Mixed Number to Improper Fraction

Mixed number to improper fraction

A mixed number combines a whole number and a fraction, such as (3\frac{2}{5}). To rewrite it as an improper fraction, convert the whole part into the same denominator and add the fractional part.

Method

1. Multiply the whole number by the denominator.
2. Add the numerator.
3. Keep the same denominator.
4. Write the result as a fraction.

Example

For (3\frac{2}{5}):

• (3 \times 5 = 15)
• (15 + 2 = 17)
• So the improper fraction is (\frac{17}{5})

Why it works

Each whole is made of (5/5), so 3 wholes equal (15/5). Adding (2/5) gives (17/5).

Check your answer

You can convert back to a mixed number by dividing the numerator by the denominator. For (\frac{17}{5}), (17 \div 5 = 3) remainder 2, so the result is (3\frac{2}{5}), which matches the original.

Common mistake

Do not add the denominator to the whole number. The denominator stays the same; only the whole part changes through multiplication and addition.