Ordering and counting with fractions
You may have already learned about representing fractions as areas of shapes.
When representing fractions the:
- denominator (the bottom number) represents how many equal parts make the whole
- numerator (the top number) represents how many equal parts are selected.
Fractions can be written in:
- words, e.g. six eighths
- pictures, e.g.
- symbols, e.g. $\frac{6}{8}$68
Watch this video to learn about counting and ordering fractions in words, symbols and pictures.
Try these questions for yourself.
Worked examples
Question 1
Danielle was counting fractions in the eighths.
Fill in the gaps for her.
$\frac{0}{8}$08 $\frac{\editable{}}{8}$8 $\frac{2}{8}$28 $\frac{3}{\editable{}}$3 $\frac{4}{8}$48 $\frac{5}{\editable{}}$5 $\frac{6}{8}$68 $\frac{\editable{}}{8}$8 $\frac{8}{8}$88
Question 2
Order these fractions from smallest to largest.
$\frac{1}{5}$15,
, $2$2 fifths$\frac{1}{5}$15, $2$2 fifths,
A, $2$2 fifths, $\frac{1}{5}$15B$2$2 fifths,
, $\frac{1}{5}$15C
Improper fractions and mixed fractions
Improper fractions have a numerator that is greater than or equal to the denominator, for example, $\frac{8}{5}$85.
Mixed fractions have a whole number and a fraction part, for example, $4$4$\frac{5}{6}$56.
Watch this video to learn about improper and mixed fractions.
Try these questions for yourself.
Worked examples
Question 3
Fill in the gaps in table by completing the conversions.
Mixed Number Improper Fraction $1\frac{2}{3}$123 $\frac{5}{3}$53 $\editable{}$$\frac{\editable{}}{\editable{}}$
$\frac{3}{2}$32 $1\frac{3}{4}$134 $\frac{\editable{}}{\editable{}}$ $2\frac{2}{3}$223 $\frac{\editable{}}{\editable{}}$ $\editable{}$$\frac{\editable{}}{\editable{}}$
$\frac{9}{4}$94
Question 4
Kenneth has two whole pies.
He cuts each pie into $6$6 slices.
How many slices of pie does Kenneth have in total?
He has $\editable{}$ slices.
Write a fraction representing one slice of one pie.
One slice is $\frac{\editable{}}{\editable{}}$ of a whole pie.
Write an improper fraction which represents one whole pie.
A whole pie is $\frac{\editable{}}{\editable{}}$ of a whole pie.
Fill in the gap in the table below.
One Slice One Pie One Pie + $\editable{}$ slice $\frac{1}{6}$16 $\frac{6}{6}$66 $\frac{7}{6}$76 Fill in the gap in the table below with an improper fraction.
One Slice One Pie One Pie + $1$1 slice One Pie + $2$2 Slices $\frac{1}{6}$16 $\frac{6}{6}$66 $\frac{7}{6}$76 $\frac{\editable{}}{\editable{}}$ Fill in the gap in the table below with an improper fraction.
One Slice One Pie One Pie + $1$1 slice One Pie + $2$2 Slices Two Pies $\frac{1}{6}$16 $\frac{6}{6}$66 $\frac{7}{6}$76 $\frac{8}{6}$86 $\frac{\editable{}}{\editable{}}$
An improper fraction has a numerator greater than or equal to the denominator
A mixed number is a whole number and a fraction part