Henry Ernest Dudeney/Puzzles and Curious Problems/173 - Short Cuts

Puzzles and Curious Problems by Henry Ernest Dudeney: $173$

Short Cuts: We have from time to time given various short cuts in mental arithmetic.; Here is an example that will interest those who are unfamiliar with the process.

Can you multiply $993$ by $879$ mentally?

It is remarkable that any two numbers of two figures each,

where the tens are the same, and the sum of the units make ten, can always be multiplied thus:

$97 \times 93 = 9021$

Multiply the $7$ by $3$ and set it down,

then add the $1$ to the $9$ and multiply by the other $9$, $9 \times 10 = 90$.

This is very useful for squaring any number ending in $5$, as $85^2 = 7225$.

With two fractions, when we have the whole numbers the same and the sum of the fractions equal unity,

we get an easy rule for multiplying them.

Take $7 \tfrac 1 4 \times 7 \tfrac 3 4 = 56 \tfrac 3 {16}$.

Multiply the fractions $= \tfrac 3 {16}$, add $1$ to one of the $7$'s, and multiply by the other, $7 \times 8 = 56$.

1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $173$. -- Short Cuts
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $237$. Short Cuts