Simplify Fractions 1

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Pre - Algebra

Fractions

Simplify Fractions

Simplify Fractions 1

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Question 1 of 3

1. Question
Simplify

$\frac{6}{10}$ $6/10$

Write fractions in the format “a/b”
- (3/5)
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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 $6$ $6$ :

$1\;\;2\;\;3\;\;6$

Factors of $10$ $10$ :

$1\;\;2\;\;5\;\;10$

Identify the highest number that is both a factor of $6$ $6$ and $10$ $10$

Factors of $6$ $6$ :

$1\;\;\color{#CC0000}{2}\;\;3\;\;6$

Factors of $10$ $10$ :

$1\;\;\color{#CC0000}{2}\;\;5\;\;10$

The $H C F$ $HCF$ of $6$ $6$ and $10$ $10$ is $2$ $2$

Divide both the numerator and denominator by $2$ $2$

$\frac{6\div\color{#CC0000}{2}}{10\div\color{#CC0000}{2}}$ $=$ $=$ $\frac{3}{5}$ $3/5$

$\frac{3}{5}$ $3/5$
Question 2 of 3

2. Question
Simplify

$\frac{15}{20}$ $15/20$

Write fractions in the format “a/b”
- (3/4)
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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 $15$ $15$ :

$1\;\;3\;\;5\;\;15$

Factors of $20$ $20$ :

$1\;\;2\;\;4\;\;5\;\;10\;\;20$

Identify the highest number that is both a factor of $15$ $15$ and $20$ $20$

Factors of $15$ $15$ :

$1\;\;3\;\;\color{#CC0000}{5}\;\;15$

Factors of $20$ $20$ :

$1\;\;2\;\;4\;\;\color{#CC0000}{5}\;\;10\;\;20$

The $H C F$ $HCF$ of $15$ $15$ and $20$ $20$ is $5$ $5$

Divide both the numerator and denominator by $5$ $5$

$\frac{15\div\color{#CC0000}{5}}{20\div\color{#CC0000}{5}}$ $=$ $=$ $\frac{3}{4}$ $3/4$

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

3. Question
Simplify

$\frac{28}{80}$ $28/80$

Write fractions in the format “a/b”
- (7/20)
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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

$\frac{28\div\color{#CC0000}{2}}{80\div\color{#CC0000}{2}}$ $=$ $=$ $\frac{14}{40}$ $14/40$ Divide by $2$ $2$ since they are both even

Simplify the fraction further by again dividing $2$ $2$

$\frac{14\div\color{#CC0000}{2}}{40\div\color{#CC0000}{2}}$ $=$ $=$ $\frac{7}{20}$ $7/20$

Since this can no longer be simplified, $\frac{7}{20}$ $7/20$ is the simplest fraction

$\frac{7}{20}$ $7/20$

Simplify Fractions 1

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