Question

How many liters are equivalent to 12 US gallons?

Answer 1

45.42 Liters

Explanation:

We can use a conversion factor to solve for this value

1 Gallon = 3.785 Liters

`12 cancel(gal) (3.785 L)/(1cancel(gal)) =`

45.42 Liters

Answer 2

Brian's method uses shortcuts. The shortcut comes from this method

`45.42" L"-= 12" US gallons"`

Explanation:

Using ratios

1 US gallon = 3.785 litres (note that the English gallon is different)

Write this as a ration but in the same format as a fraction.

`("litres")/("gallons")->(3.785)/1`

Let the unknown count of litres be represented by: `?`

So we write

`("litres")/("gallons")color(brown)(->(3.785)/1-=?/12)`

To get `?` on its own multiply both sides by `color(blue)(12)`

`color(brown)(color(blue)(12xx) 3.783/1=color(blue)(12xx)?/12)`

`45.42/1=12/12xx?`

But `12/12=1`

`45.42=?`

so 45.42 Litres are `ul("'equivalent'")` to 12 US gallons

Mathematically this is written as `45.42" L"-= 12" US gallons"`

where `-=` means equivalent to