Signed arithmetic, fractions and order of operations

Develop reliable arithmetic for algebra and precalculus with signed numbers, fractions, decimals and the order of operations. This set focuses on keeping signs, grouping and numerical representations consistent. It includes fraction subtraction and division, mixed numbers, decimal calculations, reciprocals, zero, nested expressions and the distinction between a leading negative sign and a squared base.

Questions progress from short calculations to interpretation, error analysis and expressions that require several coordinated steps. Some ask for one answer; others require every valid statement or reciprocal pair. Try solving on paper before looking closely at the choices. Estimate the size and sign of an answer first when that helps, then use exact arithmetic to confirm it.

Applications connect the same rules to temperature changes, recipe quantities and reasonable estimates. The explanations show the intermediate steps and identify common errors, including adding denominators, reversing the wrong fraction and assuming division always makes a number smaller. Familiarity with real-number order and absolute value is useful. This set prepares you for ratios and units, substitution and algebraic expressions; it does not require equation-solving methods or a calculator.