Number & Quantity

• Apply order of operations (PEMDAS) accurately in multi-step problems
• Convert between fractions, decimals, and percentages fluently
• Read number words exactly (integer, digit, distinct, consecutive, prime, factor and multiple, remainder, inclusive, even and odd) and use them to find greatest common factors and least common multiples
• Perform arithmetic with positive and negative fractions
• Finish on one ACT-hard question and say what made it hard

The ACT Math section has 45 questions in 50 minutes, meaning you have roughly 67 seconds per question. On the enhanced ACT most Math questions fall under Preparing for Higher Math (number and quantity, algebra, functions, geometry, and statistics and probability), and the rest, Integrating Essential Skills, are multi-step problems built on rates, percents, proportions, area and volume, and averages. Fraction, decimal, and integer fluency sits underneath both, so mastering these basics prevents careless mistakes and saves time for the harder questions. Know your number sets: integers are the whole numbers and their negatives (..., -2, -1, 0, 1, 2, ...); whole numbers are 0, 1, 2, 3, ...; and 'positive integers' start at 1. Consecutive integers are set up as n, n+1, n+2. For integer n, consecutive even integers are 2n, 2n+2, 2n+4, while consecutive odd integers are 2n+1, 2n+3, 2n+5. Remember: a fraction a/b is undefined when b = 0, multiplying by a negative flips an inequality, and the product of two negatives is positive. Number words are exact on the ACT: an integer is a whole number or its negative, and 0 is an even integer; a digit is one of 0 through 9, so the tens digit of a two-digit number cannot be 0; distinct means different from each other; consecutive integers differ by 1; a prime has exactly two positive factors, so 1 is not prime and 2 is the only even prime; a factor of n divides n with no remainder, while a multiple of n is n times an integer; a remainder is at least 0 and less than the divisor; and 'from 20 to 90, inclusive' includes both 20 and 90, so it contains 90 − 20 + 1 = 71 integers. 'Between' without 'inclusive' means strictly between: to count the integers between two fractions, change each to a decimal first (−17/3 ≈ −5.67 and 23/4 = 5.75 leave −5 through 5, which is 11 integers). Two repeating events line up at the multiples of their least common multiple: every 6th and every 8th customer coincide every 24th customer. An even root such as √x or ∜x is a real number only when x ≥ 0, and to place a root on a number line, square the nearby marks (2.4² = 5.76 and 2.5² = 6.25, so √6 is between 2.4 and 2.5). The hardest questions, at the end of the section: late questions on this material hinge on one of these words (a count that must include both endpoints, values that must be distinct, a remainder that has to be recomputed after the number is doubled); misreading a single word flips the answer.

• Memorize common fraction-decimal-percent equivalents (1/4 = 0.25 = 25%, 1/3 ≈ 0.333, etc.) to save time.
• Always reduce fractions to simplest form before comparing answer choices.
• When a problem says 'integer,' remember that 0 and negative numbers count too. The ACT loves testing edge cases.