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unit rate word problem

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Andrea...The answer is b (16) set it up as a proportion problem.
Messages over Time 36/2.25 = x/1 where x will be # of messages in 1 hour
Cross multiply 2.25x = 36.
Divide each side of the equation by 2.25 x = 36/2.25 = 16


oh thanks.  why don't I have to change the fraction into a whole number then multiply? 9/4 x 36/1
Hello again Andrea.  When answering a problem like this 1st get an idea in your head what a reasonable answer would be.  When I see that he texted 36 times in 2 1/4 hours I can estimate pretty quickly that he is texting less than half that amount in only one hour.  That eliminates c and d immediately.  Now to get the exact answer I need to set up a proportion but when I do that I have to make sure that I have the same things in both numerators and the other thing in both denominators.  I am going to choose to put number of text messages in the numerators(one is 36 and the other is unknown and we will call "x".  I am going to put time in each denominator(one is 2 1/4 hours and the other is 1 hour because they asked for a unit rate).  So now I have two fractions that are equivalent(36/2.25 and x/1).  I cross multiply and solve for my unknown "x".  x times 2.25 = 36 times 1.  x = 36/2.25 = 16.  I could have used 9/4 like you wanted.  Then it would have been 36/(9/4) = x/1.  Then cross multiplying I would get x times 9/4 = 36 times 1.  Now you would solve by multiplying each side by the reciprocal (4/9).
(9/4)(4/9)x = (36)(4/9) yielding x = 16.  Hope this helps.  If you need any further explanation let me know.