NZ Level 2
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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

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