Number and Operations
What this domain covers
Number and Operations questions ask you to move comfortably among whole numbers, fractions, decimals, percents, and signed numbers. You should be able to identify place value, round, compare and order integers, find factors and multiples (including greatest common factor and least common multiple), apply exponent and square-root rules, and convert freely between fractions, decimals, and percents. Ratio, rate, and proportion problems appear often, as do multi-step word problems about money, discounts, tax, tips, and unit pricing.
Order of operations
Work parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication does not automatically outrank division, and addition does not automatically outrank subtraction - position decides.
Traps to watch for
- Dropping a negative sign: subtracting a negative is the same as adding.
- Percent questions hide their base. Twenty-five percent more than 40 is 50, not 40 times 0.25.
- To divide by a fraction, multiply by its reciprocal; do not flip the first fraction.
- Convert units or forms before computing, and round only at the very end.
- Estimate first so you can reject choices that are off by a factor of ten.
Worked example
Simplify 12 − 3(4 − 6)² ÷ 6. Parentheses: 4 − 6 = −2. Exponent: (−2)² = 4. Multiply: 3 × 4 = 12. Divide: 12 ÷ 6 = 2. Subtract: 12 − 2 = 10. Rule of thumb: percent change = (new − old) ÷ old, then write the result as a percent.