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.

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

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}$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 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.

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

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 $\frac{\editable{}}{\editable{}}$

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

Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation