Sum/product of consecutive numbers and other math shortcuts

If you have studied some of the old SAT questions at some point you may have gone through questions like –

4 consecutive numbers sum to 166. What is the product of the numbers? or…

3 consecutive even numbers sum to X. What is their product?

The way the tutors and the online tutorials show seems to always be to algebraically solve this – for example 4 consecutive numbers would solve x+x+1+x+2+x+3 = 166, collect terms and solve…

However there is another way that works for this and works for other similar problems.

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Slide rule enters the 21st century

Some time ago I came across this online tool in a newsletter article – this is a very cool slide-rule-emulator that will not just let you move two slides, but actually slide it for you as you run an equivalent digital calculator calculation to the right!

If you haven’t ever used a slide rule before, it works on properties of logarithms, and the principle that log(a)+log(b) = log(a*b). Now it wouldn’t be very interesting to just have two normal rulers together, as sliding and adding would just let you do problems like 5+5 = 10 or 50+50 = 100 if you scale the numbers. With logarithmic scale, the spacings are off and it allows you to do multiplication in adding the numbers.

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