Mixed numbers

A mixed number is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+"; for example, in referring to two entire cakes and three quarters of another cake, the whole and fractional parts of the number are written next to each other: .

An improper fraction can be thought of as another way to write a mixed number; consider the example below.

We can imagine that the two entire cakes are each divided into quarters, so that the denominator for the whole cakes is the same as the denominator for the parts. Then each whole cake contributes to the total, so is another way of writing .

A mixed number can be converted to an improper fraction in three steps:

1. Multiply the whole part by the denominator of the fractional part.

2. Add the numerator of the fractional part to that product.

3. The resulting sum is the numerator of the new (improper) fraction, with the 'new' denominator remaining precisely the same as for the original fractional part of the mixed number.

Similarly, an improper fraction can be converted to a mixed number:

1. Divide the numerator by the denominator.

2. The quotient (without remainder) becomes the whole part and the remainder becomes the numerator of the fractional part.

3. The new denominator is the same as that of the original improper fraction.

Task 1. Convert these mixed numbers into improper fractions and comment your steps of conversion.