Question

Convert 30 days into minutes

Answer 1

43200 minutes

Explanation:

We start with 30 days.

The following two equations are true

• 
  `1 day = 24 hours`
• 1 hour = 60 minutes

To convert units away from days, we'll want to multiply by an expression that is equal to 1 (so that we don't change the actual amount of time we're measuring) where the units in the denominator (bottom of the fraction) are days, so that they'll cancel with the units of "days" from 30 days.

In the first equation, if we divide both sides by 1 day, we'll get a fraction, equal to 1, with days in the denominator:

`1 ~day = 24~ hours`

`(1 ~day)/(1 ~day) = (24 ~hours)/(1 ~day)`

`1= (24~ hours)/(1 ~day)`

This will cancel units of days, and give an equivalent length of time in hours.

Multiplying by 1 doesn't change anything

`30~days=30~days*1`

As shown above, 24 hours divided by 1 day is equal to "1". Substitute...

`=30~days*(24 ~hours)/(1 ~day)`

Dividing by 1 doesn't change anything...

`=(30~days)/(1)*(24 ~hours)/(1 ~day)`

Multiply fractions together by multiplying numerators, and multiplying denominators...

`=(30~days~*~24 ~hours)/(1*1 ~day)`

Commutative Property of Multiplication -- switch order of denominator...

`=(30~days~*~24 ~hours)/(1 ~day~*~1)`

Multiplying fractions together is multiplying numerators, and multiplying denominators, so this just pulls those fractions apart...

`=(30~days~)/(1 ~day)*(24 ~hours)/(1)`

Days divided by Days is like 5 divided by 5. Any non-zero thing divided by itself is 1, and cancels out...

`=(30)/(1)*(24 ~hours)/(1)`

Dividing by 1 doesn't change anything...

`=30~*~24 ~hours`

Multiply the numbers together...

`=720~hours`

From here, we can do a similar process to convert from hours to minutes:

`720~hours=720~hours*1`

`=720~hours*(60~minutes)/(1~hour)`

`=(720~hours)/(1)*(60~minutes)/(1~hour)`

`=(720~hours~*~60~minutes)/(1~*~1~hour)`

`=(720~hours~*~60~minutes)/(1~hour~*~1)`

`=(720~hours)/(1~hour)*(60~minutes)/(1)`

`=(720)/(1)*(60~minutes)/(1)`

`=720*60~minutes`

`=43200~minutes`

Side note: Some of these steps may seem "obvious" to you. If so, great! You can skip them / merge them together and process things more quickly.

Answer 2

43200 minutes

Explanation:
1440 * 30= 43200