Multiplying Proper Fractions - Maths with Mum - Free Printable

Problem Description:

The task involves solving the multiplication of fractions as shown in the image. The solutions are already provided, but we will explain the process for each part to ensure clarity and understanding.

General Rule for Multiplying Fractions:

To multiply two fractions, follow these steps:
1. Multiply the numerators of the fractions to get the numerator of the result.
2. Multiply the denominators of the fractions to get the denominator of the result.
3. Simplify the resulting fraction, if possible.

Solutions with Explanations:

#### Part (a):
$$
\frac{1}{3} \times \frac{1}{4}
$$
- Multiply the numerators: \( 1 \times 1 = 1 \)
- Multiply the denominators: \( 3 \times 4 = 12 \)
- Result: \( \frac{1}{12} \)

#### Part (b):
$$
\frac{3}{5} \times \frac{1}{5}
$$
- Multiply the numerators: \( 3 \times 1 = 3 \)
- Multiply the denominators: \( 5 \times 5 = 25 \)
- Result: \( \frac{3}{25} \)

#### Part (c):
$$
\frac{5}{6} \times \frac{1}{2}
$$
- Multiply the numerators: \( 5 \times 1 = 5 \)
- Multiply the denominators: \( 6 \times 2 = 12 \)
- Result: \( \frac{5}{12} \)

#### Part (d):
$$
\frac{2}{3} \times \frac{2}{5}
$$
- Multiply the numerators: \( 2 \times 2 = 4 \)
- Multiply the denominators: \( 3 \times 5 = 15 \)
- Result: \( \frac{4}{15} \)

#### Part (e):
$$
\frac{6}{7} \times \frac{4}{5}
$$
- Multiply the numerators: \( 6 \times 4 = 24 \)
- Multiply the denominators: \( 7 \times 5 = 35 \)
- Result: \( \frac{24}{35} \)

#### Part (f):
$$
\frac{1}{6} \times \frac{7}{9}
$$
- Multiply the numerators: \( 1 \times 7 = 7 \)
- Multiply the denominators: \( 6 \times 9 = 54 \)
- Result: \( \frac{7}{54} \)

#### Part (g):
$$
\frac{9}{11} \times \frac{3}{4}
$$
- Multiply the numerators: \( 9 \times 3 = 27 \)
- Multiply the denominators: \( 11 \times 4 = 44 \)
- Result: \( \frac{27}{44} \)

#### Part (h):
$$
\frac{7}{12} \times \frac{7}{12}
$$
- Multiply the numerators: \( 7 \times 7 = 49 \)
- Multiply the denominators: \( 12 \times 12 = 144 \)
- Result: \( \frac{49}{144} \)

Final Answer:

The solutions are already provided in the image, and they are correct. Here they are summarized:

$$
\boxed{
\begin{aligned}
&\text{(a)} \quad \frac{1}{12} \\
&\text{(b)} \quad \frac{3}{25} \\
&\text{(c)} \quad \frac{5}{12} \\
&\text{(d)} \quad \frac{4}{15} \\
&\text{(e)} \quad \frac{24}{35} \\
&\text{(f)} \quad \frac{7}{54} \\
&\text{(g)} \quad \frac{27}{44} \\
&\text{(h)} \quad \frac{49}{144}
\end{aligned}
}
$$

Each step follows the rule of multiplying the numerators and denominators separately and simplifying if necessary. All results are in their simplest forms.