Converting mixed numbers to improper fractions

Topic guide

What this worksheet practises

This worksheet provides practice on converting mixed numbers (a whole number and a fraction) into improper fractions (where the top number is bigger than the bottom). This is a crucial first step before multiplying or dividing fractions, as those operations cannot be easily done with mixed numbers.

Key method

To convert a mixed number to an improper fraction, you need to turn the whole number parts into fraction parts of the same size, and add them to the existing fraction.

• Identify the whole number, the numerator (top), and the denominator (bottom).
• Multiply the whole number by the denominator. This tells you how many pieces the whole numbers are made of.
• Add the numerator to this result. This gives you the total number of pieces.
• Write this new total over the original denominator.

Worked example

Convert 3⅖ into an improper fraction.

Step 1: Identify the parts. Whole number = 3, numerator = 2, denominator = 5.

Step 2: Multiply the whole number by the denominator.

3 × 5 = 15.

Step 3: Add the existing numerator.

15 + 2 = 17.

Step 4: Put this over the original denominator.

The answer is 17/5.

Common mistakes to avoid

The most common error is adding instead of multiplying in the first step. For example, calculating 3 + 5 instead of 3 × 5. Always remember: the whole number tells you how many "lots" of the denominator you have.

How to check your answer

To check your work, perform the reverse operation. Divide your new numerator by the denominator. 17 ÷ 5 goes 3 times, with a remainder of 2. So, it is 3 whole ones and 2 leftover fifths (3⅖). This proves your calculation is exactly right.