# How do Calculators add fractions with different denominators

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• matqkks
In summary, computer technology adds fractions with different denominators by using fixed precision floating point format. Early calculators worked in decimal floating point, while modern calculators use binary double precision floating point arithmetic. A calculator performing infinite precision rational arithmetic would evaluate the sum differently, depending on the system. In most cases, the calculator will calculate the sum numerically with limited precision. However, in a computer algebra system, the calculator will calculate the sum by finding the smallest common multiple of the denominators, expanding both fractions, adding them, and simplifying the result.

#### matqkks

How does computer technology add fractions with different denominators?

matqkks said:
How does computer technology add fractions with different denominators?
A desktop calculator will typically work using a fixed precision floating point format. https://en.wikipedia.org/wiki/Floating-point_arithmetic.

My understanding is that the early calculators worked in decimal floating point. For instance, the HP35 and HP45 had 8 decimal digits of accuracy and the SR51 had 10 decimal digits plus three undisplayed guard digits. If you key in "(3/7) + (5/6)", a modern calculator will likely compute 3/7 using binary double precision floating point arithmetic, compute 5/6 using binary double precision floating point arithmetic and add the two binary fractions [after scaling them to share a common binary exponent if needed]. It will convert the result to decimal for display purposes.

A calculator performing infinite precision rational arithmetic would evaluate the sum differently.

matqkks and jedishrfu
It depends on the system. Typically it will just calculate it numerically with limited precision, in that case see the comment above. If you put it into a computer algebra system it will probably calculate it the same way a human does: Find the smallest common multiple of the denominators, expand both fractions to get the same denominator, add them. Alternatively expand both with the denominator of the other, add them, then simplify the result.