https://file.aiquickdraw.com/mathbot/file/1726079272562p9o9kfvk.jpg

Let's go through the problems step by step.

### III. Fill in the blanks:

**a. \( \frac{15}{8} \) = ?**

Convert the mixed fraction \( \frac{15}{8} \) into a mixed number:

\[ \frac{15}{8} = 1 \frac{7}{8} \]

**b. \( \frac{3}{5} \) = ?**

\( \frac{3}{5} \) is already in its simplest form, so it remains \( \frac{3}{5} \).

**c. \( 1 \frac{9}{11} = ? \)**

Convert the mixed number to an improper fraction:

\[ 1 \frac{9}{11} = \frac{11}{11} + \frac{9}{11} = \frac{20}{11} \]

**d. \( \frac{29}{7} = ? \)**

Convert the improper fraction to a mixed number:

\[ \frac{29}{7} = 4 \frac{1}{7} \]

**e. \( ? = 5 \frac{1}{6} \)**

Convert the mixed number to an improper fraction:

\[ 5 \frac{1}{6} = \frac{30}{6} + \frac{1}{6} = \frac{31}{6} \]

### IV. Fill in the empty boxes using <, >, or = sign.

**a. \( \frac{7}{8} \) ? \( \frac{4}{5} \)**

Convert both fractions to decimals:

\[ \frac{7}{8} = 0.875 \quad \text{and} \quad \frac{4}{5} = 0.8 \]

Since \( 0.875 > 0.8 \):

\[ \frac{7}{8} > \frac{4}{5} \]

**b. \( \frac{5}{12} \) ? \( \frac{6}{11} \)**

Convert both fractions to decimals:

\[ \frac{5}{12} \approx 0.4167 \quad \text{and} \quad \frac{6}{11} \approx 0.5455 \]

Since \( 0.4167 < 0.5455 \):

\[ \frac{5}{12} < \frac{6}{11} \]

**c. \( \frac{37}{8} \) ? \( \frac{28}{9} \)**

Convert both fractions to decimals:

\[ \frac{37}{8} = 4.625 \quad \text{and} \quad \frac{28}{9} \approx 3.111 \]

Since \( 4.625 > 3.111 \):

\[ \frac{37}{8} > \frac{28}{9} \]

**d. \( \frac{10}{9} \) ? \( \frac{7}{6} \)**

Convert both fractions to decimals:

\[ \frac{10}{9} \approx 1.111 \quad \text{and} \quad \frac{7}{6} \approx 1.1667 \]

Since \( 1.111 < 1.1667 \):

\[ \frac{10}{9} < \frac{7}{6} \]

**e. \( \frac{5}{6} \) ? \( \frac{4}{3} \)**

Convert both fractions to decimals:

\[ \frac{5}{6} \approx 0.8333 \quad \text{and} \quad \frac{4}{3} \approx 1.3333 \]

Since \( 0.8333 < 1.3333 \):

\[ \frac{5}{6} < \frac{4}{3} \]

### Mindspark Questions

**1. Find the missing numeral:**

Given: \( \frac{7}{10} = \frac{49}{?} \)

To find the missing denominator, set up the equation:

\[ \frac{7}{10} = \frac{49}{x} \]

Cross-multiply:

\[ 7x = 49 \times 10 \]

\[ 7x = 490 \]

\[ x = \frac{490}{7} = 70 \]

So, the missing numeral is 70.

**2. If two fractions have the same numerator but different denominators, how do we decide which is greater?**

For fractions with the same numerator, the fraction with the smaller denominator is greater because it represents a larger portion of the whole.

**3. How many equivalent fractions can be written for a given fraction?**

There are infinitely many equivalent fractions for any given fraction because you can multiply the numerator and the denominator by the same non-zero integer to create new equivalent fractions.

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Would you like further details or have any questions? Here are some related questions you might find helpful:

1. How do you convert between improper fractions and mixed numbers?
2. What is the process for comparing fractions with different denominators?
3. Can you explain how to simplify a fraction to its lowest terms?
4. How do you find the least common multiple of denominators to compare fractions?
5. What are some methods to quickly approximate fractions as decimals?

**Tip:** When comparing fractions, converting them to decimals or finding a common denominator can make the process easier!

Solve the math worksheet involving fractions, mixed numbers, and inequality signs.

This worksheet covers important fraction concepts such as comparing fractions, converting between improper fractions and mixed numbers, and filling in blanks with appropriate signs. Learn to solve step-by-step with fractions like 15/8, 29/7, and mixed numbers.

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