Worksheet demonstrating how to multiply fractions using cross canceling, with examples and step-by-step solutions.

The task involves solving problems related to multiplying fractions using the method of cross canceling. Let's go through each problem step by step and explain the solution.

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Problem 1:

$$
\frac{3}{5} \times \frac{3}{5}
$$

#### Step-by-Step Solution:
1. Write the fractions side by side:
$$
\frac{3}{5} \times \frac{3}{5} = \frac{3 \times 3}{5 \times 5}
$$

2. Multiply the numerators and denominators:
$$
\frac{3 \times 3}{5 \times 5} = \frac{9}{25}
$$

3. There are no common factors between the numerator (9) and the denominator (25), so no cross canceling is needed.

#### Final Answer:
$$
\boxed{\frac{9}{25}}
$$

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Problem 2:

$$
\frac{2}{5} \times \frac{5}{10}
$$

#### Step-by-Step Solution:
1. Write the fractions side by side:
$$
\frac{2}{5} \times \frac{5}{10} = \frac{2 \times 5}{5 \times 10}
$$

2. Identify common factors for cross canceling:
- The numerator of the first fraction (2) and the denominator of the second fraction (10) have a common factor of 2.
- The denominator of the first fraction (5) and the numerator of the second fraction (5) have a common factor of 5.

3. Perform cross canceling:
- Divide 2 (numerator of the first fraction) by 2: \( \frac{2}{2} = 1 \).
- Divide 10 (denominator of the second fraction) by 2: \( \frac{10}{2} = 5 \).
- Divide 5 (denominator of the first fraction) by 5: \( \frac{5}{5} = 1 \).
- Divide 5 (numerator of the second fraction) by 5: \( \frac{5}{5} = 1 \).

4. After canceling, the expression becomes:
$$
\frac{1 \times 1}{1 \times 5} = \frac{1}{5}
$$

#### Final Answer:
$$
\boxed{\frac{1}{5}}
$$

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Problem 3:

$$
\frac{1}{2} \times \frac{4}{10}
$$

#### Step-by-Step Solution:
1. Write the fractions side by side:
$$
\frac{1}{2} \times \frac{4}{10} = \frac{1 \times 4}{2 \times 10}
$$

2. Identify common factors for cross canceling:
- The denominator of the first fraction (2) and the numerator of the second fraction (4) have a common factor of 2.

3. Perform cross canceling:
- Divide 2 (denominator of the first fraction) by 2: \( \frac{2}{2} = 1 \).
- Divide 4 (numerator of the second fraction) by 2: \( \frac{4}{2} = 2 \).

4. After canceling, the expression becomes:
$$
\frac{1 \times 2}{1 \times 10} = \frac{2}{10}
$$

5. Simplify the resulting fraction:
- The numerator (2) and the denominator (10) have a common factor of 2.
- Divide both by 2: \( \frac{2}{10} = \frac{1}{5} \).

#### Final Answer:
$$
\boxed{\frac{1}{5}}
$$

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Problem 4:

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

#### Step-by-Step Solution:
1. Write the fractions side by side:
$$
\frac{2}{4} \times \frac{2}{3} = \frac{2 \times 2}{4 \times 3}
$$

2. Identify common factors for cross canceling:
- The numerator of the first fraction (2) and the denominator of the first fraction (4) have a common factor of 2.

3. Perform cross canceling:
- Divide 2 (numerator of the first fraction) by 2: \( \frac{2}{2} = 1 \).
- Divide 4 (denominator of the first fraction) by 2: \( \frac{4}{2} = 2 \).

4. After canceling, the expression becomes:
$$
\frac{1 \times 2}{2 \times 3} = \frac{2}{6}
$$

5. Simplify the resulting fraction:
- The numerator (2) and the denominator (6) have a common factor of 2.
- Divide both by 2: \( \frac{2}{6} = \frac{1}{3} \).

#### Final Answer:
$$
\boxed{\frac{1}{3}}
$$

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Problem 5:

$$
\frac{2}{3} \times \frac{4}{5}
$$

#### Step-by-Step Solution:
1. Write the fractions side by side:
$$
\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5}
$$

2. Multiply the numerators and denominators:
$$
\frac{2 \times 4}{3 \times 5} = \frac{8}{15}
$$

3. There are no common factors between the numerator (8) and the denominator (15), so no cross canceling is needed.

#### Final Answer:
$$
\boxed{\frac{8}{15}}
$$

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Summary of Answers:

1. \( \frac{3}{5} \times \frac{3}{5} = \boxed{\frac{9}{25}} \)
2. \( \frac{2}{5} \times \frac{5}{10} = \boxed{\frac{1}{5}} \)
3. \( \frac{1}{2} \times \frac{4}{10} = \boxed{\frac{1}{5}} \)
4. \( \frac{2}{4} \times \frac{2}{3} = \boxed{\frac{1}{3}} \)
5. \( \frac{2}{3} \times \frac{4}{5} = \boxed{\frac{8}{15}} \)

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If you have any further questions, feel free to ask!