Topics
5. Fractions
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AustraliaNSW
Stage 3

5.05 Easily relatable denominators

Lesson
Practice
Lesson

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Identifying numbers that are  multiples of other numbers  is very useful when we work with fractions.

Examples

Example 1

True or False: 18 is a multiple of 3.

Worked Solution
Create a strategy

List multiples of 3.

Apply the idea

Using your times tables or skip counting we can find the first 8 multiples of 3: 3, \,6, \,9, \,12, \,15, \,18, \,21, \,24

Since 18 is in this list, 18 is a multiple of 3. This means the statement is true.

Idea summary

Factors and multiples are related to multiplication facts. Writing out a multiplication problem, such as 4\times 6=24 can help us remember which is which.

Related denominators

How can we see if our fractions have related denominators? Let's take a look in this video.

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Examples

Example 2

Which fraction has a denominator that is a multiple of the denominator in \dfrac{1}{2}.

A
\dfrac{3}{7}
B
\dfrac{2}{4}
C
\dfrac{2}{9}
Worked Solution
Create a strategy

List multiples of 2.

Apply the idea

The first 5 multiples of 2 are 2,\,4,\,6,\,8,\,10.

Among the choices, the fraction \dfrac{2}{4} has a denominator 4 that is in the list of multiples.

The correct answer is Option B.

Idea summary

Look for common multiples between the denominators of two different fractions as this will help us to find common denominators.

Find common denominators

This video shows us how to find equivalent fractions so that we end up with common denominators.

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Examples

Example 3

Find the equivalent fraction:\dfrac{3\times 2}{5\times 2}=\dfrac{6}{⬚}

Worked Solution
Create a strategy

Multiply the denominator by the same number that has been multiplied by the numerator.

Apply the idea

The numerator has been multiplied by 2, so we must multiply the denominator by 2:

\displaystyle \dfrac{3\times 2}{5\times 2}\displaystyle =\displaystyle \dfrac{6}{10}Multiply 5 by 2
Idea summary

To find an equivalent fraction, we must multiply the denominator and numerator by the same number.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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