Fractions

Package: ARITHMETIC_PACKAGE. Registered by createEngine(); for a slimmer engine, register it explicitly (see choosing packages).

A fraction is one whole number over another, like 1/3. Solve keeps such a quotient exact rather than turning it into a decimal straight away, so a chain of fractions adds up to the answer it should instead of drifting by a tiny amount.

A quotient of two whole numbers is kept as an exact fraction, so a chain of fractions adds up the way it should rather than drifting the way the underlying doubles do. 1/49 * 49 is exactly 1, not 0.9999999999999999.

1/3 + 1/3 + 1/3 // 1
2/7 * 14 // 4
1/49 * 49 // 1

A fraction is shown as a decimal by default, so a result still reads as a number. Ask for as fraction to see it as a fraction, reduced to lowest terms, and as decimal for the decimal.

1/3 as fraction // 1/3
10/4 as fraction // 5/2
(1/3 + 1/7) as fraction // 10/21

Only a fraction written with / is exact. A decimal literal is still floating point, so 0.1 + 0.2 stays 0.30000000000000004, and transcendental work (sqrt, sin, a non-integer power) stays floating point too.