Cody says that dividing a unit fraction by a whole number is the same as multiplying the unit fraction by a unit fraction with the whole number as the denominator. Which of the following supports Cody's reasoning?

A.1/4 ÷ 3 = 1/12 and 4 x 3 = 12
B.1/4 ÷ 3 = 1/2 and 1/4 x 1/3 = 1/12
C.1/4 ÷ 3 = 1/2 and 3 ÷ 1/4 = 12
D.3 ÷ 1/4 = 12 and 3 x 4 =12

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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