Number Concepts
What to know
Number concepts questions test the real number system and flexible work with rational numbers. Be fluent with place value through decimals and scientific notation; conversions among fractions, decimals, and percents; integer operations and absolute value; divisibility rules, prime factorization, GCF, and LCM; and order of operations. Proportional reasoning-unit rates, scale factors, and percent relationships-underpins later algebra and geometry, so know how to set up and solve a proportion and how to distinguish part, whole, and percent.
Traps
Distractors reward procedure without meaning. You may split a numerator across a sum, but never a denominator: (a+b)/c = a/c + b/c, while a/(b+c) is not a/b + a/c. A negative exponent means reciprocal, not a negative result. Dividing by a fraction less than 1 makes the quotient larger. A percent increase followed by the same percent decrease does not restore the original value. In percent problems, identify the whole before computing, because the base changes across successive changes.
Worked example
A jacket costs $80 and is marked up 15%. Find the new price: 0.15 × 80 = 12, so $92. If it then drops from $92 back to $80, the decrease is 12 ÷ 92 ≈ 13%, not 15%, because the base changed. Rule of thumb: percent change = amount of change ÷ original amount, and the original is whatever the change is measured against.