Multiplying and Dividing Fractions

The lesson below is still images taken from the fully animated PowerPoint I created that is available in my Teachers Pay Teachers store page. If the PowerPoint is not one of my freebies, you may also head over to my YouTube channel to see the slideshow fully animated and can pause as needed to be sure you grasp each concept before moving forward (each lesson will always be free there!).

In this lesson we go over how to multiply and divide fractions. The slides cover exactly what it means to multiply a fraction by another fraction visually as well as what it looks like to divide two fractions before covering the calculation method. Students get to see an understanding of how fractional quantities combine before seeing to multiply straight across or to multiply by a reciprocal (keep change flip).

So without further ado, read through the slides below to get a feel for how to multiply an divide fractions!

Mult 1Mult 2Mult 3Mult 4Mult 5Mult 6Mult 7

Phew, that’s a lot to take in. Once you’ve gone over this and found some practice problems to cement the idea in your head what integers are, you may move on to the next lesson below!

Exponent Basics

Just in case the slides aren’t your thing, here is a text outline of the main points of the lessons above!

  • Fractions
  • Multiplying and Dividing
  • Objectives
  • By the end of this lesson you should feel comfortable:
  • Multiplying and dividing fractions
  • Multiplying and dividing with mixed numbers
  • Multiplying fractions
  • If we can add and subtract fractions, it stands to reason there must be a way to multiply them, too, right?
  • And of course, our reasoning is correct:
  • But what does this actually mean?
  • We start with two fifths of something:
  • But I only want one third of what is shaded:
  • So the red represents two of fifteen pieces or:
  • Multiplying fractions
  • As always, however, drawing all of this every single time can become quite a chore, especially for very large numbers.
  • Luckily, there is a pattern here that makes multiplication of fractions even easier than adding or subtracting!
  • On the top you have 2 x 1 which is 2, the numerator of our answer.
  • On the bottom you have 5 x 3 which is 15, our new denominator!
  • Thus, multiplying fractions only requires us to multiply across the top and bottom to find our product!
  • Dividing Fractions
  • Alright, so let’s see about division now.
  • Again, what’s really happening when we see something like this?
  • We start with two fifths of something:
  • Then we want to divide each piece into thirds:
  • So each third has five parts.
  • But we have six blue pieces, or:
  • From there we may either choose to convert it to a mixed number or leave it as an improper fraction depending on what we need.
  • Dividing Fractions
  • But there is an easier way to think of division to again avoid drawing things out every time! (Thank you, lazy mathematicians!)
  • We use a method called KCF, and no, that isn’t fried chicken.
  • Keep the first fractions the same.
  • Change the sign to multiplication.
  • Flip the second fraction over.
  • (This is called a reciprocal if you want to get technical.)
  • Tada! Now we are back in familiar territory just multiplying!
  • Interesting Notes
  • Did you see how when we divided by a fraction, our number got larger?
  • Six fifths is larger than two fifths, but how?
  • This is because we asked how many fractions (smaller objects) fit inside, which makes a larger answer.
  • Also, just like before, now that we know how to multiply and divide fractions, the simplest way to work with mixed numbers is to make them improper first and then follow the same procedure!
  • conclusion
  • To multiply fractions, multiply straight across the top and bottom to find the product.
  • To divide fractions, first use KCF:
  • Keep the first fraction the same.
  • Change the sign to multiplication.
  • Flip the second fraction over.
  • Then multiply.
  • Dividing by a proper fraction will give an answer bigger than the original fraction.
  • To multiply or divide with mixed numbers, first convert them into improper fractions and then follow the same process.