Adding Fractions: Calculate 1/4 + 1/4 Using Pizza Portions

Q: Why don't we add the denominators together?

The denominator tells us how many equal pieces the whole is divided into. In this pizza problem, both pieces are quarters (4ths), so we're still working with quarters - that's why the denominator stays 4!

Q: How do I know when to simplify my answer?

Always check if your final fraction can be simplified! Look for common factors in the numerator and denominator. Since $ \frac{2}{4} $ has 2 as a common factor, it simplifies to $ \frac{1}{2} $.

Q: What if the problem had different denominators?

Great question! If Daniel ate $ \frac{1}{4} $ and Mariano ate $ \frac{1}{3} $, you'd need to find a common denominator first, then add the numerators.

Q: What does it mean that they ate half the pizza?

It means there's still $ \frac{1}{2} $ of the pizza left! Since $ \frac{1}{2} + \frac{1}{2} = 1 $ whole pizza, you can verify your answer makes sense.

Fraction Addition with Same Denominators

Daniel eats $\frac{1}{4}$ of a pizza and Mariano also eats $\frac{1}{4}$ of the pizza.

How much of the pizza do they eat between them?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What fraction did Danny and Moshe eat?

00:03 Let's add the fractions and calculate

00:07 Let's add under the common denominator

00:11 Let's calculate the numerator

00:15 Let's reduce the fraction as much as possible

00:20 Remember to divide both numerator and denominator

00:24 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

Daniel eats $\frac{1}{4}$ of a pizza and Mariano also eats $\frac{1}{4}$ of the pizza.

How much of the pizza do they eat between them?

Step-by-step solution

To solve this problem, we'll add the fractions representing the portions of pizza each person eats.

Step 1: Identify the fractions to add. Daniel eats $\frac{1}{4}$ of the pizza, and Mariano eats $\frac{1}{4}$ of the pizza.
Step 2: Since the fractions have the same denominator, add the numerators: $1 + 1 = 2$ .
Step 3: Keep the denominator the same, which is $4$ .
Step 4: The resulting fraction is $\frac{2}{4}$ .
Step 5: Simplify the fraction $\frac{2}{4}$ by dividing the numerator and the denominator by their greatest common divisor, which is $2$ .

Thus, $\frac{2}{4} = \frac{1}{2}$ .

Therefore, the total amount of pizza eaten by Daniel and Mariano together is $\frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are the same, add only the numerators
Technique: $\frac{1}{4} + \frac{1}{4} = \frac{1+1}{4} = \frac{2}{4}$
Check: Always simplify final answer: $\frac{2}{4} = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add $\frac{1}{4} + \frac{1}{4} = \frac{2}{8}$ ! Adding denominators changes the size of each piece, giving a completely wrong answer. Always keep the denominator the same when adding fractions with identical denominators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't we add the denominators together?

The denominator tells us how many equal pieces the whole is divided into. In this pizza problem, both pieces are quarters (4ths), so we're still working with quarters - that's why the denominator stays 4!

How do I know when to simplify my answer?

Always check if your final fraction can be simplified! Look for common factors in the numerator and denominator. Since $\frac{2}{4}$ has 2 as a common factor, it simplifies to $\frac{1}{2}$ .

What if the problem had different denominators?

Great question! If Daniel ate $\frac{1}{4}$ and Mariano ate $\frac{1}{3}$ , you'd need to find a common denominator first, then add the numerators.

Can I visualize this problem to check my answer?

Absolutely! Picture a pizza cut into 4 equal slices. Daniel takes 1 slice, Mariano takes 1 slice. Together they took 2 out of 4 slices, which is $\frac{2}{4} = \frac{1}{2}$ of the pizza.

What does it mean that they ate half the pizza?

It means there's still $\frac{1}{2}$ of the pizza left! Since $\frac{1}{2} + \frac{1}{2} = 1$ whole pizza, you can verify your answer makes sense.

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