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## Main Question or Discussion Point

How does computer technology add fractions with different denominators?

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- Thread starter matqkks
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How does computer technology add fractions with different denominators?

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jbriggs444

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

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.

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