Multiplying Three Fractions

By Contributing Writer

In math, you multiply three fractions by following the same basic rules that govern the multiplication of two fractions. The associative property of multiplication holds that (a x b) x c = a x (b x c). This holds true with fractions as well. Let's put this knowledge to the test.

Standard Fractions

Consider the following problem:2/5 X 1/3 X 4/7 = ?If you apply the associative property of multiplication, the result will be 2/5 X (1/3 X 4/7) = (2/5 X 1/3) X 4/7. The fractions can be grouped in any way to make the problem easier to solve.

Find the answer by multiplying two of the fractions together, then multiplying the result by the third fraction. In this example, you solve the equation by first multiplying 2/5 X 1/3 to get 3/15.Then multiply the remaining fractions:3/15 X 4/7 = 12/105

Simplify 12/105 by reducing to the lowest possible solution. 12/105 = 4/35.

Mixed Fractions

To multiply three mixed fractions, first change the mixed fractions into improper fractions. Let's use the example 1-2/3 X 3-2/5 X 2-1/4 = ?Change the mixed fractions into improper fractions by multiplying the denominator by the whole number and adding the numerator. Then make that sum the new numerator and use the same denominator.

Start with the first mixed fraction. Change 1-2/3 by multiplying the 3 x 1, which equals 3. Add the numerator 2 to equal 5, and make that 5 the numerator. Tthe result is 5/3.Repeat this process with the second mixed fraction, changing 3-2/5 to 17/5.

Repeat again with the third fraction, 2-1/4. The result is 9/4.

Group the improper fractions according to the associative property of multiplication. (5/3 x 9/4) x 17/5 = 765/60

Simplify 765/60 by dividing the numerator by the denominator; the remainder becomes the new numerator and the denominator remains the same. The result is 12-45/60. Reduce the fraction to 12-3/4.