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Let's go through each part of the problem step-by-step:

### Part (a)
We need to write the mixed fraction \( 1 \frac{2}{5} \) as an improper fraction.

To convert a mixed number to an improper fraction:
1. Multiply the whole number by the denominator.
2. Add the numerator to the result.
3. Keep the denominator the same.

For \( 1 \frac{2}{5} \):
- Multiply the whole number (1) by the denominator (5): \( 1 \times 5 = 5 \)
- Add the numerator (2): \( 5 + 2 = 7 \)

Thus, \( 1 \frac{2}{5} = \frac{7}{5} \).

### Part (b)
Now, we need to calculate \( \frac{1}{4} \times 1 \frac{2}{5} \) and give the answer as a fraction in its simplest form.

1. First, convert the mixed number \( 1 \frac{2}{5} \) to an improper fraction, which we already know from part (a) is \( \frac{7}{5} \).
   
2. Now, multiply \( \frac{1}{4} \times \frac{7}{5} \).

To multiply fractions:
- Multiply the numerators: \( 1 \times 7 = 7 \)
- Multiply the denominators: \( 4 \times 5 = 20 \)

So, \( \frac{1}{4} \times \frac{7}{5} = \frac{7}{20} \).

Therefore, the final answer to part (b) is \( \frac{7}{20} \).

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Would you like further details on any part of this solution? Here are five related questions to extend your understanding:

1. How can you simplify improper fractions into mixed numbers?
2. What is the general method for multiplying any two fractions?
3. Can improper fractions always be simplified? Why or why not?
4. How do you add or subtract mixed numbers?
5. What is the process for dividing one fraction by another?

**Tip**: When multiplying fractions, always check if you can simplify either the numerator or the denominator before multiplying. This will make calculations easier!

Write 1 2/5 as an improper fraction in its simplest form. Work out 1/4 × 1 2/5 and give your answer as a fraction in its simplest form.

Learn how to convert 1 2/5 to an improper fraction and multiply fractions like 1/4 × 1 2/5 with this step-by-step guide. This problem involves fundamental fraction concepts and multiplication rules. Ideal for Grades 5-7.

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