SAT Fractions

Correct Answer: D

Solution 1:

Tip: When dealing with fractions, one whole unit = 1.
Daniel ate $\frac{1}{7}$ of the cake, so $1- \frac{1}{7} = \frac{7}{7} -\frac{1}{7} = \frac{6}{7}$ of the cake was left.

Edward ate $\frac{1}{3}$ of what was left, so he ate $\frac{1}{3} \times \frac{6}{7} = \frac{ 2} { 7}$ of the cake.

Hence, $\frac{ 6}{7} - \frac{2}{7} = \frac{4}{7}$ of the cake is uneaten.

Solution 2:

Tip: Replace variables with numbers.
Let there be 7 equal slices of the cake. Daniel ate 1 slice, leaving 6. Edward ate $\frac{1}{3} \times 6 = 2$ slices, leaving $6 - 2 = 4$ slices. Hence, $\frac{4}{7}$ of the cake was left.

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Incorrect Choices:

(A)
Tip: Just because a number appears in the question doesn’t mean it is the answer.

(B)
If you solve for the fraction of the cake Edward ate, you will obtain this wrong answer.

(C)
If you misread the question, and think that Daniel ate $\frac{1}{7}$ of the cake and Edward ate $\frac{1}{3},$ you will solve for the fraction of uneaten cake like this:

$1 - \frac{1}{3} - \frac{1}{7} = \frac{ 21 - 7 - 3 } { 21 } = \frac{11}{21},$

but you will be wrong.

(E)
If you solve for what fraction of the cake was left after Daniel ate, you will obtain this wrong answer.