A mixed fraction (or mixed number) is a way of expressing a number that consists of two parts:

1. A whole number (integer part)
2. A proper fraction (the fractional part)

For example:

• 3 ½ is a mixed fraction where 3 is the whole number and ½ is the fractional part.

Converting Mixed Fractions to Improper Fractions:

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). To convert a mixed fraction into an improper fraction, follow these steps:

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

Example:

Convert 3 ¾ into an improper fraction.

1. Multiply the whole number (3) by the denominator of the fraction (4):
   $3 \times 4 = 12$

2. Add the numerator of the fraction (3) to the result:
   $12 + 3 = 15$

3. Place the sum (15) over the original denominator (4):
   $\frac{15}{4}$

So, 3 ¾ = 15/4 as an improper fraction.

Converting Improper Fractions to Mixed Fractions:

To convert an improper fraction to a mixed fraction:

1. Divide the numerator by the denominator to get the quotient and the remainder.
2. The quotient becomes the whole number part.
3. The remainder becomes the numerator of the fractional part, with the denominator remaining the same.

Example:

Convert 17/5 into a mixed fraction.

1. Divide 17 by 5:
   $17 \div 5 = 3$ (quotient), remainder is 2.

2. The whole number part is 3.

3. The remainder (2) is the numerator, and the denominator remains 5.

So, 17/5 = 3 2/5 as a mixed fraction.

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More Examples:

1. Mixed to Improper: Convert 5 ⅓ into an improper fraction: $5 \times 3 + 1 = 15 + 1 = 16, \quad \text{so} \quad 5 \frac{1}{3} = \frac{16}{3}$

2. Improper to Mixed: Convert 23/6 into a mixed fraction: $23 \div 6 = 3 \quad \text{(quotient)}, \quad 23 - (6 \times 3) = 5 \quad \text{(remainder)}, \quad \text{so} \quad \frac{23}{6} = 3 \frac{5}{6}$

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Key Points:

• A mixed fraction consists of a whole number and a fraction.
• An improper fraction is a fraction where the numerator is larger than or equal to the denominator.
• You can convert between mixed and improper fractions by following simple multiplication and division steps.

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Would you like any specific examples worked out? Or do you have any questions? Here are some related questions to explore further:

1. How do you simplify mixed fractions after converting them?
2. Can mixed fractions be added or subtracted directly? How?
3. How do you multiply mixed fractions?
4. What are some real-life uses for mixed fractions?
5. How can you represent mixed fractions in decimal form?

Tip: When dealing with mixed fractions, always ensure that the whole number part and the fractional part are clearly separated for clarity!