Just as fractions can be expanded, they can also be shortened. Fractions are shortened by dividing both the numerator and the denominator by the same number. This does not change the value of the fraction or the fractional number, because the part represented by the fraction is only divided into larger sections, i.e., the division is coarsened. Shortening is also used, for example, to bring the addition and subtraction of fractions to the same denominator, as described below. Also, possibly large numerators and denominators in the result after multiplying two fractions can be converted into smaller values by shortening.
Example: Shortening fractions
To reduce the fraction 1040 by 5, divide the numerator and denominator by 5 and get
10 ÷ 540 ÷ 5
= 28
1040 was therefore shortened by 5 to
28, where both fractions retain the same value.
28 could even be shortened again by 2, so that you get 14, which then cannot be shortened any further.