Fraction Subtraction: Finding Remaining Pizza After 2/7 and 1/3 are Eaten

Q: Why can't I just add 2/7 + 1/3 directly?

You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 2 sevenths and 1 third directly, just like you can't add 2 apples and 1 orange to get 3 bananas!

Q: How do I find the least common denominator of 7 and 3?

Since 7 and 3 are both prime numbers, their LCD is simply 7 × 3 = 21. For other numbers, list multiples of each until you find the smallest common one.

Q: What does it mean that 8/21 of the pizza is left?

It means Diego gets 8 pieces out of 21 equal pieces. Since $ \frac{8}{21} $ is less than half ($ \frac{10.5}{21} $), Diego gets the smallest portion of the three friends.

Q: Can I simplify 8/21 further?

No! The fraction $ \frac{8}{21} $ is already in lowest terms because 8 and 21 share no common factors other than 1. Always check if your final answer can be simplified.

Q: How can I check if my answer is correct?

Add all three portions: $ \frac{6}{21} + \frac{7}{21} + \frac{8}{21} = \frac{21}{21} = 1 $. If they equal exactly 1 whole pizza, your answer is correct!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find out what part Daniel ate.

00:14 First, subtract the given parts from the whole. This will show us what's left.

00:30 Next, to get the same bottom number, we multiply each fraction by the other's denominator.

00:36 Make sure you multiply both the top number and the bottom number of each fraction.

00:46 Now, calculate those products.

00:55 Then, add the fractions using the common bottom number.

01:00 Calculate just the top numbers of the fractions.

01:08 If needed, convert the whole number to a fraction with a common bottom number.

01:15 Subtract the fractions, keeping the common bottom number.

01:22 Finally, calculate the top number after subtracting.

01:26 And that's how we find the answer to what part Daniel ate.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Roberto, Diego, and Marcelo order a pizza.

Roberto eats $\frac{2}{7}$ of the pizza and Marcelo eats $\frac{1}{3}$ of the pizza.

How much is left for Diego to eat?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the total fraction consumed by Roberto and Marcelo.
Step 2: Find a common denominator to add these fractions.
Step 3: Subtract the total consumed from the whole pizza.

Let's work through each step:

Step 1: Roberto eats $\frac{2}{7}$ of the pizza, and Marcelo eats $\frac{1}{3}$ .

Step 2: To add these fractions, we need a common denominator. The least common denominator between 7 and 3 is 21.

Convert the fractions:
Roberto's fraction: $\frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21}$
Marcelo's fraction: $\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}$

Step 3: Add the converted fractions:
$\frac{6}{21} + \frac{7}{21} = \frac{13}{21}$

This result represents the total fraction of the pizza eaten by Roberto and Marcelo.

Step 4: Subtract the eaten fraction from the whole pizza (1, or $\frac{21}{21}$ ):
$\frac{21}{21} - \frac{13}{21} = \frac{8}{21}$

Therefore, the amount of pizza left for Diego to eat is $\frac{8}{21}$ .

3

Final Answer

$\frac{8}{21}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding or subtracting fractions
Technique: Convert $\frac{2}{7}$ to $\frac{6}{21}$ and $\frac{1}{3}$ to $\frac{7}{21}$
Check: Verify $\frac{8}{21} + \frac{6}{21} + \frac{7}{21} = \frac{21}{21} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without common denominators
Don't add $\frac{2}{7} + \frac{1}{3} = \frac{3}{10}$ ! This gives wrong denominators and numerators. You cannot add fractions with different denominators directly. Always convert to the same denominator first, then add numerators only.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{7}{5}-\frac{4}{5}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just add 2/7 + 1/3 directly?

+

You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 2 sevenths and 1 third directly, just like you can't add 2 apples and 1 orange to get 3 bananas!

How do I find the least common denominator of 7 and 3?

+

Since 7 and 3 are both prime numbers, their LCD is simply 7 × 3 = 21. For other numbers, list multiples of each until you find the smallest common one.

What does it mean that 8/21 of the pizza is left?

+

It means Diego gets 8 pieces out of 21 equal pieces. Since $\frac{8}{21}$ is less than half ( $\frac{10.5}{21}$ ), Diego gets the smallest portion of the three friends.

Can I simplify 8/21 further?

+

No! The fraction $\frac{8}{21}$ is already in lowest terms because 8 and 21 share no common factors other than 1. Always check if your final answer can be simplified.

How can I check if my answer is correct?

+

Add all three portions: $\frac{6}{21} + \frac{7}{21} + \frac{8}{21} = \frac{21}{21} = 1$ . If they equal exactly 1 whole pizza, your answer is correct!

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Fraction Subtraction: Finding Remaining Pizza After 2/7 and 1/3 are Eaten

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