The fraction of the pie given to his friend is [tex]\frac{1}{2}[/tex]
The leftover given to his friends will be determined adding the portion Christine and her brother ate which are [tex]\frac{1}{6}[/tex] and [tex]\frac{1}{3}[/tex] respectively, then subtracted from the whole portion.
= [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{3}[/tex] (The lowest common denominator of 6 and 3 = 6)
= (1 x 1) + (2 x 1) /6
= (1) + (2) / 6
= 1 + 2 / 6
= [tex]\frac{3}{6}[/tex]
Thus, total portion of the pie eaten by Christine and her brother = [tex]\frac{3}{6}[/tex] . Also the fraction of the whole portion of the pie = [tex]\frac{6}{6}[/tex]
Determining the portion given to the friend =
Subtracting [tex]\frac{6}{6}[/tex] – [tex]\frac{3}{6}[/tex]
= [tex]\frac{6}{6}[/tex] – [tex]\frac{3}{6}[/tex] (The lowest common denominator of 6 and 6 = 6)
= (1 x 6) – (1 x 3) / 6
= (6) – (3) / 6
= 6 – 3 / 6
= [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex] (further broken down to this)
Therefore the fraction given to the friend is [tex]\frac{1}{2}[/tex].
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