Question #bc229

#color(blue)("For 1:1")#

Consider the count of what you are looking at for 1 to 1.

You have 1 of something and 1 of something else. So the total count is 2. Thus as a fraction of the whole one of them is #1/2#

Converting this to the #ul("first decimal place which is 10ths")#

Multiply by 1 but in the form of #1=5/5# giving

#1/2xx5/5" "=" "(1xx5)/(2xx5) = 5/10#

This is the same as #0.5#
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#color(blue)("For 3:1 as parts of the whole")#

The count of parts is 3 of one thing and 1 of something else. So we have a total count of 4.

So as a proportion of the whole, 3 is #3/4#

Convert this to the second decimal place of 100ths

Multiply by 1 but in the form of #1=25/25#

#3/4xx25/25" "=" "(3xx25)/(4xx25)" "=" "75/100#

#75/100# is the same as #75%#
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As a proportion of the whole 1 is #1/4#

To change this into 100ths multiply by 1 but in the form of #1=25/25#

#1/4xx25/25" " =" " (1xx25)/(4xx25)" " =" " 25/100#

#25/100# is the same as #25%#
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#color(blue)("For 3:1 as direct relationship to each other")#

#300%# in fraction form is #300/100#

So if we multiply the ratio part of 1 by #300/100# we get the other part of the ratio which is 3

So 3 is 300% of 1