Numbers and Operations
What to know
Candidates should move fluently among integers, fractions, decimals, and percents, and apply the order of operations (parentheses, exponents, multiplication/division left to right, addition/subtraction left to right). Know place value, factors and multiples, prime factorization, GCF and LCM, absolute value, and the rules for signed numbers. Estimation and rounding, scientific notation, and unit conversion round out the domain.
Traps to watch
- Subtraction of negatives: 5 − (−3) = 8, not 2. Multiplying two negatives gives a positive.
- Order of operations: 2 + 3 × 4 = 14, not 20. Exponents bind before multiplication, so −3² = −9 while (−3)² = 9.
- Fraction division: multiply by the reciprocal, and reduce before multiplying to save work.
- Percent change uses the original amount as the base: a 20% rise then a 20% fall does not return to the start.
- Rounding: look only at the digit immediately right of the target place.
Worked example
Compute 3/4 ÷ 2/3. Multiply by the reciprocal: (3/4) × (3/2) = 9/8 = 1 1/8. Check by estimating: 0.75 ÷ 0.667 ≈ 1.125, which matches.
Rule of thumb
When a problem mixes fractions, decimals, and percents, convert everything to one form first-usually fractions for exact work or decimals for estimation-then compute and sanity-check the size of the answer.