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here are 4 quarts in a gallon and 2 pints in 1 qua

Tags: Mathematik

19:45 Uhr, 21.06.2022

Tag!
I would like to know if the solution to this conversion problem is good because I am still in doubt

There are 4 quarts in a gallon and 2 pints in 1 quart. what fractional part of one gallon of orange juice is left when 1 pint of orange juice is poured out?

the teacher says to convert gallons to to pints
1 gallon =four quarts and one quart =2 pints

if I pour out 1 pint of the orange juice the teacher says I am left with 7 pints so the fractional part of 7 pints in 1 gallon is 7/8

but the way I see is this:
1 gallon = 1/4 + 1/4 + 1/4 + 1/4 ( four quarters)

if there are two pints in a quart, then,

1/4 = 2 pints
1/4= 2 pints
1/4 = 2 pints
1/4 = 2 pints

a gallon has 8 pints.
if I pour out 1 pint I am left with 7/8

is this whole analysis correct?

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21:04 Uhr, 21.06.2022

$>$ is this whole analysis correct?
Sure. After all you arrive at the very same result your teacher told you.
So where were you still in doubt?

Your reeasoning was correct, but formally its not okay to write

1 gallon $=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$

because on the LHS you have a volume, but on the right hand side just a dimensionless number.

Why not 1 gallon $=4$ quart $=4\cdot \left(1$ quart) $=4\cdot \left(2$ pint) $=8$ pint

21:50 Uhr, 21.06.2022

Vielen Danke,Roman. Du habst recth. I was just trying to break it down for me in a more visible way. Thanks again.