Topics
5. Fractions
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Australia
Year 4

5.08 Tenths and hundredths

Lesson
Practice
Lesson

Are you ready?

Let's review how we  name fractions  using the parts and the whole.

Examples

Example 1

Here is a fraction bar.

A fraction bar divided into 5 equal parts.

Complete the statements below.

a

This fraction bar has ⬚ equal parts.

Worked Solution
Create a strategy

Count the number of smaller squares that make up the whole bar.

Apply the idea
A fraction bar divided into 5 equal parts. One part is shaded.

Here is one part. There are 5 pieces of this size are in the whole.

This fraction bar has 5 equal parts.

b

Each part is \dfrac{⬚}{⬚} of the whole.

Worked Solution
Create a strategy

Each part looks like this:

A fraction bar divided into 5 equal parts. One part is shaded.

We can write this fraction as:

A fraction with parts explained. Ask your teacher for more information.
Apply the idea

Each part is \dfrac{1}{5} of the whole.

Idea summary

When writing fractions:

  • The number of equal parts the whole is divided into is the denominator (bottom number).

  • The numerator (top number) is how many shaded parts.

Tenths and hundredths

This video looks at two special fractions and how they are related, tenths and hundredths.

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Examples

Example 2

What fraction is shown here?

A grid of 100 squares, 43 of which are shaded.
Worked Solution
Create a strategy

A fraction is written as \dfrac{\text{number of shaded parts}}{\text{total number of parts}}.

Apply the idea

There are a total of 100 squares and 43 of those are shaded.

\displaystyle \text{Fraction}\displaystyle =\displaystyle \dfrac{43}{100}
Idea summary

A fraction from an area model is written as: \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}

Comparison of tenths and hundredths

This video shows how to compare numbers that are in tenths or hundredths.

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Examples

Example 3

Use the greater than (\gt) or less than (\lt) symbol to complete the following:

\dfrac{6}{10}\,⬚\,\dfrac{51}{100}

Worked Solution
Create a strategy

Make the denominators of the fractions the same then compare the numerators.

Apply the idea
A grid of 100 squares, 60 of which are shaded.

Using the model, \dfrac{6}{10}=\dfrac{60}{100}

60 is greater than 51.

This means that \dfrac{60}{100} is greater than \dfrac{51}{100}. So:

\dfrac{6}{10} \gt \dfrac{51}{100}

Reflect and check

We could also have converted \dfrac{6}{10} to a fraction out of 100 by multiplying the numerator and denominator by 10 since 10\times 10=100:

\displaystyle \dfrac{6}{10}\displaystyle =\displaystyle \dfrac{6}{10} \times \dfrac{10}{10}Multiply the top and bottom by 10
\displaystyle =\displaystyle \dfrac{60}{100}Perform the multiplication
Idea summary

  • Tenths and hundredths can both be used to represent the same value.

  • 1 tenth is the same as 10 hundredths. Remembering this helps us find equivalent fractions.

Patterns with tenths and hundredths

This video looks at how to apply the concept of patterns to sequences involving fractions.

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Examples

Example 4

Create a pattern by adding \dfrac{1}{10} each time.

\dfrac{4}{10}, \,⬚, \, ⬚, \,⬚, \,⬚, \,⬚

Worked Solution
Create a strategy

Add \dfrac{1}{10} to the last given value to complete the pattern.

Apply the idea
A rectangle divided into 10 parts and 4 parts are shaded.

This picture shows \dfrac{4}{10} blocks shaded blue. If another 1 block were shaded, 5 out of 10 would be shaded in total. So the next number is \dfrac{5}{10}.

\dfrac{4}{10} + \dfrac{1}{10} = \dfrac{5}{10}

We can see that the numerator increased by 1 and the denominator stayed the same. Similarly doing this for the following numbers we can complete the pattern:\dfrac{4}{10}, \,\dfrac{5}{10}, \, \dfrac{6}{10}, \,\dfrac{7}{10}, \,\dfrac{8}{10}, \,\dfrac{9}{10}

Idea summary

We can create patterns with fractions by adding or subtracting the same fraction each time.

Outcomes

AC9M4N03

find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation

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