Integers, Fractions, and Decimals

Integer Operations

• Positive × Positive = Positive. Negative × Negative = Positive. Mixed = Negative.
• $(-3) \times (-4) = 12$. $(-5) \times 2 = -10$.
• Same rules for division.

Fraction Operations

Addition/Subtraction: Common denominator. $\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Multiplication: Multiply straight across. $\frac{2}{3} \times \frac{5}{7} = \frac{10}{21}$

Division: Flip and multiply. $\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$

Converting Between Forms

• Fraction → Decimal: divide numerator by denominator.
• Decimal → Fraction: use place value. $0.75 = \frac{75}{100} = \frac{3}{4}$.
• Decimal → Percent: multiply by 100. $0.45 = 45\%$.

Order of Operations (PEMDAS)

Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right).

• Fractions are often faster than decimals on the ACT.
• Cross-multiply to compare fractions: is $\frac{3}{7}$ or $\frac{5}{12}$ bigger? $3 \times 12 = 36$ vs $5 \times 7 = 35$, so $\frac{3}{7} > \frac{5}{12}$.