# 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.