Multiplying & Dividing Rational Numbers

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  • 0:01 Rational Numbers
  • 1:04 Multiplying
  • 2:03 Dividing
  • 3:58 Examples
  • 5:33 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how to multiply and divide rational numbers. You will know when you need to flip your number and when you don't.

Rational Numbers

Sam works for this research company that gathers data for other companies for them to use. Part of Sam's job is to look at the numbers and then make certain calculations to give to the other companies so that they will better understand the information. The kinds of numbers that Sam sees for his job are called rational numbers. These are numbers that can be written as the fraction of two integers.

So, all simple fractions are rational numbers as are all integers because we can simply rewrite an integer as that number over 1. For example, 3/8 is a rational number as is the number 25 because it can be rewritten as 25/1. The proper form for any rational number is in fraction form. Unlike regular fractions where you want your bottom number to be larger than the top number, it is perfectly okay for the top number in a rational number to be larger than the bottom. So we can have rational numbers such as 8/7 and even 50/3.


One of the calculations that Sam needs to make with his rational numbers is that of multiplying them together. Looking down at his papers, Sam sees 2/3*17/3 as one of his problems. How will he solve this problem?

Sam remembers from a long time ago when he was in school that to multiply two rational numbers together, all he has to do is multiply the tops together and the bottoms together and he will get his answer. Sometimes, he'll need to simplify his answer, too.

So multiplying the tops of his problem, he gets:

2*17 = 34

Multiplying the bottoms. He gets:

3*3 = 9

Putting it together, he gets 34/9 for his answer.

Can this be simplified? No. So 34/9 is his answer. Sam can leave his answer in this form even though the top number is larger than the bottom number because he is working with rational numbers.


The other type of calculation that Sam needs to make is that of dividing rational numbers. The next problem that Sam sees on his paper is this:

multiply divide rationals

How does Sam solve this problem now? Sam remembers that to divide rational numbers, he can actually turn this problem into a multiplication problem by flipping the second rational number. So 7/8 becomes 8/7 and the division symbol turns into a multiplication symbol.

multiply divide rationals

Before Sam goes ahead with his multiplication, he sees that he can actually simplify his problem a little bit. This is just like any other multiplication problem now, so if Sam can simplify his problem before going ahead with the multiplication, it will be easier for him to solve it.

Sam sees that he has an 8 on the top and a 6 on the bottom that he can simplify. Because this is a multiplication problem, Sam is able to take any number on the top and simplify it with any number on the bottom. It doesn't have to be in the same fraction. He can simplify these numbers by dividing both by 2. Remember that to simplify, you need to be able to divide both numbers by the same number. The 8 divided by 2 turns into a 4 and the 6 divided by a 2 turns into a 3.

So now the problem becomes


And Sam can go ahead with the multiplication of the tops and bottoms together. He gets:

5*4 = 20

3*7 = 21

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