Fractions 4
Mixed Numbers and Vulgar (Improper) Fractions

So far we have worked with fractions of the form where a < b,

e.g. , , , ...

We also need to work with what are sometimes called vulgar or improper fractions, e.g. , , which are of the form when a and b are whole numbers and a > b.

Worked Examples

1

Show that the numbers and are equivalent.

Show me

You can illustrate as opposite.

If you count the quarters, you can see that there are 4 + 4 + 4 + 1 = 13, i.e. the number is .

(You can see that = = .)

Note that is called a mixed number.

Exercises

Write each of the numbers represented by these diagrams, in two different ways.

Remember to always write fractions in their simplest form.

(a)
=
(b)
=
(c)
=
(d)
=
(e)
=
(f)
=
(g)
=

Draw diagrams for these mixed numbers and write each number as an improper fraction.

(a)

(b)

(c)

Draw diagrams to show these improper fractions and write each improper fraction as a mixed number.

(a)

(b)

(c)

Convert these improper fractions to mixed numbers.

(a)
=
(b)
=
(c)
=
(d)
=
(e)
=
(f)
=
(g)
=
(h)
=
(i)
=
(j)
=
(k)
=
(l)
=
(m)
=
(n)
=
(o)
=

Convert these mixed numbers to improper fractions.

(a)
=
(b)
=
(c)
=
(d)
=
(e)
=
(f)
=
(g)
=
(h)
=
(i)
=
(j)
=
(k)
=
(l)
=
(m)
=
(n)
=
(o)
=

Write these fractions in order of increasing size.

,   ,   ,   ,  

< < < <

Write out each of these pairs of fractions, inserting either < , > or = into each one to make it correct.

(a)
(b)
(c)
4
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)

In an office there are packets of paper. There are 500 sheets of paper in each full packet. How many sheets of paper are there in the office?

sheets

A young child is 44 months old. Find the age of the baby in years as a mixed number in the simplest form.

years