# 5.08 Tenths and hundredths

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.

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

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:

We can write this fraction as:

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.

### Examples

#### Example 2

What fraction is shown here?

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.

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.

### 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

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:

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.

### 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

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

#### MA2-7NA

represents, models and compares commonly used fractions and decimals