To solve the problem shown in the uploaded image, we will follow a similar process of converting fractions to decimals for easier comparison. The given fractions are:

Part (a)

The fractions are: $\frac{3}{5}, \frac{7}{8}, \frac{4}{7}, \frac{7}{12}$

Step 1: Convert the fractions to decimals for easier comparison

$\frac{3}{5} = 0.6$ $\frac{7}{8} = 0.875$ $\frac{4}{7} \approx 0.5714$ $\frac{7}{12} \approx 0.5833$

Step 2: Arrange the decimals in ascending order

$0.5714, 0.5833, 0.6, 0.875$

Step 3: Convert the decimals back to fractions in ascending order

$\frac{4}{7}, \frac{7}{12}, \frac{3}{5}, \frac{7}{8}$

Step 4: Arrange the fractions in descending order

$\frac{7}{8}, \frac{3}{5}, \frac{7}{12}, \frac{4}{7}$

Part (b)

The fractions are: $\frac{9}{4}, \frac{7}{3}, \frac{5}{8}, \frac{6}{5}$

Step 1: Convert the fractions to decimals for easier comparison

$\frac{9}{4} = 2.25$ $\frac{7}{3} \approx 2.3333$ $\frac{5}{8} = 0.625$ $\frac{6}{5} = 1.2$

Step 2: Arrange the decimals in ascending order

$0.625, 1.2, 2.25, 2.3333$

Step 3: Convert the decimals back to fractions in ascending order

$\frac{5}{8}, \frac{6}{5}, \frac{9}{4}, \frac{7}{3}$

Step 4: Arrange the fractions in descending order

$\frac{7}{3}, \frac{9}{4}, \frac{6}{5}, \frac{5}{8}$

Summary

For part (a):

• Ascending order: $\frac{4}{7}, \frac{7}{12}, \frac{3}{5}, \frac{7}{8}$
• Descending order: $\frac{7}{8}, \frac{3}{5}, \frac{7}{12}, \frac{4}{7}$

For part (b):

• Ascending order: $\frac{5}{8}, \frac{6}{5}, \frac{9}{4}, \frac{7}{3}$
• Descending order: $\frac{7}{3}, \frac{9}{4}, \frac{6}{5}, \frac{5}{8}$

Would you like more details or have any questions about this solution?

Here are 8 related questions for further practice:

1. How would you find the least common denominator (LCD) for a set of fractions?
2. What steps are involved in converting a mixed number to an improper fraction?
3. How can you compare two fractions without converting them to decimals?
4. What is the process for simplifying a fraction to its lowest terms?
5. How can you convert a fraction to a percentage?
6. What method can you use to find the greatest common divisor (GCD) of two numbers?
7. How do you perform addition of fractions with unlike denominators?
8. How do you multiply two fractions together and simplify the result?

Tip: When comparing fractions, it's often useful to visualize them on a number line to better understand their relative sizes.