Calculating Remaining Fraction: 1/4 and 1/3 Cake Portions Problem

Q: Why can't I just add 1/4 + 1/3 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add apples and oranges. You need common denominators to make the pieces the same size first.

Q: What does 'remaining cake' mean in fraction problems?

Remaining means what's left over after parts are taken away. Start with 1 whole cake, then subtract the fractions that were eaten: $ 1 - \frac{7}{12} = \frac{5}{12} $

Q: Can I solve this problem a different way?

Yes! You could visualize it by drawing a cake divided into 12 equal pieces. Lionel eats 3 pieces, Armando eats 4 pieces, so 5 pieces remain. This gives the same answer: $ \frac{5}{12} $

Q: How do I know if 5/12 can be simplified?

Check if 5 and 12 share any common factors. Since 5 is prime and doesn't divide 12, the fraction $ \frac{5}{12} $ is already in simplest form!

Fraction Subtraction with Common Denominators

Silvina buys a birthday cake. Lionel eats $\frac{1}{4}$ of the cake and Armando eats $\frac{1}{3}$ of the cake.

How much of the cake is left?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How much cake is left?

00:04 Subtract the given parts from the whole to find the remaining part

00:13 Multiply each fraction by the second denominator to find the common denominator

00:16 Be sure to multiply both numerator and denominator

00:27 Calculate the multiplications

00:41 Add with the common denominator

00:44 Calculate the numerator

00:49 Convert from whole to the appropriate fraction

00:56 Subtract with the common denominator

01:00 Calculate the numerator

01:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Silvina buys a birthday cake. Lionel eats $\frac{1}{4}$ of the cake and Armando eats $\frac{1}{3}$ of the cake.

How much of the cake is left?

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Determine the total amount of cake eaten by adding $\frac{1}{4}$ and $\frac{1}{3}$ .

Step 2: Find a common denominator for the fractions. The denominators 4 and 3 have a least common multiple of 12.

Step 3: Convert the fractions to have a denominator of 12:
$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$
$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Step 4: Add the fractions:
$\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$

Step 5: Subtract the total eaten portion from the whole cake (1):
$1 - \frac{7}{12} = \frac{12}{12} - \frac{7}{12} = \frac{5}{12}$

Therefore, the fraction of the cake that is left is $\frac{5}{12}$ .

Final Answer

$\frac{5}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding or subtracting fractions
Technique: Convert $\frac{1}{4}$ to $\frac{3}{12}$ and $\frac{1}{3}$ to $\frac{4}{12}$
Check: Verify $\frac{5}{12} + \frac{7}{12} = \frac{12}{12} = 1$ whole cake ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add $\frac{1}{4} + \frac{1}{3} = \frac{2}{7}$ ! This gives a completely wrong fraction because denominators show unit size, not quantities. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{2}-\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add 1/4 + 1/3 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add apples and oranges. You need common denominators to make the pieces the same size first.

How do I find the least common multiple of 4 and 3?

List multiples of each number: 4: 4, 8, 12, 16... 3: 3, 6, 9, 12, 15... The first number that appears in both lists is 12, so that's your LCD!

What does 'remaining cake' mean in fraction problems?

Remaining means what's left over after parts are taken away. Start with 1 whole cake, then subtract the fractions that were eaten: $1 - \frac{7}{12} = \frac{5}{12}$

Can I solve this problem a different way?

Yes! You could visualize it by drawing a cake divided into 12 equal pieces. Lionel eats 3 pieces, Armando eats 4 pieces, so 5 pieces remain. This gives the same answer: $\frac{5}{12}$

How do I know if 5/12 can be simplified?

Check if 5 and 12 share any common factors. Since 5 is prime and doesn't divide 12, the fraction $\frac{5}{12}$ is already in simplest form!

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