Fraction math

Nine small tools, one habit: the exact answer first, simplified, and the steps folded underneath for when the answer alone is not the point.

Simplify 24/64 → 3/8, by GCD. Equivalent fractions 3/8 = 6/16 = 9/24, or pick the denominator. Add 3/8 + 1/4 = 5/8, common denominator shown. Subtract 3/8 − 1/4 = 1/8, negatives handled. Multiply 2/3 × 3/4 = 1/2, straight across. Divide 1/2 ÷ 1/8 = 4, by the reciprocal. Mixed → improper 1 3/4 → 7/4. Improper → mixed 7/4 → 1 3/4. Rational approximation 3.14159 → 22/7, 355/113, with errors.

Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. See the full methodology.