Simplify Fractions 3

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Year 9

Fractions

Simplify Fractions

Simplify Fractions 3

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Question 1 of 4

1. Question
Simplify

$\frac{21}{72}$ $21/72$

Write fractions in the format “a/b”
- (7/24)
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The Highest Common Factor ( $H C F$ $HCF$ ) between two numbers is the highest possible number that divides evenly to both numbers.

To simplify a fraction, divide the numerator and denominator by their $H C F$ $HCF$

Start by listing out the factors of each number

Factors of $21$ $21$ :

$1\;\;3\;\;7\;\;21$

Factors of $72$ $72$ :

$1\;\;2\;\;3\;\;4\;\;6\;\;8\;\;9\;\;12\;\;18$

Identify the highest number that is both a factor of $21$ $21$ and $72$ $72$

Factors of $21$ $21$ :

$1\;\;\color{#CC0000}{3}\;\;7\;\;21$

Factors of $72$ $72$ :

$1\;\;2\;\;\color{#CC0000}{3}\;\;4\;\;6\;\;8\;\;9\;\;12\;\;18$

The $H C F$ $HCF$ of $21$ $21$ and $72$ $72$ is $3$ $3$

Divide both the numerator and denominator by $3$ $3$

$\frac{21\div\color{#CC0000}{3}}{72\div\color{#CC0000}{3}}$ $=$ $=$ $\frac{7}{24}$ $7/24$

$\frac{7}{24}$ $7/24$
Question 2 of 4

2. Question
Simplify

$\frac{120}{135}$ $120/135$

Write fractions in the format “a/b”
- (8/9)
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The Highest Common Factor ( $H C F$ $HCF$ ) between two numbers is the highest possible number that divides evenly to both numbers.

To simplify a fraction, divide the numerator and denominator by their $H C F$ $HCF$

Alternatively, we can use any common factor and keep dividing until we get the simplest form

$\frac{120\div\color{#CC0000}{5}}{135\div\color{#CC0000}{5}}$ $=$ $=$ $\frac{24}{27}$ $24/27$ Numbers ending at $5$ $5$ or $0$ $0$ are multiples of $5$ $5$

Simplify the fraction further by dividing $3$ $3$

$\frac{24\div\color{#CC0000}{3}}{27\div\color{#CC0000}{3}}$ $=$ $=$ $\frac{8}{9}$ $8/9$

Since this can no longer be simplified, $\frac{8}{9}$ $8/9$ is the simplest fraction

$\frac{8}{9}$ $8/9$
Question 3 of 4

3. Question
Simplify

$\frac{600}{700}$ $600/700$

Write fractions in the format “a/b”
- (6/7)
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The Highest Common Factor ( $H C F$ $HCF$ ) between two numbers is the highest possible number that divides evenly to both numbers.

Aside from using $H C F$ $HCF$ , we can use an obvious common factor until we get the simplest form

Since both numerator and denominator end with $2$ $2$ zeroes, both are divisible by $100$ $100$

$\frac{600\div\color{#CC0000}{100}}{700\div\color{#CC0000}{100}}$ $=$ $=$ $\frac{6}{7}$ $6/7$

Since this can no longer be simplified, $\frac{6}{7}$ $6/7$ is the simplest fraction

$\frac{6}{7}$ $6/7$
Question 4 of 4

4. Question
Simplify

$\frac{160}{240}$ $160/240$

Write fractions in the format “a/b”
- (2/3)
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The Highest Common Factor ( $H C F$ $HCF$ ) between two numbers is the highest possible number that divides evenly to both numbers.

To simplify a fraction, divide the numerator and denominator by their $H C F$ $HCF$

Alternatively, we can use any common factor and keep dividing until we get the simplest form

$\frac{160\div\color{#CC0000}{10}}{240\div\color{#CC0000}{10}}$ $=$ $=$ $\frac{16}{24}$ $16/24$ Numbers ending at $0$ $0$ are multiples of $10$ $10$

Simplify the fraction further by dividing $8$ $8$

$\frac{16\div\color{#CC0000}{8}}{24\div\color{#CC0000}{8}}$ $=$ $=$ $\frac{2}{3}$ $2/3$

Since this can no longer be simplified, $\frac{2}{3}$ $2/3$ is the simplest fraction

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

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