# Browsing category algebra

## Ask Uncle Colin: Why does the line with equation $10y+36x=16.5$ have a gradient of -3.6?

Dear Uncle Colin, I've got a line with equation $10y+36x=16.5$. That equation has no negative numbers in it, yet its gradient is apparently negative. I don't understand why. -- Silly Line, Only Positive Equation Dear SLOPE, It looks like we're in misconception-land! In fact, you can write the equation of

## Getting your $x$s in one basket

A reader asks: I need to solve $\frac ac \frac {NP}{N_0 + N} = mP$ for $N$, and I don't know where to start. Help! I had a maths teacher in the early 90s who loved nothing more than making the class groan with bad jokes. If she showed up

A student asks: How do I simplify horrible product and quotient rule expressions? The example they gave was differentiating: $f(x) = (2x - 3)^4 (x^2 + x + 1)^5$ First up, a careful bit of product rule: $u = (2x - 3)^4$, so $\diff{u}{x} = 8(2x- 3)^3$ $v = (x^2 Read More ## The Mathematical Ninja and The$n\$th Term

Note: this post is only about arithmetic and quadratic sequences for GCSE. Geometric and other series, you're on your own. Quite how the Mathematical Ninja had set up his classroom so that a boulder would roll through it at precisely that moment, the student didn't have time to ponder. He