Quick way on a calculator #->2.5#
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#color(blue)("Without a calculator and making the numbers easier") #
#color(blue)("This takes a lot longer to explain than to do")#
#color(red)("My objective in this answer is to show what can be done with numbers")#
Don't like manipulating decimals if I can help it so lets get rid of them.
Multiply by 1 and you do not change the value. However 1 comes in many forms. So you can change the way something looks without changing its value.
Demonstrating another fact by example:
#1/2-=2/4-=0.5/1" all the same as 0.5"#
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#color(blue)("Answering the question")#
So we can write: #" "color(green)(2.5/3.5 =[2.5/3.5color(red)(xx1)] =[2.5/3.5color(red)(xx10/10)] =25/35#
In the same way we have: #" "color(green)([0.7/0.2color(red)(xx10/10)] = 7/2#
So #2.5/3.5xx0.7/0.2" is the same as "25/35xx7/2#
In the same that way you can right #2xx5=5xx2# (move them around)
we can also do this: #color(green)(25/35)xxcolor(red)(7/2)" "=" "color(green)(25/(color(red)(2))xx(color(red)(7))/35)#
#color(green)(25/(color(red)(2))xx(cancel(color(red)(7))^1)/(cancel(35)^5) = (25xx1)/(2xx5)= 25/10 = 2.5#
