Calculate Remaining Fraction: 1/4 Eaten from 3/8 of a Chocolate Cake

Fraction Subtraction with Different Starting Amounts

A chocolate cake is divided into 8 equal slices.

When Jorge goes to try the cake, he sees that only 3 slices are left.

If Jorge eats 14 \frac{1}{4} of the cake, then how much of the chocolate cake is left?

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Step-by-step written solution

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1

Understand the problem

A chocolate cake is divided into 8 equal slices.

When Jorge goes to try the cake, he sees that only 3 slices are left.

If Jorge eats 14 \frac{1}{4} of the cake, then how much of the chocolate cake is left?

2

Step-by-step solution

To solve this problem, we need to determine how much of the cake is left after Jorge consumes part of it. We know the following:

  • The cake initially has 8 slices, with only 3 slices left, meaning 38\frac{3}{8} of the cake remains.
  • Jorge eats 14\frac{1}{4} of the entire original cake.

We need to find 14\frac{1}{4} in terms of eighths to subtract it from 38\frac{3}{8}:

14=28\frac{1}{4} = \frac{2}{8} since multiplying both the numerator and the denominator by 2 converts it.

Thus, the amount of cake Jorge eats from the original amount available is equivalent to 28\frac{2}{8} of the cake.

Now, we perform the subtraction to find the remaining portion of the cake:

3828=18\frac{3}{8} - \frac{2}{8} = \frac{1}{8}

Therefore, the amount of cake left after Jorge eats his portion is 18\frac{1}{8} of the original cake. Thus, the final solution is:

18 \frac{1}{8} .

3

Final Answer

18 \frac{1}{8}

Key Points to Remember

Essential concepts to master this topic
  • Initial State: Identify what fraction of cake remains before eating
  • Conversion: Convert 14 \frac{1}{4} to 28 \frac{2}{8} for subtraction
  • Check: Verify 3828=18 \frac{3}{8} - \frac{2}{8} = \frac{1}{8} makes sense ✓

Common Mistakes

Avoid these frequent errors
  • Eating 1/4 of the remaining cake instead of the whole cake
    Don't eat 14 \frac{1}{4} of the 3 slices left = 34 \frac{3}{4} slice eaten! The problem states Jorge eats 14 \frac{1}{4} of the entire original cake, not just what's remaining. Always read carefully to determine what the fraction refers to.

Practice Quiz

Test your knowledge with interactive questions

You have a pair of denominators, what is their least common multiple?

\( \boxed 2~~~\boxed5 \)

FAQ

Everything you need to know about this question

Why do I need to convert 1/4 to eighths?

+

You need a common denominator to subtract fractions! Since the remaining cake is 38 \frac{3}{8} , convert 14 \frac{1}{4} to 28 \frac{2}{8} so you can subtract directly.

Is Jorge eating 1/4 of what's left or 1/4 of the whole cake?

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Jorge eats 14 \frac{1}{4} of the entire original cake, not just the remaining portion. This is a crucial distinction that affects your calculation!

How do I know 3/8 - 2/8 = 1/8 is right?

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Check by adding back: 18+28=38 \frac{1}{8} + \frac{2}{8} = \frac{3}{8} ✓. Also, 18 \frac{1}{8} of 8 slices = 1 slice remaining, which makes sense!

What if I get confused about what the fractions mean?

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Always ask yourself: "Fraction of what?" In this problem, 38 \frac{3}{8} is of the whole cake (what's left), and 14 \frac{1}{4} is also of the whole cake (what Jorge eats).

Can I work with slices instead of fractions?

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Yes! 3 slices left, Jorge eats 14 \frac{1}{4} of 8 = 2 slices, so 3 - 2 = 1 slice = 18 \frac{1}{8} remaining. Both methods work!

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