Converting Mixed Numbers to Fractions

On this Page:
1. Mixed Number to Improper Fraction
2. Improper Fraction to Mixed Number

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}}

{\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.

1) Carry out the division of 14 divided by 3. 14 ÷ 3 = 4 remainder 2

2) From this division, the main number 4 will be the whole number of the new mixed number. ₄

3) The remainder of the division will now be the top line of the fraction part, above the original denominator. 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.

Home
Fractions and Decimals

Return to TOP of page

Converting Mixed Numbers to Fractions