Multiplying fractions using cross canceling method.

The image you uploaded contains a series of problems involving the multiplication of fractions using cross-cancellation. Below, I will solve each problem step by step and explain the process.

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Problem 1:

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

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

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 3.
- The denominator of the second fraction is 5.
- There are no common factors between 3 and 5.

- The numerator of the second fraction is 2.
- The denominator of the first fraction is 4.
- The greatest common factor (GCF) between 2 and 4 is 2.

#### Step 3: Perform the cancellation.
$$
\frac{3}{\cancel{4}^2} \times \frac{\cancel{2}^1}{5}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{3 \times 1}{2 \times 5} = \frac{3}{10}
$$

#### Final Answer:
$$
\boxed{\frac{3}{10}}
$$

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Problem 2:

$$
\frac{5}{6} \times \frac{3}{10}
$$

#### Step 1: Write the fractions side by side.
$$
\frac{5}{6} \times \frac{3}{10}
$$

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 5.
- The denominator of the second fraction is 10.
- The GCF between 5 and 10 is 5.

- The numerator of the second fraction is 3.
- The denominator of the first fraction is 6.
- The GCF between 3 and 6 is 3.

#### Step 3: Perform the cancellation.
$$
\frac{\cancel{5}^1}{\cancel{6}^2} \times \frac{\cancel{3}^1}{\cancel{10}^2}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{2 \times 2} = \frac{1}{4}
$$

#### Final Answer:
$$
\boxed{\frac{1}{4}}
$$

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Problem 3:

$$
\frac{7}{8} \times \frac{4}{7}
$$

#### Step 1: Write the fractions side by side.
$$
\frac{7}{8} \times \frac{4}{7}
$$

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 7.
- The denominator of the second fraction is 7.
- The GCF between 7 and 7 is 7.

- The numerator of the second fraction is 4.
- The denominator of the first fraction is 8.
- The GCF between 4 and 8 is 4.

#### Step 3: Perform the cancellation.
$$
\frac{\cancel{7}^1}{\cancel{8}^2} \times \frac{\cancel{4}^1}{\cancel{7}^1}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{2 \times 1} = \frac{1}{2}
$$

#### Final Answer:
$$
\boxed{\frac{1}{2}}
$$

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Problem 4:

$$
\frac{9}{10} \times \frac{5}{12}
$$

#### Step 1: Write the fractions side by side.
$$
\frac{9}{10} \times \frac{5}{12}
$$

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 9.
- The denominator of the second fraction is 12.
- The GCF between 9 and 12 is 3.

- The numerator of the second fraction is 5.
- The denominator of the first fraction is 10.
- The GCF between 5 and 10 is 5.

#### Step 3: Perform the cancellation.
$$
\frac{\cancel{9}^3}{\cancel{10}^2} \times \frac{\cancel{5}^1}{\cancel{12}^4}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{3 \times 1}{2 \times 4} = \frac{3}{8}
$$

#### Final Answer:
$$
\boxed{\frac{3}{8}}
$$

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Problem 5:

$$
\frac{11}{12} \times \frac{6}{11}
$$

#### Step 1: Write the fractions side by side.
$$
\frac{11}{12} \times \frac{6}{11}
$$

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 11.
- The denominator of the second fraction is 11.
- The GCF between 11 and 11 is 11.

- The numerator of the second fraction is 6.
- The denominator of the first fraction is 12.
- The GCF between 6 and 12 is 6.

#### Step 3: Perform the cancellation.
$$
\frac{\cancel{11}^1}{\cancel{12}^2} \times \frac{\cancel{6}^1}{\cancel{11}^1}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{2 \times 1} = \frac{1}{2}
$$

#### Final Answer:
$$
\boxed{\frac{1}{2}}
$$

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Problem 6:

$$
\frac{13}{14} \times \frac{7}{13}
$$

#### Step 1: Write the fractions side by side.
$$
\frac{13}{14} \times \frac{7}{13}
$$

#### Step 2: Look for common factors to cancel.
- The numerator of the first fraction is 13.
- The denominator of the second fraction is 13.
- The GCF between 13 and 13 is 13.

- The numerator of the second fraction is 7.
- The denominator of the first fraction is 14.
- The GCF between 7 and 14 is 7.

#### Step 3: Perform the cancellation.
$$
\frac{\cancel{13}^1}{\cancel{14}^2} \times \frac{\cancel{7}^1}{\cancel{13}^1}
$$

#### Step 4: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{2 \times 1} = \frac{1}{2}
$$

#### Final Answer:
$$
\boxed{\frac{1}{2}}
$$

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Final Answers:

1. $\boxed{\frac{3}{10}}$
2. $\boxed{\frac{1}{4}}$
3. $\boxed{\frac{1}{2}}$
4. $\boxed{\frac{3}{8}}$
5. $\boxed{\frac{1}{2}}$
6. $\boxed{\frac{1}{2}}$

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