Weird Arithmetic

“No, Henry, you can’t do that,” said the teacher, pointing to Henry’s exercise book, where he had written:

\frac{1}{4} \times \frac{8}{5}=\frac{18}{45}

“Sorry, sir<” said Henry. “What’s wrong? I checked it on my calculator and it seemed to work.

“Well, Henry, the answer is right, I guess,” the teacher admitted. “Though you should probably cancel the 9’s to get \frac{2}{5}, which is simpler. What’s wrong is —”

Explain the mistake to Henry. Then, find all the sums, with single non-zero  digits in the first two fractions, that are correct.

Answers later.

More later,

Nalin Pithwa

Ref: Professor Ian Stewart’s Cabinet of Mathematical Curiosities.

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