Number Sense and Operations
Number Sense and Operations tests whether you can move fluently among fractions, decimals, percents, and signed numbers, and apply the order of operations without a calculator. Items lean heavily on proportional reasoning and on estimating to judge whether a computed answer is plausible.
Core rules
- Order of operations: parentheses, then exponents and roots, then multiplication and division left to right, then addition and subtraction left to right. So 2 + 3 × 4² = 50, not 400.
- To divide by a fraction, multiply by its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c).
- Percent change = (new − old) ÷ old × 100. The base in a percent problem is whatever follows "of."
- For two positive integers, GCF × LCM = their product - a fast check on factor questions.
- Negative exponents flip the base: x⁻ⁿ = 1/xⁿ. Absolute value is distance from zero, so it is never negative.
Worked example
Compute (3/4 − 1/6) ÷ 5/12. Rewrite over a common denominator of 12: 9/12 − 2/12 = 7/12. Dividing by 5/12 means multiplying by 12/5: 7/12 × 12/5 = 7/5. The twelves cancel cleanly, so the answer is 7/5, or 1.4 - a little larger than the original 7/12, which makes sense because the divisor is less than 1.
Traps that cost marks
- Adding across numerators and denominators: 1/2 + 1/3 is 5/6, not 2/5.
- Sign handling in powers: −3² = −9 while (−3)² = 9.
- Chained percent changes: a 25% increase followed by a 20% decrease returns to the starting price, because the second percent applies to a larger base.
- Rounding mid-problem instead of at the end, which shifts the final answer off the offered choices.
- Confusing "what percent of 40 is 8" (20%) with "8 is what percent more than 40."