Express the following ratio in the simplest form: $30 m i n u t e s : 2800 s e c o n d s$ .

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Solution

Step 1: Convert $m i n u t e s$ into $s e c o n d s$
$s e c o n d s$ is the smaller unit than $m i n u t e s$ .
$30 m i n u t e s = 30 \times 60 = 1800 s e c o n d s$ $(1 m i n u t e s = 60 s e c o n d s)$
Step 2: Convert the ratio in fraction
$1800 s e c o n d s : 2800 s e c o n d s = \frac{1800}{2800}$
Step 3: Divide the numerator and the denominator by 200
The Highest Common Factor of 1800 and 2800 is 200.
$\frac{1800 \div 200}{2800 \div 200} = \frac{9}{14} = 9 : 14$
Hence ,the simplest form of $30 m i n u t e s : 2800 s e c o n d s$ is $9 : 14$ .

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