https://file.aiquickdraw.com/mathbot/file/17265475378312zd3eeac.jpg

Let's analyze the problem step by step:

1. **Part (a)**:
   - Lila rewrote \( \frac{10}{25} \) as \( \frac{40}{100} \), and represented it with the picture on the right.
   - Tony thinks this fraction is also equal to \( \frac{2}{5} \).

Looking at the picture, it consists of a 5x5 grid. 10 of the squares are shaded, which corresponds to \( \frac{10}{25} \). If we reduce this fraction by dividing both the numerator and the denominator by 5, we indeed get \( \frac{2}{5} \). Hence, Tony is correct because \( \frac{10}{25} = \frac{2}{5} \).

Additionally, Lila's representation of \( \frac{10}{25} \) as \( \frac{40}{100} \) is valid because multiplying both the numerator and denominator by 4 gives \( \frac{40}{100} \), which represents the same portion of the grid.

2. **Part (b)**:
   - To write an equivalent fraction using tenths, we need to find an equivalent fraction in the form \( \frac{?}{10} \).
   - Since \( \frac{2}{5} \) is equivalent to \( \frac{4}{10} \) (by multiplying both numerator and denominator by 2), the fraction that can represent Lila's picture in tenths is \( \frac{4}{10} \).

Thus:

- **(a)**: Yes, Tony is correct. \( \frac{10}{25} = \frac{2}{5} \), and both fractions represent the same portion of the grid.
- **(b)**: An equivalent fraction using tenths is \( \frac{4}{10} \).

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. How do you find an equivalent fraction of \( \frac{3}{4} \) in tenths?
2. Can you reduce \( \frac{12}{36} \) to its simplest form?
3. How can you represent \( \frac{6}{15} \) in hundredths?
4. What is the decimal representation of \( \frac{7}{10} \)?
5. How do you convert \( \frac{8}{20} \) to an equivalent fraction with a denominator of 5?

**Tip**: Always remember to simplify fractions by dividing both the numerator and denominator by their greatest common divisor (GCD).

In problem 1-95, Lila rewrote 10/25 as 40/100 and represented it with the picture at right. Tony thinks this fraction is also equal to 2/5. a. Is Tony correct? Use the picture or calculations to explain your reasoning. Write your answer in complete sentences. b. How could Tony write an equivalent (equal) fraction using tenths? That is, what fraction in the form ?/10 can represent Lila’s picture?

Explore how to determine equivalent fractions such as 10/25, 40/100, and 2/5, using a visual 5x5 grid. Learn how to simplify and rewrite fractions in different forms. Suitable for students in Grades 5-6.

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