The value of AE is 5 1/2.
What is the difference of two fractions?
If a/b and c/d are two fractions, then their difference is
a/b - c/d = (ad - bc)/bd.
Given
AG = 9 3/4,
EG = 4 1/4.
Relation between lengths
The point E lies on the line. So, we have the relation that the sum of AE and EG equals total length of the segment AG -
AE + EG = AG. ...( 1 )
Find EG
Put the given values in the equation ( 1 ),
AE + 4 1/4 = 9 3/4
⇒ AE = 9 3/4 - 4 1/4
= (9 + 3/4) - (4 + 1/4)
= 9 - 4 + (3/4 - 1/4)
= 5 + 2/4 = 5 + 1/2
⇒ AE = 5 1/2.
The required value of AE is 5 1/2.
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