Convert between improper fractions and mixed numbers

Improper fractions and mixed numbers are two different ways to write the same value for numbers greater than one.

What is a Mixed Number?
A mixed number has a whole number part and a fraction part.
*   Example: 2 ½ (two and one-half)
*   This means you have 2 whole things and ½ of another.

What is an Improper Fraction?
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
*   Example: 5/2 (five-halves)
*   This means the number of pieces you have is more than the number of pieces in one whole.

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Converting an Improper Fraction to a Mixed Number (Divide!)

Let's convert 11/4 to a mixed number.

1.  Divide the numerator by the denominator: 11 ÷ 4
    *   11 divided by 4 is 2 with a remainder of 3.
2.  Use the parts of the division answer:
    *   The whole number answer (2) becomes the big whole number of the mixed number.
    *   The remainder (3) becomes the new numerator.
    *   The denominator (4) stays the same.
3.  Result: 11/4 = 2 ¾

Visual: If you have 11 quarter-pieces of a pizza, you can make 2 whole pizzas (using 8 pieces) and you'll have 3 quarter-pieces left over.

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Converting a Mixed Number to an Improper Fraction (Multiply and Add!)

Let's convert 3 ½ to an improper fraction.

1. Multiply the whole number by the denominator: 3 x 2 = 6 2. Add the numerator to that result: 6 + 1 = 7 3. Keep the denominator: The denominator stays a 2. 4. Result: 3 ½ = 7/2

Visual (The "MAD" Method - Multiply, Add, Denominator):
*   Multiply: Whole number x Denominator
*   Add: The result + Numerator
*   Denominator: Stays the same!

Key Idea: Think of it as breaking down the whole numbers into fractional pieces. In 3 ½, each of the 3 whole things contains 2 halves (3x2=6 halves), plus the 1 half you already had gives you 7 halves in total.

Practice converting between fraction types!

Improper to Mixed Number: 1. 7/3 = ? 2. 10/4 = ? 3. 15/6 = ? 4. 23/5 = ?

Mixed Number to Improper Fraction: 5. 1 ¾ = ? 6. 2 ⅕ = ? 7. 4 ½ = ? 8. 3 ⅔ = ?

Word Problems: 9. A recipe needs 13/4 cups of flour. Write this as a mixed number. 10. You ran 3 ½ miles. Write this distance as an improper fraction. 11. If 11 people each eat ¼ of a pizza, how much pizza was eaten? Write your answer as both an improper fraction and a mixed number.

Challenge Problems: 12. What is 35/8 as a mixed number? 13. What is 5 ⅚ as an improper fraction? 14. Which is greater: 14/3 or 4 ½? (Hint: convert one to match the other).