NZ Level 2 Ordering and counting with fractions
Lesson  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.

1. $\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.

1. $\frac{1}{5}$15, , $2$2 fifths

$\frac{1}{5}$15, $2$2 fifths, A , $2$2 fifths, $\frac{1}{5}$15

B

$2$2 fifths, , $\frac{1}{5}$15

C

$\frac{1}{5}$15, $2$2 fifths, A , $2$2 fifths, $\frac{1}{5}$15

B

$2$2 fifths, , $\frac{1}{5}$15

C

## 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.

1. 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. 1. How many slices of pie does Kenneth have in total?

He has $\editable{}$ slices.

2. Write a fraction representing one slice of one pie.

One slice is $\frac{\editable{}}{\editable{}}$ of a whole pie.

3. Write an improper fraction which represents one whole pie.

A whole pie is $\frac{\editable{}}{\editable{}}$ of a whole pie.

4. 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
5. 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 $\frac{\editable{}}{\editable{}}$
6. 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 $\frac{\editable{}}{\editable{}}$

Remember!

An improper fraction has a numerator greater than or equal to the denominator

A mixed number is a whole number and a fraction part

### Outcomes

#### NA2-5

Know simple fractions in everyday use