Improper Fractions

A fraction like 7/3, with a numerator at least as big as its denominator, is called improper. The same amount can be written as a mixed number: 2 wholes and 1 third more, said 'two and one third'. It means 2 plus one third, 2 + 1/3, and it is written 2 1/3, the whole number right beside the fraction.

To turn a mixed number into an improper fraction, count everything in thirds. Each whole is 3 thirds, so 2 wholes are 6/3. Add the 1 third: 6/3 + 1/3 is 7 thirds, 7/3. The bottom stays 3 because the pieces are still thirds; only their number grows.

In one step: multiply the whole number by the denominator, add the numerator, and keep the denominator: 2 × 3 + 1 is 7, so it is 7 thirds. An improper fraction is a single fraction to work with, which is what multiplying and dividing fractions will need later in this section.