Number Sense and Operations
Number Sense and Operations
This domain tests how fluently you reason with whole numbers, fractions, decimals, integers, and percents, and how well you choose an operation and justify it. Expect place-value questions, multi-step order-of-operations items, fraction/decimal/percent equivalence, and estimation.
Core rules
- Place value drives regrouping: each position is ten times the value to its right. In 4,072, the 0 is a placeholder; the 7 means 70.
- Order of operations: parentheses/brackets, exponents, multiplication/division left to right, addition/subtraction left to right. A fraction bar groups the entire numerator and denominator.
- Fraction operations: add/subtract only with a common denominator; multiply numerators and denominators; divide by multiplying by the reciprocal. Simplify by common factors, not by adding across.
- Decimal operations: line up decimal points for addition/subtraction; the product has the total number of decimal places of the factors; move both decimal points equally when dividing.
- Percents are ratios per 100: part = percent × whole. Percent change = (new − old) ÷ old.
Worked example
Compute 3/4 ÷ 2/5. Keep the first fraction, change division to multiplication, and use the reciprocal of 2/5: 3/4 × 5/2 = 15/8 = 1 7/8. Reason: dividing by 2/5 asks how many groups of size 2/5 fit in 3/4; multiplying by 5/2 rescales that comparison.
Traps
Do not add across fractions. Do not clear a decimal point by moving only one side. In order of operations, do not multiply before finishing parentheses, and do not treat subtraction as automatically before addition. Check whether a percent question asks for the part, the whole, or the percent.