Working with fractions is often a difficult concept to grasp for students of math. Dividing with fractions, in particular, can be quite confusing. This article will walk through examples of how to multiply and divide fractions, and offer a conceptual device that will ease comprehension of the topic moving forward.

Multiplying two fractions is relatively straightforward operation-wise, but conceptually it can be confusing. A major misconception of students at this stage in math is that multiplying makes numbers bigger. When multiplying with fractions, however, it actually makes them smaller. This concept is easy to understand when you consider that a fraction is a portion of one, so if you are taking a portion of something, you are making it smaller. Grasping this notion will make division with fractions much easier.

½ * ¾ =

In order to multiply two fractions, as in our example, simply multiply the nominators, (1*3) for the nominator of your solution (3), and multiply the denominators (2*4) for the denominator (8). Put it all together and we have a solution of 3/8. It is that simple, but what does it mean? It means you just took one half of three-quarters! Simple enough, but what about division?

Here is where things get tricky. Dividing does not always result in a smaller solution, just like multiplying does not always mean an increase. When dividing with fractions, you are asking how much of a unit lower than one there is inside another unit. Because the unit itself is divided by one, it stands to reason that dividing by a number lower than 1 will give you a larger answer. But why? Let’s look at an example.

½ / 1/6 =

Think about our pie. In our example, we are asking how many of 1/6 slices there are in ½ of a slice. If you start placing 1/6 slices, you will see that there are 3 in ½. To divide two fractions, we actually want to turn it into a multiplication operation. An easy way to remember is “Leave me, change me, turn me over.��� Leave the first fraction as is (½), change the division sign into a multiplication sign (*), and turn over the second fraction (1/6 becomes 6/1). When you divide by a fraction, you are multiplying by its reciprocal. Now we have ½ * 6/1 = 6/2, which simplifies to 3. That’s what we figured out with our pie!

By remembering that fractions are only pieces of a whole, it is easier to understand the processes and results behind multiplying and dividing with fractions. At The Dr Phillips Tutoring Center in Orlando, FL, we help children struggling with fractions and other mathematical concepts. We also offer one-to-one tutoring in math, writing, reading, and test preparation for students of all levels. Check out our website for more information about our academic programs. Then give us a call at 407-286-2389 to schedule a free diagnostic assessment.

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