Division and fractions. Mixed numbers

A fraction arises naturally from division: if

a

is divided by

b

and the division is not exact, you get a whole part and a remainder. If

a=bq+r

(with

0\le r<b

), then

\frac{a}{b}=q+\frac{r}{b}

. A symbol like

q\frac{r}{b}

is called a mixed number: -

q

— whole part, -

\frac{r}{b}

— fractional part. Reverse step:

q\frac{r}{b}=\frac{qb+r}{b}

Division with remainder links to fractions

\frac{a}{b}=q+\frac{r}{b}

when

a=bq+r

Mixed number = whole + proper fraction

q\frac{r}{b}=\frac{qb+r}{b}

From improper fraction to mixed number

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