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

This page will show how to approach converting mixed numbers to 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

As well as converting mixed numbers to 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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