Multiplying Fractions by Fractions w/Models - WORKSHEET for students! - Free Printable

Let’s solve each problem step by step. We’re multiplying two fractions. To multiply fractions, we:

1. Multiply the top numbers (numerators) together.
2. Multiply the bottom numbers (denominators) together.
3. Write the new fraction with the product of numerators on top and product of denominators on bottom.
4. Simplify if needed — but in these problems, we’ll just write the unsimplified answer as shown in the boxes.

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First Problem:
\[
\frac{1}{3} \times \frac{4}{7}
\]

Multiply numerators: \(1 \times 4 = 4\)
Multiply denominators: \(3 \times 7 = 21\)
So, the answer is \(\frac{4}{21}\)

Filling in the boxes:
\[
\frac{1}{3} \times \frac{4}{7} = \frac{1 \times 4}{3 \times 7} = \frac{4}{21}
\]

---

Second Problem:
\[
\frac{2}{7} \times \frac{3}{5}
\]

Numerators: \(2 \times 3 = 6\)
Denominators: \(7 \times 5 = 35\)
Answer: \(\frac{6}{35}\)

Boxes:
\[
\frac{2}{7} \times \frac{3}{5} = \frac{2 \times 3}{7 \times 5} = \frac{6}{35}
\]

---

Third Problem:
\[
\frac{3}{8} \times \frac{3}{4}
\]

Numerators: \(3 \times 3 = 9\)
Denominators: \(8 \times 4 = 32\)
Answer: \(\frac{9}{32}\)

Boxes:
\[
\frac{3}{8} \times \frac{3}{4} = \frac{3 \times 3}{8 \times 4} = \frac{9}{32}
\]

---

Fourth Problem:
\[
\frac{4}{6} \times \frac{5}{6}
\]

Numerators: \(4 \times 5 = 20\)
Denominators: \(6 \times 6 = 36\)
Answer: \(\frac{20}{36}\)

Note: This can be simplified to \(\frac{5}{9}\), but since the worksheet shows empty boxes for numerator and denominator without simplifying instructions, we leave it as \(\frac{20}{36}\).

Boxes:
\[
\frac{4}{6} \times \frac{5}{6} = \frac{4 \times 5}{6 \times 6} = \frac{20}{36}
\]

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Final Answer:

First row:
\(\frac{1}{3} \times \frac{4}{7} = \frac{1 \times 4}{3 \times 7} = \frac{4}{21}\)

Second row:
\(\frac{2}{7} \times \frac{3}{5} = \frac{2 \times 3}{7 \times 5} = \frac{6}{35}\)

Third row:
\(\frac{3}{8} \times \frac{3}{4} = \frac{3 \times 3}{8 \times 4} = \frac{9}{32}\)

Fourth row:
\(\frac{4}{6} \times \frac{5}{6} = \frac{4 \times 5}{6 \times 6} = \frac{20}{36}\)