Comparing Fractions 1

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Year 9

Fractions

Comparing Fractions

Comparing Fractions 1

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Question 1 of 4

1. Question
Which is a bigger fraction?
- 1. $\frac{7}{8}$ $7/8$
- 2. $\frac{3}{4}$ $3/4$
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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 $4$ $4$ to get $8$ $8$ .

$4 \times$ $4xx$ $?$ $?$ $=$ $=$ $8$ $8$

$4 \times$ $4xx$ $2$ $2$ $=$ $=$ $8$ $8$ You can also get $2$ $2$ by dividing $8$ $8$ by $4$ $4$

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

$\frac{3\times\color{#CC0000}{2}}{4\times\color{#CC0000}{2}}$ $=$ $=$ $\frac{6}{8}$ $6/8$

Choose the fraction with a larger numerator

$\frac{6}{8}$ $6/8$ or $\frac{7}{8}$ $7/8$

Since $\frac{7}{8}$ $7/8$ has a larger numerator, it is the larger fraction

$\frac{7}{8}$ $7/8$
Question 2 of 4

2. Question
Which is a bigger fraction?
- 1. $\frac{1}{2}$ $1/2$
- 2. $\frac{1}{3}$ $1/3$
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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 $2$ $2$ by listing their multiples

Multiples of $3$ $3$ :

$3\;\;\color{#004ec4}{6}\;\;9\;\;12$

Multiples of $2$ $2$ :

$2\;\;4\;\;\color{#004ec4}{6}\;\;8$

The LCD of $3$ $3$ and $2$ $2$ is $6$ $6$

Convert the two fractions so that their denominator is $6$ $6$

$\frac{1\times\color{#CC0000}{2}}{3\times\color{#CC0000}{2}}$ $=$ $=$ $\frac{2}{\color{#004ec4}{6}}$

$\frac{1\times\color{#CC0000}{3}}{2\times\color{#CC0000}{3}}$ $=$ $=$ $\frac{3}{\color{#004ec4}{6}}$

Choose the fraction with a larger numerator

$\frac{2}{6}$ $2/6$ or $\frac{3}{6}$ $3/6$

Since $\frac{3}{6}$ $3/6$ has a larger numerator, $\frac{1}{2}$ $1/2$ is the larger fraction

$\frac{1}{2}$ $1/2$

Question 3 of 4

Organise the fractions from smallest to biggest.

Drag the fractions to arrange them

$\frac{1}{6}$ $1/6$
$\frac{2}{7}$ $2/7$
$\frac{5}{21}$ $5/21$

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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

7

$7$ ,

6

$6$ and

21

$21$ .

Multiples of

7

$7$ :

7142128354249

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

Multiples of

6

$6$ :

612182430364248

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

Multiples of

21

$21$ :

21426384

$21\;\;\color{#004ec4}{42}\;\;63\;\;84$

The

L C D

$LCD$ of

7

$7$ ,

6

$6$ and

21

$21$ is

42

$42$

Transform the fractions so that they have $42$ $42$ as the denominator

\frac{2 \times 6}{7 \times 6}

$\frac{2\times\color{#CC0000}{6}}{7\times\color{#CC0000}{6}}$

=

$=$

\frac{12}{42}

$\frac{12}{\color{#004ec4}{42}}$

\frac{1 \times 7}{6 \times 7}

$\frac{1\times\color{#CC0000}{7}}{6\times\color{#CC0000}{7}}$

=

$=$

\frac{7}{42}

$\frac{7}{\color{#004ec4}{42}}$

\frac{5 \times 2}{21 \times 2}

$\frac{5\times\color{#CC0000}{2}}{21\times\color{#CC0000}{2}}$

=

$=$

\frac{10}{42}

$\frac{10}{\color{#004ec4}{42}}$

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

	$\frac{12}{42},\frac{7}{42},\frac{10}{42}$

$=$ $=$	$\frac{7}{42},\frac{10}{42},\frac{12}{42}$

$=$ $=$	$\frac{1}{6}, \frac{5}{21}, \frac{2}{7}$ $1/6,5/21,2/7$	Reduce back to lowest terms

$1/6,5/21,2/7$

Question 4 of 4

4. Question
Organise the fractions from largest to smallest.

Drag the fractions to arrange them
- $8/9$
- $5/6$
- $2/3$
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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 $LCD$ of $6$ , $9$ and $3$ .

Multiples of $6$ :

$6\;\;12\;\;\color{#004ec4}{18}\;\;24$

Multiples of $9$ :

$9\;\;\color{#004ec4}{18}\;\;27\;\;36$

Multiples of $3$ :

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

The $LCD$ of $6$ , $9$ and $3$ is $18$

Transform the fractions so that they have $18$ as the denominator

$\frac{5\times\color{#CC0000}{3}}{6\times\color{#CC0000}{3}}$ $=$ $\frac{15}{\color{#004ec4}{18}}$

$\frac{8\times\color{#CC0000}{2}}{9\times\color{#CC0000}{2}}$ $=$ $\frac{16}{\color{#004ec4}{18}}$

$\frac{2\times\color{#CC0000}{6}}{3\times\color{#CC0000}{6}}$ $=$ $\frac{12}{\color{#004ec4}{18}}$

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

$\frac{15}{18},\frac{16}{18},\frac{12}{18}$

$=$ $\frac{12}{18},\frac{15}{18},\frac{16}{18}$

$=$ $8/9,5/6,2/3$ Reduce back to lowest terms

$8/9,5/6,2/3$

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Quizzes

$4 \times$ $4xx$ $?$ $?$	$=$ $=$	$8$ $8$
$4 \times$ $4xx$ $2$ $2$	$=$ $=$	$8$ $8$	You can also get $2$ $2$ by dividing $8$ $8$ by $4$ $4$

	$\frac{15}{18},\frac{16}{18},\frac{12}{18}$

$=$	$\frac{12}{18},\frac{15}{18},\frac{16}{18}$

$=$	$8/9,5/6,2/3$	Reduce back to lowest terms