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Answer:
[tex]\frac{2}{9}[/tex] of the original cake each friend will receive, so Tari is right.
Step-by-step explanation:
You know that Genesis has [tex]\frac{2}{3}[/tex] of her birthday cake left and she wants to share it between 3 of her friends.
To determine the amount of original cake that each friend will receive is determined by dividing the [tex]\frac{2}{3}[/tex] of the cake into 3 pieces, which is the number of friends.
[tex]\frac{2}{3}[/tex] ÷3
To divide fractions by natural numbers, the whole is considered as a fraction (that is, over the denominator 1). Then you invert this the second fraction and multiply the fractions. For this, you multiply the numerators of the fractions on one side and multiply the denominators of the fractions on the other. If necessary, you simplify the resulting fraction.
In summary, to divide a fraction by a whole number, all you have to do is convert the whole number to a fraction, find the reciprocal of that fraction, and multiply the result by the first fraction.
In this case:
[tex]\frac{2}{3}[/tex] ÷3= [tex]\frac{2}{3} *\frac{1}{3}=\frac{2*1}{3*3} =\frac{2}{9}[/tex]
[tex]\frac{2}{9}[/tex] of the original cake each friend will receive, so Tari is right.