Signed Fractions and Decimals

The sign rules do not change when the numbers stop being whole. −½ + ¼ works exactly like −4 + 2.

Decide the sign, then the size

Which number is further from zero? That one decides the sign of the answer.

Fractions still need common denominators

−½ + ¼ becomes −2/4 + 1/4, which is −1/4.

Estimate to catch sign errors

−2.7 + 1.2 is roughly −3 + 1, so about −2. An answer of +1.5 is visibly wrong.

The sign rules do not care about the number type

−3/4 + 1/2 follows exactly the same reasoning as −3 + 2. Find a common denominator, then apply the signed-addition rule. Fractions and decimals make the arithmetic messier but change nothing about the signs.

Where the sign goes on a fraction

−3/4, (−3)/4 and 3/(−4) are all the same number. The negative can sit in front, on the top or on the bottom. Putting it in front is conventional and least confusing, so move it there before calculating.

Negative fractions on the line

−3/4 sits between −1 and 0, three quarters of the way from 0 towards −1. Note that −3/4 is less than −1/2, mirroring how −3 is less than −1. Plotting a negative fraction is where the mirror image becomes concrete.

Estimate with benchmarks and signs

−3/4 + 1/2 is a bit less than −1 plus a half, so somewhere around −1/4. The exact answer is −1/4. Combining a sign check with a benchmark estimate catches both kinds of error at once.