Calculator Magic #8 Arithmetic Shortcuts

Summing Numbers and Fractions the Easy Way

Here are two methods for processing arithmetic terms without the calculator's memory, permitting it to be used for another purpose.

ADDING A FRACTION

Suppose that you would like to sum a series of fractions, such as:

One easy solution would be to divide each fraction and put the combined results into memory:

2 ÷ 7 M+
3 ÷ 8 M+
11 ÷ 15 M+
MR

This is well and good, providing that the memory function is available.  But if it isn't:

This is easily processed on the calculator without the memory.

Rule: multiply the current total by the next denominator, add (or subtract) the next numerator, then divide by the next denominator:

a ÷ b × d + c ÷ d =

It makes no difference whether the original term was a fraction.  It also makes no difference how many additional fractions are in the series.  Example:

Note that negative values are merely subtracted at the appropriate time:

6 ÷ 7
× 8 + 5 ÷ 8
− 2
× 5 − 4 ÷ 5
× 3 + 1 ÷ 3 =

ADDING A PRODUCT

Rule: divide by one of factors in the next term, add the other, then multiply by the first one.

a × b ÷ c + d × c =

This program is equally straightforward:

23 × 35
÷ 14 + 70 × 14
÷ 48 − 69  × 48 =

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