An improper fraction is a fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). This means the fraction represents a value that is equal to or greater than 1.

For example:

• $\frac{7}{4}$
• $\frac{9}{3}$
• $\frac{5}{2}$

Converting Improper Fractions to Mixed Numbers

To convert an improper fraction to a mixed number:

1. Divide the numerator by the denominator.
2. Write the quotient as the whole number part.
3. The remainder becomes the new numerator, while the denominator remains the same.

For instance, with $\frac{7}{4}$:

• $7 \div 4 = 1$ with a remainder of $3$, so $\frac{7}{4} = 1 \frac{3}{4}$.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number back to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the result to the numerator.
3. Place the result over the original denominator.

Example: $1 \frac{3}{4}$:

• $1 \times 4 + 3 = 7$, so $1 \frac{3}{4} = \frac{7}{4}$.

Would you like to see more details or have any questions?

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1. What are some examples of improper fractions and their mixed number conversions?
2. How do improper fractions compare to proper fractions?
3. Why are improper fractions used in mathematics, and what are their advantages?
4. How can improper fractions be simplified?
5. What are some common uses of improper fractions in real-world problems?

Tip: When converting fractions, keep the denominator constant when moving between improper fractions and mixed numbers.