Multiply the numerators, or the top numbers of the fractions. Using 1/4 x 1/2 as an example, multiply 1 x 1. Therefore, the new numerator is 1.
Multiply the denominators, or the bottom numbers of the fractions. Using the same example, multiply 4 x 2, making the new denominator 8. Therefore, 1/4 x 1/2 = 1 x 1/4 x 2 = 1/8, which is already in lowest terms, so you do not need to simplify.
Simplify the resulting fraction, if necessary. For example, 1/2 x 2/3 = 2/6, which is not in its lowest term. To simplify, find the highest common denominator between 2 and 6, which is 2, then separately divide the numerator and the denominator by the highest common factor. Therefore, 2/6 is reduced to 1/3, since 2 divided by 2 is 1, and 6 divided by 2 is 3.
Simplify the fractions before multiplying them as an alternative to simplifying the resulting fraction. For example, write 1/2 x 2/3 as 1 x 2/2 x 3, then find the common factors between the combined numerators and the combined denominators. The only common factor in the example is 2, so divide the 2 in the numerator and the 2 in the denominator by 2. Therefore, 1 x 2/2 x 3 becomes 1 x 1/1 x 3, which equals 1/3.