Let's carefully analyze the image and solve the problem using the
area model for dividing a
fraction by a whole number.
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🔢 Problem:
$$
\frac{3}{4} \div 2 = ?
$$
The image shows a visual step-by-step method to divide the fraction $\frac{3}{4}$ by the whole number $2$ using an
area model.
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✔ Step-by-Step Explanation:
####
Step 1: Model the Fraction $\frac{3}{4}$
- A rectangle is divided into
4 equal horizontal parts.
-
3 out of 4 parts are shaded (blue), representing $\frac{3}{4}$.
- This models the original fraction.
---
####
Step 2: Split the Fraction into Equal Parts (Divide by 2)
We are dividing $\frac{3}{4}$ by 2, which means we want to split the shaded portion ($\frac{3}{4}$) into
2 equal parts.
- The rectangle is now divided into
2 columns, labeled
1 and
2.
- The shaded region ($\frac{3}{4}$) is split vertically into two equal halves.
- Each half represents
half of $\frac{3}{4}$.
> So, each column gets
$\frac{1}{2}$ of $\frac{3}{4}$.
This results in
8 smaller rectangles total (4 rows × 2 columns), but only
3 rows were shaded originally.
Now, the shaded area is split between the two columns — so each column has
$\frac{3}{8}$ of the whole rectangle.
---
####
Step 3: Overlapping Parts over Total Parts
- Now, look at one of the two columns (say, column 1).
- Column 1 has
3 shaded parts (from the original 3/4), but now the whole rectangle is divided into
8 equal small parts (4 rows × 2 columns).
- So, the shaded part in
one column is
3 out of 8 total parts.
Thus, the result is:
$$
\frac{3}{4} \div 2 = \frac{3}{8}
$$
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✔ Final Answer:
$$
\boxed{\frac{3}{8}}
$$
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📌 Why Does This Work?
Dividing a fraction by a whole number means splitting that fraction into equal groups. Here’s the mathematical reasoning:
$$
\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}
$$
Which matches the area model.
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✔ Summary:
- We modeled $\frac{3}{4}$ as 3 out of 4 parts.
- Divided it into 2 equal parts (columns).
- Each part is $\frac{3}{8}$ of the whole.
- Therefore, $\frac{3}{4} \div 2 = \frac{3}{8}$.
✔ The area model visually confirms this result!
Parent Tip: Review the logic above to help your child master the concept of dividing fractions using models worksheet.
