Dividing Fractions

Dividing fractions is based upon another basic concept, that multiplying the numerator and the denominator of a fraction by the same number doesn't change its value.

As with whole numbers, division involves finding one of the multipliers (here the number of pieces to divide the total into) when you know the product and the other multiplier (here, the size of each piece).

Here, the numerator and the denominator are themselves fractions (3/4 and 1/8, respectively - see the bottom of the figure.) Multiplying top and bottom by the inverse of the denominator converts the bottom to 1 and the numerator to a familiar form, multiplication. This is where the rule: invert divisor and multiply comes from.

This also introduces students to recursion and the extensibility of operations. For example, numerators and denominators can themselves have parts with numerators and denominators that are subject to the same concepts and operations.