How to Multiply & Divide Expressions

Series Summary

Mathematics is the body of knowledge centered on such concepts as quantity, structure, space and change; and it is also the academic discipline that studies them. Mathematics education is a term that refers both to the practice of teaching and learning mathematics, as well as to a field of scholarly research on this practice. At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives, including the teaching of basic numeracy skills to students, and teaching both practical and abstract mathematics. In this free video series on math and science, teacher Steve Jones demonstrates how to calculate a variety of different mathematical formulas. Jones explains how to multiply and divide expressions, graph linear equations, find the volume of figures, calculate the surface area and even how to find the median. These equations and mathematical expressions are practical and useful in everyday life. Watch these free videos and learn more about math and science today.

Video Transcript

"Hi, I'm Steve Jones and I'm going to tell you a little about multiplying and dividing expressions. First of all, multiplying. We have two expressions, here x squared and x cubed and you want to multiply those two expressions together. Because they are, x squared is x times x, and x cubed is x times x times x we call these numbers indices, and we can multiply these together by adding the indices. So x squared times x cubed is x, add the indices, two plus three which is x to the power of five. So I've added the indices and I get x to the power of five. So this is x to the fifth. I can do the same here , but I have to be careful because I've got numbers. So I have to first multiply the numbers together. Five times six is thirty and then x times x squared. Well the index on x is x to the power of one. So it's in fact x to the power of three. Two plus one makes three. And the final one here, four y times three x. Y and x are separate variables, but the numbers can be multiplied together to give me twelve. Four times three gives me twelve, times y, times x. So that is multiplying expressions. Dividing expressions is not entirely different. Here I've got x to the fifth divided by x cubed. So I can write it in this way. X to the fifth divided by x cubed and in fact division is, we subtract the indices. This is the same as x to the five, the one on top first, minus three, the one below, and this equals x squared. Right with six xy divided by two y we have to separate things out. So six times x times y, and we'll divide it by two times y. As you see we've got y on top and bottom and they cancel. Six divided by two is three, so I'm left with three x so that is the result of that. With four x squared, I've got four x squared and then on the bottom I've got x times y. So the y stays because there's no y on the top. There's no numbers on the bottom, the four stays, so we get four. Now I've got x squared on the top and x to the one so this will be just x because it's x to the two minus one, and then on the bottom I've got y and that equals four x over y. So as you can see, we can soon simplify two equations, multiplying or dividing and this routine way will give us a single expression from any two expressions dividing or multiplying."