Number Operations & Fractions

Order of Operations (PEMDAS)

When a calculation has multiple operations, follow PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication & Division (left to right)
4. Addition & Subtraction (left to right)

Example: 3 + 4 × 2 = 3 + 8 = 11 (not 14 — multiply before adding).

Fractions & Decimals

• Adding/subtracting fractions: find a common denominator first. ½ + ⅓ = 3/6 + 2/6 = 5/6
• Multiplying fractions: multiply numerators × numerators, denominators × denominators. ½ × ¾ = 3/8
• Dividing fractions: flip and multiply (keep-change-flip). ½ ÷ ¼ = ½ × 4 = 2
• Converting: ¾ = 0.75 = 75%

Ratios & Proportions

A ratio compares two quantities: 3:4 means 3 for every 4.

A proportion is two equal ratios: 3/4 = 6/8. Cross-multiply to solve for unknowns: 3/4 = x/12 → 4x = 36 → x = 9.

Tip: Always check whether a ratio question wants a part-to-part or part-to-whole ratio.

Tips

• When comparing fractions, convert to decimals or find a common denominator.
• Estimation is powerful — use it to eliminate obviously wrong answers.
• Know perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) and cubes (8, 27, 64, 125).