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Fractions

Mixed Numbers and Improper Fractions

A mixed number contains a whole part and a fractional part.

is a mixed number. It contains both a whole part , 3, and a fractional part, 2/5. We read the fraction as "three and two fifths" and this is exactly what we mean.

=

Adding a whole number to a fraction is a special case of addition of two fractions. Click on the question mark to see the addition step-by-step:

=

We usually skip the intermediate steps. Click on the question mark below to see the improved method:

In writing these mixed numbers as a single fraction, we are writing improper fractions. An improper fraction is any fraction which has a numerator that is greater than the denominator. For example , is an improper fraction. Mixed numbers can always be written as improper fractions.

Think about pies. If we had two pies and 3/8 of a pie, we can figure out how many 1/8-sized pieces we have.

2 3/8 = (2*8 + 3)/8 = 19/8

More Examples

Exercise

Practice changing positive mixed numbers to improper fractions:

Take a few minutes to practise the reverse process - making an improper fraction into a mixed number. Think of a multiple of the denominator that is just smaller than the numerator. This multiple gives you the whole part of the mixed number. The difference between the multiple and the numerator gives you the numerator for the fractional part.

Example

Again pies come to mind.

17 =

17/6 = (12 + 5)/6 = (2*6 + 5)/6 = 2 5/6

Exercise

For these exercises, convert the improper fraction to a mixed number.

Signed Mixed Numbers

Consider the mixed fraction . Here the sign applies to all of .

That is,

Beware: which is in fact

In short, you can convert the numeric part of a negative mixed number to an improper fraction in the same way as a positive one, except the improper fraction gets a negative sign.

Study a few more examples of changing negative mixed numbers into improper fractions:

Exercise

Try some of these exercises of changing negative mixed numbers into improper fractions:

Now the reverse process - making a negative improper fraction into a mixed number. Treat a negative improper fraction in the same way as a positive improper fraction giving the result a negative sign. Ignoring the sign for a moment, think of a multiple of the denominator that is just smaller than the numerator. This multiple gives you the integer part of the mixed number. The difference between the multiple and the numerator gives the numerator of the fractional part. Remember to include the negative sign on the mixed number.

Example

Exercise

For these exercises, convert the improper fraction to a mixed number.

<< Subtraction | Fractions Index | Operations with Mixed Numbers >>