Grade 4–5 Multi-Digit Multiplication

Multi-Digit Multiplication: 2-Digit Partial Products

Steps

Estimate first: round each factor. 23 × 45 ≈ 20 × 50 = 1,000.
Break apart by place value: 23 = 20 + 3 and 45 = 40 + 5.
Area model: find every partial product: 40 × 20 = 800, 40 × 3 = 120, 5 × 20 = 100, 5 × 3 = 15.
Add the partial products: 800 + 120 + 100 + 15 = 1,035.
Standard algorithm: row 1 = 45 × 3 = 135; row 2 starts with the zero hero: 45 × 20 = 900. 135 + 900 = 1,035. Check: close to 1,000 ✓
Rhyme: “Multiply the ones, then place the zero hero, multiply the tens, then add them up — check, don’t guess!”