How do you write 13 quarts to 4 gallons in fractional notation in lowest terms?

1 Answer
Feb 22, 2017

#color(purple)("NOTE THAT A RATIO DOES NOT BEHAVE LIKE A FRACTIONS")#

#13/16#

Explanation:

#color(blue)("Preamble")#

You can write ratios two ways

Method 1#->"one number : the other number"#
Method 2#->("one number")/("the other number")#

Method 2 is easier for general calculations and conversions and it is the required format for this question.

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#color(blue)("Answering the question")#

We need to make the units of measurement the same. So they either have to be all in gallons or quarts

#color(brown)("I am going to do this the opposite way to that most people would just to make a point.")#

I select to use gallons as the common units.

As the name suggests, a quart is #1/4# a gallon

So as we have 13 quarts we have 13 of #1/4# gallons

This is #13/4# gallons

Thus

#("13 quarts")/("4 gallons") # which is the same volume ratio as #("gallons")/("gallons")->(color(white)(.)13/4color(white)(.))/4#

#13/4-:4" "->" "13/4xx1/4" " =" "color(magenta)( 13/16)#
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#color(brown)("Now the other way round")#

Convert them all into quarts

there are 4 quarts in 1 gallon so 4 gallons is #4xx4=16# quarts

#("quarts")/("gallons")->13/4 -= ("quarts")/("quarts")->color(magenta)(13/16)#

Note that 13 is a prime number so #13/16# can not be simplified any further.