MPM1D Dividing monomials; Algebra and measurement 2016-03-21

We were back in the swing of things today with a quick review of the skills we’ve learned so far this semester, and then we tacked on our last two items for this unit.

Dividing Monomials

We talked at length about how to multiply monomials, but we didn’t ever look at examples where we divided them. Thankfully, it works in exactly the same way:

-34x^3 \div (2x) = -17x^2

We divide the numerical coefficients, and we divide the variable components. Notice that I used brackets around 2x because I wanted to be clear that I was dividing by the 2 and the x , not just the 2.

Sometimes you’ll have or end up with fractions; that’s fine:

\frac{2}{3}xy^4 \div (\frac{1}{5}xy^2) = \frac{10}{3}y^2

Why \frac{10}{3} ? Because \frac{2}{3} \div \frac{1}{5} = \frac{2}{3} \times \frac{5}{1} .

Of course, the division sign is kind of gross since it makes us put brackets everywhere. In real life we usually use a division bar:

\frac{-34x^3}{2x} = -17x^2

See? No need for brackets here!

Algebra and Measurement

The whole point of algebra is that sometimes we don’t know a specific value, but we know some relationships among values. For example, if you have a rectangle with length l and width w you can find the perimeter P=2l + 2w . We don’t have to know  l and w to use this relationship.

For homework I gave you a rectangular prism with dimensions in terms of an unknown value x :

We then worked out that the volume of the prism could be found using

V = (x)(x+3)[2(x+3)]

Your homework was to expand and simplify this equation for volume so that the right-hand side is a nice polynomial.


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