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Question 1186575: I would be grateful for any help her. I am confused and not sure how to explain. Thank you in advance.
When 2 fractions have the same denominator, we add or subtract them by keeping the same denominator & adding or subtracting the numerators. Example:
Patti says: We should add the tops AND the bottoms. She shows you this picture to explain why:
S _ _ _ _ + S S S _ _ =S _ _ _ _
S S S _ _ make blocks in here. The S's mean that is
a block that is shaded. So according to Patti: 1/5 + 3/5 = 1+3 =4/10
5+5
Explain what is wrong with Patti's reasoning. In your explanation use our definition of fractions (our definition of fractions is from Common Core State Standards)
How could Patti use benchmark fractions to realize her answer is wrong?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
a. Petti’s method is not valid because she added both denominators (which changes total) instead of keeping it  , and add only numerators like this:
 and  have denominator, so
b. how could Patti use estimation and benchmark fractions to see if her answer is reasonable?
Benchmark fractions are easy to visualize and identify, and thus, help in estimating the parts.(she can also count all green squares, total is  )
Benchmark fractions are especially helpful on number lines.
draw a number line, divide the distance from  to into  equal pieces, each of them represents
staring from , go one step to the right (draw a vertical line at ) and  more steps to the right (draw second vertical line at  )
so, it’s easy to see that you are of unit away from zero
c. only using proper way, we will get correct answer
Patti’s answer  is  , when we simplify it we get  (which would be correct only if she have  )
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