Chapter 6: Rationals: Multiplication, Division, and Applications
Let's go back to Day One's lesson. In that exercise, we dealt with multiplying with fractions. We will work some with that today, so you may want to go back and review the lesson.
The idea of multiplicative inverse is pretty straightforward. The definition of multiplicative inverse is as follows:
The product of a number and its multiplicative inverse is 1.
Today we want to look at a few graphs on Algebra Xpresser and see how we can look at the idea of multiplicative inverses.
The basic way of finding multiplicative inverse is to take a fraction and reverse the numerator and denominator. For instance, the multiplicative inverse of 3/4 is 4/3. We then need to reduce the new fraction to 1 1/3. So the multiplicative inverse of 3/4 is 1 1/3. Likewise the multiplicative inverse of 1 1/3 is 3/4. Let's check this. If we multiply 3/4 * 4/3 = 12/12 = 1.
Can you find the multiplicative inverse of 5/7?
It is also important to remember that we can find the multiplicative inverse of a whole number. Remember a whole number is just a fraction with a 1 in the denominator. For example, 8 can be written as the fraction 8/1. The multiplicative inverse of this is 1/8. To check we have 8*1/1*8 = 8/8 = 1.
The multiplicative inverse of 5/7 is 7/5 = 1 2/5. Did you get it right?
Today's assignment is the following worksheet. In the first part you will be required to find multiplicative inverses. Make sure you reduce all of your answers, as well as make mixed numerals of all your improper fractions. The second part of the exercise is a review of multiplication, which you will need for tomorrow's lesson. Finally, the last part of the worksheet is an interesting exploration dealing with multiplicative inverses. Have fun!!