The following image was made from Multiply Fractions with Lines Designer:

Multiply Fractions-Strict is similar to the previous program MULTIPLY FRACTIONS except that both factors may be mixed numbers and the product must be written as a mixed number or whole number and in lowest terms.

See the program MIXED NUMBERS for information on writing fractions in mixed number form.

See the program RENAME IN LOWEST TERMS for information on writing fractions in lowest terms.

In most examples, it may be easier to determine the product by calculation.

You can see from the picture that the first factor is 4 1/2 units in length and the second factor is 2 4/9 units in length. To calculate the product, first write each factor in fraction form. Then multiply the numerators of each factor for the numerator of the product and the denominators of each factor for the denominator of the product.

This illustration shows a short-cut method known as canceling. To cancel, first write each factor in fraction form. Then think of a number that will divide evenly into any number in the numerator and also any number in the denominator. You can cancel if the number you divide by - the greatest common factor of the numbers - is larger than 1. In the example, 9 will divide into 9 in the numerator of the first fraction and 9 in the denominator of the second fraction. 2 will divide evenly into the denominator of the first fraction and the numerator of the second fraction. After you divide by the common factor, cross off the original term and write the answer near the original term. Then multiply across by the new number instead of the original terms. Canceling will give you smaller numbers to multiply and will give you a product in lowest terms.

How to Cancel will play a short animation that demonstrates this shortcut way to write a fraction in lowest terms.

A more advanced method for students who are studying multiplying polynomials in algebra is illustrated below:

You can see that the 4, the 1, the 3/2, and the 3/8 can be found in the visual illustration above. Some algebra texts call this the FOIL method for multiplying binomials for (F)irst, (O)utside, (I)nside, and (L)alst.