A fraction is a numeric piece of information that represents a comparison between two sets of data. This includes the numerator at the top of the fraction that is considered relative to the denominator at the bottom. For example, consider a survey taken of 100 participants to find out their favorite holiday. If 56 out of 100 (56/100) say Christmas, we see that the data set of interest is the 56 as it relates to the total number of 100. A fraction can also be expressed exactly in the form of percentages, ratios and decimals. Fractions just like any other number can be added, subtracted, multiplied, divided and used in any other type algebraic operation. This article will provide you with the basics of how to multiply fractions with or without like denominators.
Unlike when you are adding or subtracting a set of fractions, to multiply fractions, it is not necessary for the fractions to have common or like denominators. In fact, when you multiply two or more fractions, you can think of the situation as being that you have one fraction being multiplied by a couple of factors. These factors can be less than 1 (i.e. 1/2, 1/5, 4/7, etc.) or greater than 1 (i.e. 4/3, 3/2, 10/7, etc.). For example, if we consider the product of (1/2)(1/4)(8/8), we can see by inspection that 8/8 = 1, 1 is multiplied by 1/4 which then becomes 1/4, it is then multiplied by 1/2 which then becomes 1/8.
Also unlike in the addition or subtraction of a fraction set, when multiplying fractions, you will work with both the numerators and denominators. To perform the multiplication of two or more fractions, you simply have to find the product of the numerators from each fraction to create a new, final numerator. Likewise, you find the product of the denominators of each fraction to get a new, final denominator. From here, with the final numerator and final denominator you have your final fraction. Multiplying a set of fractions is just that simple. Let's look a few examples.
1.) Find the product of 3/6 and 6/8's.
(3/6)(6/8) = (3 x 6)/(6 x 8) = 18/48 = 3/8
This answer is reasonable when we consider that 3/6 is a factor of 0.5 being multiplied by 6/8 and so the answer is exactly one half of 6/8.
2.) Find (12/34)(1/7)(6/18).
(12/34)(1/7)(6/18) = (12 x 1 x 6)/(34 x 7 x 18) = 72/4284 = 2/119
3.) What is 7/8's of (5/3) times (4/10)?
(7/8)(5/3)(4/10) = (7 x 5 x 4)/(8 x 3 x 10) = 140/240 = 35/60 = 7/12