Solve Half Plus Half Using Rectangle Models: Adding 1/2 + 1/2

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

The denominator tells us the size of each piece. When adding $ \frac{1}{2} + \frac{1}{2} $, both pieces are the same size (halves), so we keep that size and just count how many pieces we have!

Q: How does the rectangle model show the answer?

The rectangle is divided into 2 equal parts. We're adding 1 part + 1 part = 2 parts total. Since 2 parts out of 2 parts equals the whole rectangle, our answer is 1!

Q: Do I always get a whole number when adding halves?

Not always! For example, $ \frac{1}{2} + \frac{1}{2} = 1 $ (whole number), but $ \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2} = 1\frac{1}{2} $ (mixed number).

Q: How do I check if my answer is right?

Use the visual model! If your answer is 1, check that you've shaded the entire rectangle. You can also convert back: does 1 = $ \frac{2}{2} $? Yes! ✓

Fraction Addition with Visual Rectangle Models

$\frac{1}{2}+\frac{1}{2}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's color the appropriate number of squares, according to the given data

00:08 Now let's count and add to the numerator in the new fraction

00:11 The denominator equals the number of cells we divided

00:14 Any number divided by itself always equals 1

00:16 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

$\frac{1}{2}+\frac{1}{2}=$

Step-by-step solution

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

Step 1: Verify that both fractions have the same denominator.
Step 2: Add the numerators of the two fractions.
Step 3: Retain the common denominator.
Step 4: Simplify the resulting fraction if needed.

Let's work through each step to add $\frac{1}{2} + \frac{1}{2}$ :
Step 1: Both fractions have the same denominator: 2.
Step 2: Add the numerators: $1 + 1 = 2$ .
Step 3: The denominator remains the same: 2.
Now the sum is: $\frac{2}{2}$ .
Step 4: Simplify if needed: $\frac{2}{2} = 1$ .

Therefore, the solution to the problem is $1$ , which corresponds to answer choice 2.

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: When denominators match, add numerators and keep denominator
Visual Method: Two halves fill one complete rectangle: $\frac{1}{2} + \frac{1}{2} = \frac{2}{2}$
Simplify Check: Always reduce final answer: $\frac{2}{2} = 1$ whole unit ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add both numerators AND denominators like $\frac{1}{2} + \frac{1}{2} = \frac{2}{4}$ = wrong answer! This changes the size of each piece completely. Always keep the same denominator when adding fractions with equal 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 I add the denominators together?

The denominator tells us the size of each piece. When adding $\frac{1}{2} + \frac{1}{2}$ , both pieces are the same size (halves), so we keep that size and just count how many pieces we have!

How does the rectangle model show the answer?

The rectangle is divided into 2 equal parts. We're adding 1 part + 1 part = 2 parts total. Since 2 parts out of 2 parts equals the whole rectangle, our answer is 1!

What if my answer is greater than 1?

That's perfectly normal! When adding fractions, you can get answers greater than 1 (like $\frac{3}{2} = 1\frac{1}{2}$ ). Always simplify to see if it's a whole number or mixed number.

Do I always get a whole number when adding halves?

Not always! For example, $\frac{1}{2} + \frac{1}{2} = 1$ (whole number), but $\frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2} = 1\frac{1}{2}$ (mixed number).

How do I check if my answer is right?

Use the visual model! If your answer is 1, check that you've shaded the entire rectangle. You can also convert back: does 1 = $\frac{2}{2}$ ? Yes! ✓

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