Numbers and Operations
Core concepts
Numbers and Operations carries the most weight on the test. You need fluent place value (reading, writing, comparing, and rounding whole numbers and decimals), the four operations on whole numbers, decimals, and fractions, and easy movement among fraction, decimal, and percent forms. Also expect factors and multiples, prime and composite numbers, GCF and LCM, integer arithmetic on a number line, and the order of operations.
Common traps
- Dividing by a fraction: keep the first fraction, multiply by the reciprocal, and simplify before multiplying. A quotient larger than the dividend is normal when the divisor is less than 1.
- The word "of" usually signals multiplication. A percent increase or decrease is always computed from the original amount.
- Adding decimals requires aligned decimal points; multiplying decimals does not. Count total decimal places in the factors for the product.
- GCF answers "largest shared factor"; LCM answers "smallest shared multiple." Questions swap these deliberately.
- Subtracting across zeros requires regrouping through each place value.
- Rounding: look only at the digit immediately to the right of the target place.
Worked example
Compute 5/6 ÷ 2/3. Rewrite as 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4. Check for reasonableness: since 2/3 is less than 1, the answer must exceed 5/6, and 1 1/4 fits.
A second quick check: 15% of 80 = 0.15 × 80 = 12, which is a bit more than 10% of 80 (8).
Rule of thumb: write one operation per line, keep units attached to numbers, and estimate before computing so a misplaced decimal place stands out immediately.