part is proper.

Inputs

The formula used

a b/c = (ac + b)/c

Multiply the whole part by the denominator and add the numerator. The denominator never changes in this conversion.

Improper numerator

17

Improper fraction
17/5
Decimal value
3.40000000
Percentage
340.0000 %
Fraction part proper?
yes
Reciprocal
0.29411765
Doubled
6.80000000

Improper fractions are easier to compute with.

Mixed numbers read naturally and multiply awkwardly, because the whole and fractional parts each need handling. Converting to an improper fraction first makes every operation a single step, which is why textbooks want mixed numbers in answers and improper fractions in the working.

Questions about mixed fraction

Which form should an answer use?
Whatever the question asks. Where it does not say, a mixed number is conventional for a final answer.
How do I convert back?
Divide: the quotient is the whole part and the remainder becomes the new numerator over the same denominator.
Is 7/7 improper?
Technically yes, since the numerator is not smaller than the denominator. It simplifies to 1.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.