Correct!

Figures you wouldn’t be able to resist a math problem, Stu!

For those of you who are like me (i.e., unable to leap to spectacular

conclusions of numerical perfection), here’s one way to get at the

solution (and sorry, I can’t write fractions properly, so I’ll write m

/ n instead, and x means times):

The area of the rectangle is 121/2 x 143/3 = (11×11)/2 x (11×13)/3.

From here, we want to try to massage the equation so that it expresses

an integer times a square of some number (it has to be a square since

the little squares would be written as such, remember?, and an integer

because there are so-and-so many of these squares).

So, the above equation is rearranged to say: (11×11)/2 x (11×13)/3 =

(11×13)/6 x 11squared. I.e., you have multiplied the denominators (2,

3) to get 6, and the numerators have become 11×13 (still as a

numerator, over denominator 6) and 11squared. You haven’t changed the

value by writing 11squared (think of it as a numerator with a

denominator of 1), since, written as such [(11×11)/1], we’re still all

ok on the values we had in place before we started rearranging things.

The next part is where I lost it, and had to ask my mathematician

husband for help in following the solution (oh yeah, the problem[s]

come with a sheet of solutions …you didn’t think I can do this by

myself, did you?). You now multiply the expression (11×13)/6 x

11squared by 6 in order to make the denominator (6) a square. Thus you

get: (6x11x13)/6squared x 11squared. At this point, you can further

rearrange the numerical furniture and put the 6squared denominator in

place (so to speak, I know that’s not mathematically correctly

expressed) in place of the denominator 1 under the 11squared, while the

denominator 1 under the 11squared (a denominator we don’t bother

writing out, I’m just mentioning it to avoid confusion) under the

6x11x13. What you end up with is: 6x11x13 x (11squared(/(6squared), or

(11/6)squared. 6x11x13 is 858, so you now have your integer times a

square, namely (11/6)squared. Easy, eh? Well, wish it were, but this is

the kind of thing I can understand when I work through it, but give me

the next problem, and I’m again staring at it, thinking, “Dude…!”

For these examples and many more, visit The Centre for Education in Mathematics and Computing

(U. of Waterloo), grade 9 Pascal test, scroll down and open a couple of

pdfs with past exams. Quite humbling for some of us, let me tell you!

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