Fraction of the Cake Left After Eating
In this scenario, two individuals, Lindsay and Emily, consume portions of a cake. We need to calculate and understand the fraction of the cake that remains uneaten after their nibbles.
Initial Conditions
Let's start with the initial fraction of the cake:
Total cake: 1 (assumed to be the whole cake)
Lindsay Eats Her Portion
First:
Lindsay eats ( frac{1}{3} ) of the cake.
Calculating the Remaining Cake After Lindsay
The remaining cake after Lindsay is:
(1 - frac{1}{3} frac{3}{3} - frac{1}{3} frac{2}{3})
Emily Eats Her Portion
Next, Emily eats ( frac{1}{4} ) of the remaining cake:
Remaining cake before Emily: ( frac{2}{3} )
Emily’s portion: ( frac{1}{4} times frac{2}{3} frac{1}{4} times frac{2}{3} frac{2}{12} frac{1}{6} )
Calculating the Total Eaten and Remaining Cake
The total portion eaten by both individuals:
( frac{1}{3} frac{1}{6} frac{2}{6} frac{1}{6} frac{3}{6} frac{1}{2} )
Therefore, the remaining fraction of the cake:
( 1 - frac{1}{2} frac{1}{2} )
Alternatively, using a different method:
( frac{1}{3} frac{1}{4} frac{4}{12} frac{3}{12} frac{7}{12} )
The remaining fraction:
( 1 - frac{7}{12} frac{12}{12} - frac{7}{12} frac{5}{12} )
Conclusion
Thus, ( frac{5}{12} ) of the cake remains uneaten. This can also be expressed as a decimal: ( 0.416666ldots ) or ( approx 0.42 ).
Keywords: fraction of cake, uneaten cake, fraction calculation