Mixed Numbers and Improper Fractions

A mixed number combines a whole number and a proper fraction, like 2 1/4. An improper fraction has a top number greater than or equal to its bottom number, like 9/4. Both write the same amount in two different ways. Knowing how to switch between them makes adding, subtracting, and comparing fractions much easier.

The Parts of Each Form

• A mixed number has a whole part and a fractional part: in 2 1/4, the whole part is 2 and the fractional part is 1/4.
• An improper fraction has a numerator greater than or equal to its denominator: 9/4 means 9 quarter-pieces.
• A proper fraction has a numerator smaller than its denominator: 1/4 is proper because 1 is less than 4.
• A mixed number and an improper fraction can describe the same amount: 2 1/4 = 9/4.

Mixed Number to Improper Fraction

• Multiply the whole number by the denominator: 2 x 4 = 8.
• Add the numerator: 8 + 1 = 9.
• Keep the same denominator: the answer is 9/4.
• Quick formula: (whole x denominator + numerator) / denominator.

Improper Fraction to Mixed Number

• Divide the numerator by the denominator: 9 div 4 = 2 remainder 1.
• The quotient becomes the whole part: 2.
• The remainder becomes the new numerator over the same denominator: 1/4.
• Write them together: 9/4 = 2 1/4.

Simplify When You Can

• After converting, check if the fractional part can be reduced to lowest terms.
• Find the greatest common factor of the numerator and denominator and divide both by it.
• Example: 10/4 = 2 2/4, and 2/4 simplifies to 1/2, so the final answer is 2 1/2.
• A fraction is in lowest terms when the numerator and denominator share no common factor besides 1.