The image shows a worksheet focused on converting mixed numbers to improper fractions. Let's go through each step and solve the problems:

Step-by-Step Explanation:

1. General Rule:

• To convert a mixed number to an improper fraction: $\text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator}$ The result becomes the numerator of the improper fraction, while the denominator remains the same.

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a) Convert $3 \frac{2}{3}$ to an improper fraction:

• Step 1: Multiply the whole number by the denominator: $3 \times 3 = 9$.
• Step 2: Add the numerator to this product: $9 + 2 = 11$.
• Step 3: Place the result over the original denominator: $\frac{11}{3}$.

Result: $3 \frac{2}{3} = \frac{11}{3}$

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b) Convert $2 \frac{5}{6}$ to an improper fraction:

• Step 1: Multiply the whole number by the denominator: $2 \times 6 = 12$.
• Step 2: Add the numerator: $12 + 5 = 17$.
• Step 3: Place the result over the original denominator: $\frac{17}{6}$.

Result: $2 \frac{5}{6} = \frac{17}{6}$

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c) Convert $7 \frac{1}{4}$ to an improper fraction:

• Step 1: Multiply the whole number by the denominator: $7 \times 4 = 28$.
• Step 2: Add the numerator: $28 + 1 = 29$.
• Step 3: Place the result over the original denominator: $\frac{29}{4}$.

Result: $7 \frac{1}{4} = \frac{29}{4}$

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d) Convert $2 \frac{1}{2}$ to an improper fraction:

• Step 1: Multiply the whole number by the denominator: $2 \times 2 = 4$.
• Step 2: Add the numerator: $4 + 1 = 5$.
• Step 3: Place the result over the original denominator: $\frac{5}{2}$.

Result: $2 \frac{1}{2} = \frac{5}{2}$

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Summary of Answers:

• $3 \frac{2}{3} = \frac{11}{3}$
• $2 \frac{5}{6} = \frac{17}{6}$
• $7 \frac{1}{4} = \frac{29}{4}$
• $2 \frac{1}{2} = \frac{5}{2}$

Would you like more details on any of these conversions or have any questions?

Related Questions:

1. How do you convert an improper fraction back into a mixed number?
2. What happens if the numerator and denominator have a common factor?
3. How do you compare improper fractions with different denominators?
4. What is the relationship between improper fractions and division?
5. Can an improper fraction be greater than 1?

Tip: When converting mixed numbers to improper fractions, always double-check your multiplication and addition to avoid mistakes!