Fraction connections | Year 4

01 / LEARN

Understand the idea.

Read the denominator as a place name

Fractions and decimals can name the same amount. A denominator of $10$ means tenths, matching the first decimal place. A denominator of $100$ means hundredths, matching the second decimal place. Read the denominator before choosing where to write the numerator.

For example, $\frac{3}{10} = 0.3$ , while $\frac{3}{100} = 0.03$ . Both use the digit three, but their parts have different sizes. The zero in $0.03$ holds the empty tenths place.

Make a useful equivalent fraction

For a familiar fraction, first make an equivalent fraction with denominator $10$ or $100$ . One half is five tenths, so $\frac{1}{2} = 0.5$ . Multiply the numerator and denominator by the same amount to keep the fraction's value unchanged.

Quarters fit into hundredths because $4 \times 25 = 100$ . One quarter is twenty-five hundredths, or $0.25$ . For several quarters, count the same number of twenty-five-hundredth groups. A hundred-grid helps check that the converted decimal covers the same area.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert a fifth

Write $\frac{2}{5}$ as a decimal.

Worked solution

1
Choose a factor that makes tenths.
$5 \times 2 = 10$
Splitting every fifth into two equal parts gives tenths.
2
Scale both counts by two.
$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
The numerator must double as well as the denominator to preserve the amount.
3
Write four tenths in decimal form.
$\frac{4}{10} = 0.4$
Four tenths places 4 immediately after the decimal point.

Answer

$0.4$

EXAMPLE 02

Convert three quarters

Write $\frac{3}{4}$ as a decimal.

Worked solution

1
Find the number of hundredths in one quarter.
$\frac{1}{4} = \frac{25}{100}$
Four equal groups of twenty-five hundredths fill one whole.
2
Count the hundredths in three quarters.
$3 \times 25 = 75$
Each of the three quarters contains twenty-five hundredths.
3
Rename the total as a decimal.
$\frac{3}{4} = \frac{75}{100} = 0.75$
Seventy-five hundredths has seven tenths and five hundredths.

Answer

$0.75$

03 / YOUR TURN

Try it yourself.

Check your understanding

What decimal equals $\frac{1}{4}$ ?

Show answer & reasoning

$0.25$

One quarter is $0.25$ , since $\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}$ . Twenty-five hundredths has two tenths and five hundredths.

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Write $\frac{3}{10}$ as a decimal.
1 mark
Write $\frac{7}{100}$ as a decimal.
1 mark
Write 0.23 as a fraction with denominator 100.
1 mark
Write 0.8 as a fraction in tenths and in hundredths.
2 marks
Write $\frac{1}{2}$ and $\frac{1}{4}$ as decimals.
2 marks
Which is larger, $\frac{2}{5}$ or 0.35? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Write $\frac{3}{10}$ as a decimal.
1 mark
The fraction counts three tenths.
$0.3$
Write $\frac{7}{100}$ as a decimal.
1 mark
Seven belongs in the hundredths place.
$0.07$
Write 0.23 as a fraction with denominator 100.
1 mark
The amount is twenty-three hundredths.
$\frac{23}{100}$
Write 0.8 as a fraction in tenths and in hundredths.
2 marks
Eight tenths contain eighty hundredths.
$\frac{8}{10} = \frac{80}{100}$
Write $\frac{1}{2}$ and $\frac{1}{4}$ as decimals.
2 marks
One half is five tenths; one quarter is twenty-five hundredths.
$0.5$ and $0.25$ .
Which is larger, $\frac{2}{5}$ or 0.35? Explain.
2 marks
$\frac{2}{5} = 0.4 = 0.40$ ; forty hundredths is more than thirty-five hundredths.
$\frac{2}{5}$

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Tenths/hundredths; representations; notation; fraction connections.

Official curriculum source ↗

In this lesson

Understand the idea.

Read the denominator as a place name

Make a useful equivalent fraction

See the method in action.

Convert a fifth

Choose a factor that makes tenths.

Scale both counts by two.

Write four tenths in decimal form.

Convert three quarters

Find the number of hundredths in one quarter.

Count the hundredths in three quarters.

Rename the total as a decimal.

Try it yourself.

Check your understanding

Keep practising