Mixed and improper fractions

Objective. Convert fluently between mixed numbers and improper fractions.

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2. Worked example
3. Practice
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Learn: the key idea

Mixed and improper fractions are two ways of writing a fraction greater than one whole, and converting fluently between them is essential for calculation. A mixed number like 2¾ shows whole parts and a fraction part separately, while an improper fraction like 11/4 shows the same value as a single fraction larger than the denominator. To convert a mixed number to improper form, multiply the whole number by the denominator and add the numerator, keeping the same denominator, so 2¾ becomes (2 × 4 + 3)/4 = 11/4. To reverse this, divide the numerator by the denominator to find the whole part and the remainder becomes the new numerator.

Worked example

Convert the improper fraction 17/5 to a mixed number.

1 $Divide the numerator by the denominator: 17 \div 5.$
2 $5 goes into 17 three times (15), remainder 2.$
3 $The whole part is 3 and the remainder 2 stays over 5.$
4 $17/5 = 3 2/5.$

Answer: 3 2/5

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Common mistake. Pupils sometimes convert 3⅖ by multiplying only the whole number and denominator and forgetting to add the numerator, getting 15/5 instead of the correct (3 × 5 + 2)/5 = 17/5.

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