Mixed numbers and fractions that are classed as “improper” were touched on in the understanding fractions page.

This page will show how to convert between mixed numbers and fractions that are improper, where the value of the fraction is greater than 1.

## Converting Mixed Numbers to Fractions,

Converting to Improper Fractions

Say you had the mixed number _{2}\bf{\frac{3}{4}}.

Which you wan to convert to an entire fraction, an improper fraction.

This is possible, and can be done in 3 clear steps.

**1)***Multiply the whole number of the mixed number by the denominator of the fraction part.*

**2)***Add the result of this multiplication to the top numerator of the fraction part of the mixed number.*

*The result will be the top line of the new fraction.*

**3)***To complete the conversion, the original denominator on the bottom will also be the denominator of the new fraction.*

### Steps in Action:

Let’s look at this process in action for_{2}\bf{\frac{3}{4}}.

**2**×

**4**=

**8**

**8**+

**3**=

**11**Now the new fraction we have is \bf{\frac{11}{4}}.

Or alternatively, we could also layout the steps as the following sums which can be a bit quicker and simpler.

_{2}\bf{\frac{3}{4}} = \boldsymbol{\frac{2 \space \times \space 4 \space + \space 3}{4}} = \boldsymbol{\frac{8 \space + \space 3}{4}} = \bf{\frac{11}{4}}

So {\frac{11}{4}} is the improper fraction form of

_{2}{\frac{3}{4}}, they are the same value.

__Examples__

*(1.1)*Convert the mixed number

_{3}\bf{\frac{4}{7}} to a standard fraction.

*Solution*_{3}\bf{\frac{4}{7}} = \boldsymbol{\frac{3 \space \times \space 7 \space + \space 4}{7}} = \boldsymbol{\frac{21 \space + \space 4}{7}} = \bf{\frac{25}{7}}

*(1.2)*Convert the mixed number –

_{2}\bf{\frac{1}{6}} to a standard fraction.

*Solution*With negative mixed numbers and fractions, a simple way to proceed is to just carry out the sums as normal, but keep a minus sign at the side ready to use at the end.

–

_{2}\bf{\frac{1}{6}} = – ( \boldsymbol{\frac{2 \space \times \space 6 \space + \space 1}{6}} ) = – ( \boldsymbol{\frac{12 \space + \space 1}{6}} ) = –\bf{\frac{13}{6}}

## Converting Improper Fractions to a

Mixed Number

With mixed numbers and fractions, an improper fraction can also be converted to a mixed number when required.

The steps are slightly different, but again fairly easy to learn.

Let’s look at how to proceed with the fraction \bf{\frac{14}{3}} as our guide.

__Carry out the division of 14 divided by 3.__

**1)****14**÷

**3**=

**4**remainder

**2**

__From this division, the main number 4 will be the whole number of the new mixed number.__

**2)**_{4}

__The remainder of the division will now be the top line of the fraction part, above the original denominator.__

**3)**_{4}\bf{\frac{2}{3}}

__Examples__

*(2.1)*Convert the improper fraction \bf{\frac{17}{6}} to a mixed number.

*Solution***17**÷

**6**=

**2**remainder

**5**, giving us

_{2}\bf{\frac{5}{6}} as the mixed number form.

*(2.2)*Convert the improper fraction –\bf{\frac{10}{3}} to a mixed number.

*Solution*The initial fraction being negative doesn’t have to affect the steps we perform. The process is just the same.

–

**10**÷

**3**= –

**3**remainder

**1**, giving us –

_{3}\bf{\frac{1}{3}} as the mixed number form here.

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