Rates, and Reading a Scale

Before reading anything off a scale, work out what one mark is worth, because it is very often not one. Take two labels, subtract to get the distance between them, and divide by the number of gaps. Gaps, not marks — six marks between two labels make five gaps, and counting the marks gives you the wrong size. Here the labels are ten apart with five gaps, so each mark is two. The arrow sits three marks above ten, which makes the reading sixteen.

When the pointer sits between two marks, first say out loud which two marks it lies between. That alone often rules out three of the four options, because they fall outside the interval. Then judge the fraction: halfway between sixteen and seventeen is sixteen point five. The temptation is to round to the nearest labelled number because labels are easier to read, but the question is not usually that generous, and a reading that lands neatly on a label is worth double-checking.

A rate is a per, and it runs in both directions. One degree every twenty minutes, run forwards, tells you the rise in a given time: two hours is a hundred and twenty minutes, which is six lots of twenty, so the rise is six degrees. Run backwards, it tells you the time for a given rise: six degrees needs six times twenty, which is a hundred and twenty minutes. The practical advice is to work throughout in the unit the rate is written in — minutes here — and convert to hours only at the very end, because mixing hours and minutes halfway through is where these questions fall apart.

Now the two skills together. Read the scale first: the thermometer shows twelve degrees at six o'clock. Then run the rate to the target. The rise you need is the difference, eighteen take twelve, which is six degrees — not eighteen, and that is the mistake the question is fishing for. Six degrees at twenty minutes each is a hundred and twenty minutes, which is two hours, so the answer is eight o'clock in the morning. Subtract before you multiply, every time.

When a rate does not divide neatly, reduce it to per one before doing anything else. Two degrees every thirty minutes becomes one degree every fifteen. Three degrees an hour becomes one degree every twenty minutes. Once the rate is per one, everything after it is arithmetic you can actually do in your head. And watch the conversion at the end: a rise of five degrees at two degrees an hour takes two and a half hours, which is two hours thirty minutes, not two hours fifty, because an hour is sixty minutes and not a hundred. Quiz and exercises now.