Comparing Fractions 3

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Year 10

Fractions

Comparing Fractions

Comparing Fractions 3

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Question 1 of 3

1. Question
Which is a bigger fraction?
- 1. $\frac{2}{3}$ $2/3$
- 2. $\frac{5}{8}$ $5/8$
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Fractions are easier compared when they have the same denominator.

First, make sure the two fractions have the same denominator

Identify the $L C D$ $LCD$ of $3$ $3$ and $8$ $8$ by listing their multiples

Multiples of $3$ $3$ :

$3\;\;6\;\;9\;\;12\;\;15\;\;18\;\;21\;\;\color{#004ec4}{24}\;\;27$

Multiples of $8$ $8$ :

$8\;\;16\;\;21\;\;\color{#004ec4}{24}\;\;32$

The LCD of $3$ $3$ and $8$ $8$ is $24$ $24$

Convert the two fractions so that their denominator is $24$ $24$

$\frac{2\times\color{#CC0000}{8}}{3\times\color{#CC0000}{8}}$ $=$ $=$ $\frac{16}{\color{#004ec4}{24}}$

$\frac{5\times\color{#CC0000}{3}}{8\times\color{#CC0000}{3}}$ $=$ $=$ $\frac{15}{\color{#004ec4}{24}}$

Choose the fraction with a larger numerator

$\frac{16}{24}$ $16/24$ or $\frac{15}{24}$ $15/24$

Since $\frac{16}{24}$ $16/24$ has a larger numerator, $\frac{2}{3}$ $2/3$ is the larger fraction

$\frac{2}{3}$ $2/3$

Question 2 of 3

Organise the fractions from largest to smallest.

Drag the fractions to arrange them

$\frac{2}{3}$ $2/3$
$\frac{3}{4}$ $3/4$
$\frac{4}{5}$ $4/5$

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Fractions are easier compared when they have the same denominator.

First, make sure the three fractions have the same denominator

Since

4

$4$ ,

5

$5$ and

3

$3$ doesn’t have any immediate common multiple, simply multiply them to find their

L C D

$LCD$

4 \times 5 \times 3

$4xx5xx3$

=

$=$

60

$60$

The

L C D

$LCD$ of

4

$4$ ,

5

$5$ and

3

$3$ is

60

$60$

Transform the fractions so that they have $60$ $60$ as the denominator

\frac{3 \times 15}{4 \times 15}

$\frac{3\times\color{#CC0000}{15}}{4\times\color{#CC0000}{15}}$

=

$=$

\frac{45}{60}

$\frac{45}{\color{#004ec4}{60}}$

\frac{4 \times 12}{5 \times 12}

$\frac{4\times\color{#CC0000}{12}}{5\times\color{#CC0000}{12}}$

=

$=$

\frac{48}{60}

$\frac{48}{\color{#004ec4}{60}}$

\frac{2 \times 20}{3 \times 20}

$\frac{2\times\color{#CC0000}{20}}{3\times\color{#CC0000}{20}}$

=

$=$

\frac{40}{60}

$\frac{40}{\color{#004ec4}{60}}$

Finally, arrange the fractions from the largest numerator to the smallest

	$\frac{45}{60},\frac{48}{60},\frac{40}{60}$

$=$ $=$	$\frac{48}{60},\frac{45}{60},\frac{40}{60}$

$=$ $=$	$\frac{4}{5}, \frac{3}{4}, \frac{2}{3}$ $4/5,3/4,2/3$	Reduce back to lowest terms

\frac{4}{5}, \frac{3}{4}, \frac{2}{3}

$4/5,3/4,2/3$

Question 3 of 3

3. Question
Organise the fractions from largest to smallest.

Drag the fractions to arrange them
- $\frac{11}{15}$ $11/15$
- $\frac{7}{10}$ $7/10$
- $\frac{3}{5}$ $3/5$
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Fractions are easier compared when they have the same denominator.

First, make sure the three fractions have the same denominator

Find the $L C D$ $LCD$ of $10$ $10$ , $5$ $5$ and $15$ $15$ .

Multiples of $10$ $10$ :

$10\;\;20\;\;\color{#004ec4}{30}\;\;40$

Multiples of $5$ $5$ :

$5\;\;10\;\;15\;\;\color{#004ec4}{30}\;\;35$

Multiples of $15$ $15$ :

$15\;\;\color{#004ec4}{30}\;\;45\;\;60$

The $L C D$ $LCD$ of $10$ $10$ , $5$ $5$ and $15$ $15$ is $30$ $30$

Transform the fractions so that they have $30$ $30$ as the denominator

$\frac{7\times\color{#CC0000}{3}}{10\times\color{#CC0000}{3}}$ $=$ $\frac{21}{\color{#004ec4}{30}}$

$\frac{3\times\color{#CC0000}{6}}{5\times\color{#CC0000}{6}}$ $=$ $\frac{18}{\color{#004ec4}{30}}$

$\frac{11\times\color{#CC0000}{2}}{15\times\color{#CC0000}{2}}$ $=$ $\frac{22}{\color{#004ec4}{30}}$

Finally, arrange the fractions from the largest numerator to the smallest

$\frac{21}{30},\frac{18}{30},\frac{22}{30}$

$=$ $\frac{18}{30},\frac{21}{30},\frac{22}{30}$

$=$ $11/15,7/10,3/5$ Reduce back to lowest terms

$11/15,7/10,3/5$

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	$\frac{21}{30},\frac{18}{30},\frac{22}{30}$

$=$	$\frac{18}{30},\frac{21}{30},\frac{22}{30}$

$=$	$11/15,7/10,3/5$	Reduce back to lowest terms