Fraction of the Cake Left After Eating

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