Comparing Fractions 2

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Year 10

Fractions

Comparing Fractions

Comparing Fractions 2

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Question 1 of 4

1. Question
Which is a bigger fraction?
- 1. $\frac{7}{10}$ $7/10$
- 2. $\frac{4}{5}$ $4/5$
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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 what number can be multiplied to $5$ $5$ to get $10$ $10$ .

$5 \times$ $5xx$ $?$ $?$ $=$ $=$ $10$ $10$

$5 \times$ $5xx$ $2$ $2$ $=$ $=$ $10$ $10$ You can also get $2$ $2$ by dividing $10$ $10$ by $5$ $5$

Multiply $2$ $2$ to both the numerator and denominator

$\frac{4\times\color{#CC0000}{2}}{5\times\color{#CC0000}{2}}$ $=$ $=$ $\frac{8}{10}$ $8/10$

Choose the fraction with a larger numerator

$\frac{8}{10}$ $8/10$ or $\frac{7}{10}$ $7/10$

Since $\frac{8}{10}$ $8/10$ has a larger numerator, $\frac{3}{5}$ $3/5$ is the larger fraction

$\frac{4}{5}$ $4/5$
Question 2 of 4

2. Question
Which is a bigger fraction?
- 1. $\frac{2}{7}$ $2/7$
- 2. $\frac{1}{6}$ $1/6$
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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 $6$ $6$ and $7$ $7$ by listing their multiples

Multiples of $6$ $6$ :

$6\;\;12\;\;18\;\;24\;\;30\;\;36\;\;\color{#004ec4}{42}\;\;48$

Multiples of $7$ $7$ :

$7\;\;14\;\;21\;\;28\;\;35\;\;\color{#004ec4}{42}\;\;49$

The LCD of $6$ $6$ and $7$ $7$ is $42$ $42$

Convert the two fractions so that their denominator is $42$ $42$

$\frac{1\times\color{#CC0000}{7}}{6\times\color{#CC0000}{7}}$ $=$ $=$ $\frac{7}{\color{#004ec4}{42}}$

$\frac{2\times\color{#CC0000}{6}}{7\times\color{#CC0000}{6}}$ $=$ $=$ $\frac{12}{\color{#004ec4}{42}}$

Choose the fraction with a larger numerator

$\frac{7}{42}$ $7/42$ or $\frac{12}{42}$ $12/42$

Since $\frac{12}{42}$ $12/42$ has a larger numerator, $\frac{2}{7}$ $2/7$ is the larger fraction

$\frac{2}{7}$ $2/7$

Question 3 of 4

Organise the fractions from smallest to biggest.

Drag the fractions to arrange them

$\frac{3}{10}$ $3/10$
$\frac{1}{2}$ $1/2$
$\frac{1}{4}$ $1/4$

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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

$10$ ,

2

$2$ and

4

$4$ .

Multiples of

10

$10$ :

102030

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

Multiples of

2

$2$ :

2468101214161820

$2\;\;4\;\;6\;\;8\;\;10\;\;12\;\;14\;\;16\;\;18\;\;\color{#004ec4}{20}$

Multiples of

4

$4$ :

4812162024

$4\;\;8\;\;12\;\;16\;\;\color{#004ec4}{20}\;\;24$

The

L C D

$LCD$ of

10

$10$ ,

2

$2$ and

4

$4$ is

20

$20$

Transform the fractions so that they have $20$ $20$ as the denominator

\frac{3 \times 2}{10 \times 2}

$\frac{3\times\color{#CC0000}{2}}{10\times\color{#CC0000}{2}}$

=

$=$

\frac{6}{20}

$\frac{6}{\color{#004ec4}{20}}$

\frac{1 \times 10}{2 \times 10}

$\frac{1\times\color{#CC0000}{10}}{2\times\color{#CC0000}{10}}$

=

$=$

\frac{10}{20}

$\frac{10}{\color{#004ec4}{20}}$

\frac{1 \times 5}{4 \times 5}

$\frac{1\times\color{#CC0000}{5}}{4\times\color{#CC0000}{5}}$

=

$=$

\frac{5}{20}

$\frac{5}{\color{#004ec4}{20}}$

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

	$\frac{6}{20},\frac{10}{20},\frac{5}{20}$

$=$ $=$	$\frac{5}{20},\frac{6}{20},\frac{10}{20}$

$=$ $=$	$\frac{1}{4},\frac{3}{10},\frac{1}{2}$	Reduce back to lowest terms

\frac{1}{4}, \frac{3}{10}, \frac{1}{2}

$1/4,3/10,1/2$

Question 4 of 4

Organise the fractions from smallest to biggest.

Drag the fractions to arrange them

$\frac{2}{3}$ $2/3$
$\frac{3}{4}$ $3/4$
$\frac{7}{8}$ $7/8$

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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

8

$8$ ,

3

$3$ and

4

$4$ .

Multiples of

8

$8$ :

8162432

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

Multiples of

3

$3$ :

369121518212427

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

Multiples of

4

$4$ :

481216202428

$4\;\;8\;\;12\;\;16\;\;20\;\;\color{#004ec4}{24}\;\;28$

The

L C D

$LCD$ of

8

$8$ ,

3

$3$ and

4

$4$ is

24

$24$

Transform the fractions so that they have $24$ $24$ as the denominator

\frac{7 \times 3}{8 \times 3}

$\frac{7\times\color{#CC0000}{3}}{8\times\color{#CC0000}{3}}$

=

$=$

\frac{21}{24}

$\frac{21}{\color{#004ec4}{24}}$

\frac{2 \times 8}{3 \times 8}

$\frac{2\times\color{#CC0000}{8}}{3\times\color{#CC0000}{8}}$

=

$=$

\frac{16}{24}

$\frac{16}{\color{#004ec4}{24}}$

\frac{3 \times 6}{4 \times 6}

$\frac{3\times\color{#CC0000}{6}}{4\times\color{#CC0000}{6}}$

=

$=$

\frac{18}{24}

$\frac{18}{\color{#004ec4}{24}}$

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

	$\frac{21}{24},\frac{16}{24},\frac{18}{24}$

$=$ $=$	$\frac{16}{24},\frac{18}{24},\frac{21}{24}$

$=$ $=$	$\frac{2}{3}, \frac{3}{4}, \frac{7}{8}$ $2/3,3/4,7/8$	Reduce back to lowest terms

\frac{2}{3}, \frac{3}{4}, \frac{7}{8}

$2/3,3/4,7/8$

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Quizzes

$5 \times$ $5xx$ $?$ $?$	$=$ $=$	$10$ $10$
$5 \times$ $5xx$ $2$ $2$	$=$ $=$	$10$ $10$	You can also get $2$ $2$ by dividing $10$ $10$ by $5$ $5$