Improper to mixed fractions
Converting improper fractions to mixed numbers is a handy skill when working with measurements, recipes, or dividing items into groups. It helps break down a fraction into a whole number and a simpler fraction, making it easier to understand and use in everyday situations like cooking or carpentry! Jump to the questions
Practise now
Convert these improper fractions into mixed numbers in their simplest form.
Topic guide
What this worksheet practises
This worksheet provides practice on converting improper fractions (where the top number is larger than the bottom number, also known as top-heavy fractions) into mixed numbers (a whole number alongside a smaller proper fraction). This is often required as the final step when answering fraction addition or multiplication questions.
Key method
The fraction line literally means "divide". You must figure out how many whole times the bottom number fits into the top number.
- Divide the top number (numerator) by the bottom number (denominator).
- The whole-number result of this division becomes your large whole number.
- The remainder of the division becomes your new top number (numerator).
- The bottom number (denominator) never changes.
Worked example
Convert 17/5 into a mixed number.
Step 1: Divide 17 by 5.
5 fits into 17 three whole times (because 5 × 3 = 15).
This '3' is our large whole number.
Step 2: Calculate the remainder.
17 − 15 = 2. The remainder is 2.
This '2' becomes the new top number.
Step 3: Keep the original bottom number (5).
The final mixed number is 3⅖.
Common mistakes to avoid
A common error is changing the denominator during the process. If you start with "fifths" (something divided by 5), your final mixed fraction must still end in "fifths". The denominator represents the size of the slice, which does not change just because you've organised the slices into whole cakes.
How to check your answer
You can easily reverse the process to check your work. Multiply the whole number by the denominator, and then add the numerator. In our example, (3 × 5) + 2 = 15 + 2 = 17. Because we arrive back at 17/5, our mixed number is definitely correct.