Number and Quantity
What this domain covers
Number and Quantity supplies roughly 30% of the scored questions on Praxis Core Math, more than any other strand. Expect fluent computation with integers, fractions, decimals, and percents, plus ratio, proportion, unit rate, exponents, radicals, scientific notation, and number properties such as factors, multiples, and absolute value.
Rules that must be automatic
- Fraction division: dividing by a/b is the same as multiplying by b/a. Cancel common factors before multiplying so the arithmetic stays small.
- Percent change: change ÷ original × 100. A p% increase multiplies by (1 + p/100); a p% decrease multiplies by (1 − p/100).
- Successive percents do not add. Two 10% discounts give 0.9 × 0.9 = 0.81, an effective 19% reduction, not 20%.
- Proportions: line up matching units on each side, then cross-multiply. If the units do not match, the proportion is wrong.
- Exponent rules: x^a · x^b = x^(a+b); (x^a)^b = x^(ab); x^0 = 1 for x ≠ 0; x^(−a) = 1/x^a.
- Scientific notation: exactly one nonzero digit before the decimal point; the exponent counts decimal places moved, positive for large numbers.
- Absolute value is distance from zero, so |x| = 5 has two solutions, 5 and −5.
Worked example
A jacket lists at $80, is marked down 25%, and the register takes another 10% off the reduced price. Final price?
Markdown: 80 × 0.75 = $60. Register discount: 60 × 0.90 = $54. Equivalently, 80 × 0.75 × 0.90 = $54.
Traps that cost marks
- Adding the two discounts (35% off, giving $52) instead of compounding them.
- Reversing percent change: a 20% decrease needs a 25% increase to undo it, because the base changed.
- Taking a percent of the wrong whole: 15% of the original price is not 15% of the sale price.
- Confusing LCM with GCF: LCM is the smallest shared multiple, used for common denominators; GCF is the largest shared factor, used to simplify.