Fraction Worksheets | Free - CommonCoreSheets - Free Printable

Let's solve each of these fraction multiplication problems visually and numerically, as the worksheet asks for a visual representation using boxes (like grids) to show how two fractions are multiplied.

---

🔷 Concept: Multiplying Fractions Visually

When multiplying two fractions, such as $ \frac{a}{b} \times \frac{c}{d} $, you:
1. Divide a rectangle into $ b $ rows and $ d $ columns (or vice versa), making $ b \times d $ total parts.
2. Shade $ a $ out of $ b $ rows (representing the first fraction).
3. Shade $ c $ out of $ d $ columns (representing the second fraction).
4. The overlapping shaded area represents the product — count how many small squares are double-shaded.

The result is:
$$
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
$$

---

We'll go through each problem step by step.

---

✔ Example: $ \frac{2}{7} \times \frac{1}{4} $

- Draw a rectangle divided into 7 rows and 4 columns → 28 total parts.
- Shade 2 out of 7 rows (vertical shading).
- Shade 1 out of 4 columns (horizontal shading).
- Overlap = 2 × 1 = 2 shaded squares.
- Result: $ \frac{2}{28} = \frac{1}{14} $

✔ Answer: $ \boxed{\frac{1}{14}} $

---

Now let’s solve each problem:

---

1) $ \frac{1}{4} \times \frac{4}{7} $

- Grid: 4 rows × 7 columns = 28 parts.
- Shade 1 row (out of 4) → vertical shading.
- Shade 4 columns (out of 7) → horizontal shading.
- Overlap: 1 × 4 = 4 squares.
- $ \frac{4}{28} = \frac{1}{7} $

✔ Answer: $ \boxed{\frac{1}{7}} $

---

2) $ \frac{1}{3} \times \frac{1}{2} $

- Grid: 3 rows × 2 columns = 6 parts.
- Shade 1 row (1/3).
- Shade 1 column (1/2).
- Overlap: 1 square.
- $ \frac{1}{6} $

✔ Answer: $ \boxed{\frac{1}{6}} $

---

3) $ \frac{2}{7} \times \frac{2}{4} $

Note: $ \frac{2}{4} = \frac{1}{2} $, but we’ll keep it as is.

- Grid: 7 rows × 4 columns = 28 parts.
- Shade 2 rows (2/7).
- Shade 2 columns (2/4).
- Overlap: 2 × 2 = 4 squares.
- $ \frac{4}{28} = \frac{1}{7} $

✔ Answer: $ \boxed{\frac{1}{7}} $

---

4) $ \frac{2}{8} \times \frac{3}{6} $

Simplify first:
- $ \frac{2}{8} = \frac{1}{4} $
- $ \frac{3}{6} = \frac{1}{2} $
So: $ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} $

But visually:
- Use 8 rows × 6 columns = 48 parts.
- Shade 2 rows (2/8).
- Shade 3 columns (3/6).
- Overlap: 2 × 3 = 6 squares.
- $ \frac{6}{48} = \frac{1}{8} $

✔ Answer: $ \boxed{\frac{1}{8}} $

---

5) $ \frac{8}{9} \times \frac{3}{3} $

Note: $ \frac{3}{3} = 1 $, so this is just $ \frac{8}{9} \times 1 = \frac{8}{9} $

Visually:
- Grid: 9 rows × 3 columns = 27 parts.
- Shade 8 rows (8/9).
- Shade all 3 columns (since 3/3 = 1).
- Overlap: 8 × 3 = 24 squares.
- $ \frac{24}{27} = \frac{8}{9} $

✔ Answer: $ \boxed{\frac{8}{9}} $

---

6) $ \frac{3}{8} \times \frac{1}{2} $

- Grid: 8 rows × 2 columns = 16 parts.
- Shade 3 rows (3/8).
- Shade 1 column (1/2).
- Overlap: 3 × 1 = 3 squares.
- $ \frac{3}{16} $

✔ Answer: $ \boxed{\frac{3}{16}} $

---

7) $ \frac{2}{6} \times \frac{1}{5} $

Simplify: $ \frac{2}{6} = \frac{1}{3} $

- Grid: 6 rows × 5 columns = 30 parts.
- Shade 2 rows (2/6).
- Shade 1 column (1/5).
- Overlap: 2 × 1 = 2 squares.
- $ \frac{2}{30} = \frac{1}{15} $

✔ Answer: $ \boxed{\frac{1}{15}} $

---

8) $ \frac{5}{9} \times \frac{1}{2} $

- Grid: 9 rows × 2 columns = 18 parts.
- Shade 5 rows (5/9).
- Shade 1 column (1/2).
- Overlap: 5 × 1 = 5 squares.
- $ \frac{5}{18} $

✔ Answer: $ \boxed{\frac{5}{18}} $

---

9) $ \frac{3}{8} \times \frac{2}{9} $

- Grid: 8 rows × 9 columns = 72 parts.
- Shade 3 rows (3/8).
- Shade 2 columns (2/9).
- Overlap: 3 × 2 = 6 squares.
- $ \frac{6}{72} = \frac{1}{12} $

✔ Answer: $ \boxed{\frac{1}{12}} $

---

10) $ \frac{5}{9} \times \frac{1}{2} $

Same as #8? No, same values!

Wait — this is same as #8: $ \frac{5}{9} \times \frac{1}{2} $

So again: $ \frac{5}{18} $

✔ Answer: $ \boxed{\frac{5}{18}} $

---

11) $ \frac{1}{7} \times \frac{2}{7} $

- Grid: 7 rows × 7 columns = 49 parts.
- Shade 1 row (1/7).
- Shade 2 columns (2/7).
- Overlap: 1 × 2 = 2 squares.
- $ \frac{2}{49} $

✔ Answer: $ \boxed{\frac{2}{49}} $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{1}{7} $ |
| 2 | $ \frac{1}{6} $ |
| 3 | $ \frac{1}{7} $ |
| 4 | $ \frac{1}{8} $ |
| 5 | $ \frac{8}{9} $ |
| 6 | $ \frac{3}{16} $ |
| 7 | $ \frac{1}{15} $ |
| 8 | $ \frac{5}{18} $ |
| 9 | $ \frac{1}{12} $ |
| 10 | $ \frac{5}{18} $ |
| 11 | $ \frac{2}{49} $ |

---

📌 How to Fill in the Boxes (Visual):

For each box:
- Draw a rectangle.
- Divide it into appropriate rows and columns based on denominators.
- Shade one direction for the first fraction, another for the second.
- The overlapping region is the product.

Example for #1 ($ \frac{1}{4} \times \frac{4}{7} $):
- Draw a rectangle with 4 rows and 7 columns.
- Shade 1 entire row (top row).
- Shade 4 columns (leftmost 4).
- The overlap is a 1×4 block → 4 squares out of 28 → $ \frac{4}{28} = \frac{1}{7} $

---

Let me know if you'd like printable visual diagrams or help drawing them!