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Multiplying and Dividing Rationals - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

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

Multiplying rational expressions is basically two simplifying problems put together. When multiplying rationals, factor both numerators and denominators and identify equivalents of one to cancel. Dividing rational expressions is the same as multiplying with one additional step: we take the reciprocal of the second fraction and change the division to multiplication.

I'm a Math teacher and I have lots of different types of students in my classes. Some students I have don't like to write anything down and those students get in really big trouble when we start multiplying and dividing rational expressions. And here's why, when you're multiplying and dividing rational expressions you're going to have to do all kinds of factoring, you're going to have to cross out stuff that's the same on top and bottom, you're going to have to be careful with exponents. And if you have a division problem, you have to remember what you guys already know about dividing fractions.
They to complete this sentence, dividing fractions is the same as, did you get it? Dividing fractions is the same as multiplying by the reciprocal. Let me show you what I mean, you learnt this stuff when you were in like third or fourth grade. One fourth divided by three halves is the same as one fourth multiplied by the reciprocal. That's going to become really important when you start dividing rational expressions. It's going to be the same thing, and you're going to be flipping your second fraction keeping all the same exponents, all the same positives and negatives if you have a division problem your second guy just turns up side down. So be really careful with that if all else fails when it comes to multiplying and dividing rational expressions just remember with division flip your second fraction and then multiply across top, multiply across the bottom factor everything and then reduce. It sounds easy but you guys are going to see these problems can be pretty tricky.

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