# How do Calculators add fractions with different denominators

• I

## Main Question or Discussion Point

How does computer technology add fractions with different denominators?

jbriggs444
Homework Helper
2019 Award
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
mfb
Mentor
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.