# Question f749d

Apr 15, 2014

Since there are 60 seconds in a minute:

Number of minutes x 60 s/min = number of seconds

Example:

Convert 75.6 minutes to seconds.

75.6 min x 60 s/min = 4,536 s

Jan 27, 2018

Full explanation given

#### Explanation:

Conversions usually have their roots in ratio

Did you know that you can and may write ratios in the format of a fraction. In such a case you must never loose sight of what the relationship is.

Consider the ratio $\text{minutes : seconds} \to 1 : 60$

Fraction format $\left(\text{minutes")/("seconds}\right) \to \frac{1}{60}$

The thing is; that in this case we also have a link to the fraction side of things as 1 second is $\frac{1}{60} {\textcolor{w h i t e}{}}^{\text{th}}$ of 1 minute

If it is more convenient there is nothing to stop you writing this 'ratio' the other way up.

Fraction format $\left(\text{seconds")/("minutes}\right) \to \frac{60}{1}$

This is where the term 60 seconds per minute comes from.
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Example: How many seconds are there in 35 minutes

By ratio

$\textcolor{g r e e n}{\left(\text{seconds")/("minutes}\right) \to \frac{60}{1} \textcolor{red}{\times 1}}$

$\textcolor{g r e e n}{\left(\text{seconds")/("minutes}\right) \to \frac{60}{1} \textcolor{red}{\times \frac{35}{35}}}$

$\textcolor{g r e e n}{\left(\text{seconds")/("minutes}\right) \to \frac{2100}{35}}$

So 35 minutes has 2100 seconds
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How do we relate this to algebraic manipulation?

Let $t$ be the final count in seconds

$t \text{ seconds" = ("seconds")/("minutes")xx"minutes used}$

t" seconds" = (60" seconds")/(1color(white)(.) cancel("minutes"))xx35cancel(" minutes used")#

You can cancel units of measurement in the same way you do numbers

$t \text{ seconds"=60xx35" seconds" = 2100" seconds}$