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

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

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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