MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
When asked to find the multiplicative inverse of a number, first remember that two numbers are multiplicative inverses if their product is 1. Think about what a number needs to be multiplied by in order for the product of the two numbers to equal 1. To find the multiplicative inverse of a the given number, find the reciprocal of that number. The resulting number is the multiplicative inverse. Multiplicative inverses are used often in equations for cancellation.
This problem is asking me to find multiplicative inverses and if you remember the definition, two numbers are multiplicative inverses if their product is 1. Product means they multiply to 1. So here we go, ½ times what number gives me the answer 1? This is tricky because you're working with fractions but you guys you can do it, I promise you. ½ times 2/1 is what gives me the answer 1, because if I do ½ times 2/1, with fractions you multiply across the top, multiply across the bottom, 2/2 that reduces to 1. So what's the additive inverse? 2 means, what's the multiplicative inverse of 1/2? The answer would be 2 or 2/1.
How about with 4? 4 times what gives me the answer 1? Well keep in mind those fractions, 4 times 1/4 is what gives me the answer 1. So my multiplicative inverse is going to be 1/4.
Last but not least, this one's kind of tricky because it's negative. -3/2x what is going to give me +1? Well in order to get from a negative to an answer that's positive I'm going to have to multiply by another negative fraction and then if I want to have something that multiplies to 1. I'm going to look at the pattern here. See how I'm multiplying by the reciprocal, ½ times 2/1 or 4 times 1/4? Same idea here, I'm going to multiply by the reciprocal 2/3. And you can check yourself by making sure the product on top and the product on the bottom are the same so when you reduce that fraction you get the answer 1. So what is the multiplicative inverse of -3/2? The answer would be -2/3.
The thing to keep in mind when you're working with multiplicative inverses is reciprocals. If you're given a fraction, you turn it upside down. If you're given a whole number, you multiply it by that fraction turned upside down. It's kind of tricky but you guys will get the hang of it. Don't be scared of fractions, you can totally do it.
